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By D. W. Olson

Garnet has been used as a gemstone for centuries. However, garnet’s angular fractures, relatively high hardness and specific gravity, being chemically inert and non-toxic and free of crystalline silica, and its ability to be recycled make garnet ideal for many industrial applications. Garnet is the general name given to a group of

Jan 1, 2005

By J. R. Thoenen

IF ASKED whether limestone production was a mining problem I would; not hesitate to answer emphatically in the affirmative. The question, "When is a quarry a mine?" is familiar. The immediate mental picture induced by the thought of limestone production is that of an open quarry. All are familiar with the open pit in the iron-producing districts of Minnesota and Michigan and the open cuts of the so-called "porphyry" coppers of the West. If these are mines, they differ little from limestone quarries in general mode of operation; if quarries, why do they need the attention of mining engineers? During 1923, the United States produced in round numbers 70,000,000, tons of ore. The limestone production of the United States for the same period was something over 100,000,000 tons. In tons, it about equals the oil production of the United States. The uses of limestone are legion. A paper read by a prominent engineer of Chicago, at the meeting of the National. Crushed Stone Association held last February in St. Louis says: "There is no industry in the United States today that is more basic in its operation or by itself controls. more industries. There is hardly a chemical operation, hardly a metallurgical operation or building operation that a crushed-stone man does not control if he will jump in and make the full utilization of it." Some of the many uses are for road metal, concrete, railway ballast, building stone, riprap, and rubble, the manufacture of iron and steel, alkalies, calcium carbide, magnesia, carbolic and carbonic acids, asphalt filler, mineral wool, poultry grit, sulfuric acid, phosphates, nitrates, soap, baking powder, the purification of copper and prevention of coal-mine explosions, to say nothing of the quantities used in the making of lime and cement. It has been said that without iron we would revert to the Stone Age; how much iron would we have without limestone? From the point. of view of the mining engineer, using the term in its broad sense to include geologists and metallurgists, the production of limestone is important because of its occurrence, volume, commercial importance, and the problems presented by its recovery and treatment.

Jan 2, 1925

By Muhlis Nezihi Saridede, Burak Birol

"Plastic wastes become a huge problem day after day due to the growth of plastic industry. Hence, plastic wastes are used as a raw material for other industries to eliminate this problem. Polyethylene Terephthalate (PET), which is a commonly used for plastic bottles, may be used as a reductant for iron production because of its C and H content. In this study, composite pellets containing iron ore concentrate, flux and reductant were prepared. Crystallized PET bottles and coke were used as reductant after ground. The prepared pellets were reduced at 1400°C for 30 min. and iron nuggets were produced successfully. Usage of waste PET purely as reductant in composite pellets gives a higher metallization degree and proper carbon content than coke or PET and coke mixture.IntroductionPlastics can be seen everywhere, especially at packaging industry in our common life. The increase of plastic usage ends up with an important problem, the increase of plastic wastes. Many studies have been carried out about usage of plastics as reductant in blast furnace such as Ogaki et al.[1], Heo and Baek [2], Saridede [3], Minoru et al.[4], etc. Besides, Kato et al. [5], Nomura and Kato [ 6] and Rongfang et al. [7] have pointed out the use of plastics in coke ovens regarding to its calorific content. In EAF steelmaking, a mixture of coal/coke and plastics can be used as an energy resource instead of only coal or coke. [8] Also, the usage of PET and PC in self-reducing composite pellets increased the reduction rate. [12]PET (Polyethylene terephthalate ), which is commonly used for soft drink plastic bottles, is an important municipal waste due to its C and H content. Its molecular formula is (C10H8O 4)n. Demir and Dincer showed that PET can be crystallized at 250°C to have the ability to be ground to a size of -100 µm. [11]"

Jan 1, 2011

By Jeffery L. Kohler, Eric R. Bauer

Prolonged exposure to noise over a period of years generally causes permanent damage to the auditory nerve and/or its sensory components. This irreversible damage, known as noise-induced hearing loss (NIHL), is the most common occupational disease in the United States today. Workers suffering from NIHL have difficulty understanding human speech and hearing other workplace cues. Despite the use of regulations and efforts by government and industry to reduce NIHL, the problem today is as prevalent as it was more - than two decades ago. Recently, the Mine Safety and Health Administration (MSHA) promulgated a new regulation that is designed to reduce NIHL in the mining industry. One of the more significant provisions is the elimination of MSHA's past practice of giving "credit" for the use of personal hearing protection, thereby reestablishing the primacy of engineering and administrative controls. However, there is a knowledge gap that is impeding the development and implementation of engineering and administrative controls. Although significant data exist on the exposure to noise by occupational code, little is known about the noise sources that contribute the most to the worker's dose. This is problematic in a workplace with multiple noise sources and workers who travel among noise sources. Yet without this knowledge, it is difficult to focus control efforts in any practical manner. Thus, it is important to characterize noise sources sufficiently well so that the sources most hazardous to hearing are identified and those conditions of exposure that are most amenable to engineering controls are pinpointed as well. The Pittsburgh Research Laboratory (PRL) of the National Institute for Occupational Safety and Health (NIOSH) is conducting a cross-sectional survey of noise sources and worker noise exposures in the mining industry to address this deficiency. The initial effort, conducted at a coal preparation plant and results are described in this paper. Preliminary analyses indicate that the noise levels on all floors exceeds 90 dBA in most areas, and that levels as high as 115 dBA were recorded. In addition, the one worker whose responsibility is to monitor the equipment and "house clean" the plant is slightly overexposed, even though he spends only half the shift in the plant. General information on the hearing loss problem in mining, a review of hearing protection use and noise regulations in mining, and other background materials are also presented.

By S. Tandanand

The Bureau of Mines, U.S. Department of the Interior, assessed the geological effects on the ratio of maximum subsidence and extraction thickness, hown as the subsidence factor, to develop a simple method for predicting the maximum subsidence. The study is restricted to the Northern Appalachian Coal basin where data were collected from 13 coal mines. A model previously developed to relate the subsidence factor with the lithology and with the width and depth of working panels was used in the assessment. The result shows the possibility of determining maximum subsidence without resorting to a rigorous method.

Jan 1, 1982

By Frank Chase, M. Terry Hoch, George Karabin, Joseph C. Zelanko, Christopher Mark

Pillar recovery continues to be a significant ground control hazard. During the past decade, 10 miners were killed during pillar extraction operations in southern West Virginia. Studies conducted during the past decade have identified a number of “risk factors” that can be used to evaluate pillar extraction plans: •Cut sequence •Final stump •Timber or Mobile Roof Supports •Roof bolting •Intersection span •Depth of cover •Roof quality •Age of workings For each of these factors, rock mechanics science suggests which alternative would be expected to be more risky. For example, numerical models were used to evaluate different cut sequences, and indicated that less roof convergence occurred with the outside lift method than with the Christmas tree in the particular environment simulated. For many of the risk factors, accident statistics confirm the science. One finding was that currently almost 70% of the retreat coal in southern WV is being mined with MRS. In contrast, timber supports were used in 70% of the past decade’s pillaring fatalities. This paper discusses each of the risk factors in turn, presents the relevant accident statistics, and shows how the risk factors can be combined to estimate the overall hazard. It also addresses the use of pillar design to minimize the risk of global stability hazards including squeezes, massive collapses, and bumps.

By A. Arik

Reliable ore reserve estimates for deposits with highly skewed grade disributions are difficult tasks to perform. Although some recent geostatistical techniques are available to handle problems with these estimations, ordinary kriging or conventional interpolation methods are still widely used to estimate the ore reserves for such deposits. The estimation results can be very sensitive to the search parameters used during the interpolation of grades with these methods. This paper compares the ore reserve estimates from ordinary kriging using several cases in which certain search parameters are varied. The comparisons are extended to different mineralizations to show the changing effects of these parameters.

Jan 1, 1990

By Mandius C. Lundal

This report describes the work done to develop a coal mining machine to increase productivity and recovery from thin seams beyond the highwall, in addition to decreasing the miner's susceptibility to to highwall hazards. First, radar transducers were adapted to measure coal thinkness and detect rock and coal interfaces; Then, the radar was incorporated into a cutterhead with steering controls. Next, visual displays were designed to show cutter position in the coal seam, and anticipated change In coal seam inclination. Finally, development of a telemetry system made remote control of the cutterhead possible. Simultaneously, a high-performance extended depth (HPxD) auger machine was designed with an automatic system to handle 600 ft of 36-in. diameter dual spiral flight conveyor sections. A two man crew controls all operations from a weather conditioned cab outside the VDZ, either at night or day time. As a primary mining tool, working 4000 hr/yr (2 shifts/day) recovering 60% of the coal 600 ft beyond the highwall, production to 500,000 ton/yr can be achieved. Volume II contains technical discussion of subsystems and machine drawings.

Jan 1, 1977

By David Hopkins, Steve Klein, Bradford Townsend, Ed Sum, Derek Penrice

INTRODUCTION The Transbay-Caltrain Downtown Extension (DTX) Project involves the construction of an approximately 1.5-mile rail line that will extend Caltrain commuter service and the future California High Speed Rail system into downtown San Francisco. The underground rail extension will be constructed by mined tunnel and cut-and-cover methods. Tunneling challenges include difficult ground conditions, low rock cover, the presence of historic buildings along the alignment, and the large tunnel span, ranging from approximately 50 to 65 feet. Three mined tunnel construction methods were evaluated: the Stacked Drift Method, the New Austrian Tunneling Method/Sequential Excavation Method (NATM/SEM), and Tunnel Boring Machines (TBM). This paper describes the challenges presented within the mined tunnel section, and summarizes the evaluation of tunneling methods that led to the selection of NATM/SEM. PROJECT OVERVIEW The existing Transbay Terminal opened in downtown San Francisco in 1939. This facility is antiquated, and does not meet current building seismic safety standards or the transportation needs of the Bay Area. For these reasons, San Francisco voters approved Proposition H in 1999, which proposed to construct a new or rebuilt regional transit center at the site of the existing terminal and extend Caltrain commuter rail ser-vice to the new transit center. The new transit center is the hub of the Transbay Transit Center (TTC) Program, which will greatly enhance regional transit service by providing connectivity for six Bay Area transit providers at one facility. The program will be the largest inter-modal centerwest of New York City. The TTC Program is comprised of two major projects, the Transit

Jan 1, 2007

The challenge of planning to minimize interaction effects in multi-seam mining is compounded by the difficulties inherent in extrapolating essential geological and spatial data between sampling points. To predict the effects of ultra-close mining on lower seam entry stability, simulated mine openings were studied using finite element analysis and body loaded photoelastic models. Both symmetrical and unsymmetrical loading was used to represent stress fields generated under multi-seam conditions. Results were correlated with field data to determine stress levels at which failure could be expected to occur. Stability predictions require precise definitions of geologic and spatial data, which could not be accurately defined by interpolation between sampling points. To overcome this problem an expanded roof stability model, SESAME2, was developed to incorporate reliability concepts based on Monte Carlo sampling. The model was demonstrated in terms of variations of innerburden thickness using a case study.

Jan 1, 1994

By Xiaohong He, Qing Yu, Kaixiang Zhang, Rui Guo, Minghua Lin, Haoyu Miao

With the increasing depth of coal mining, the coal mine shaft traverses’ strata conditions become more and more complex. Shafts are often located in deep thick strata with unstable aquifers, and coal mining requires short-term rapid drainage of aquifers; the additional stress caused by aquifer water drainage is the direct cause of the shaft-lining failure. Over the years, many experts have conducted research on the shaft-lining damage caused by the consolidation and subsidence of the soil layer induced by the long-term drainage of the aquifer. On this basis, this paper conducts an in-depth study of the dynamic change of the pore water pressure of the aquifer in the short-term drainage and its influence on the response of shaft-lining strain and surface subsidence. The result shows that the Mandel effect of pore water pressure around the shaft-lining is obvious at the beginning of drainage, and the pore water pressure suddenly increases; the increase is independent of the drainage rate, which leads to the sudden increase of the shaft-lining strain value unrelated to the drainage rate. The result also shows that with the gradual dissipation of pore water pressure, the increase of shaft-lining strain is positively related to the drainage rate and negatively related to the drainage distance, and the variation trend of horizontal strain is greater than that of vertical strain, which appoints the main cause of shaft-lining damage.

Mar 16, 2023

By F. Hassani, K. Moozar, J. Ouellet, P. Gauthier

"This paper describes a sudden spill of waste rock used for backfilling from a waste pass at an underground mine in Canada, thus causing a major failure/accident. The mine operator immediately launched a detailed investigation to understand the causes of this accident and develop procedures to prevent any recurrence of such events in the future. The authors from McGill University were invited to collaborate with the engineers at the mine to examine this accident. The events leading to the accident were studied, appropriate measurements were taken and samples of the waste material were collected for further testing and analysis.The field visit and the interview of the witnesses allowed the detailed documentation of the events. The sequence of events related to the incident, along with the experimental results obtained in the course of the investigation, are presented. The waste material was characterized in the laboratory with regard to its behaviour in the presence of water. This information is discussed and the failure mechanism involved in the accident is identified. Finally, the full recommendations as well as the immediate operational measures implemented by the mine to prevent the future occurrence of such events are presented and discussed."

Jan 1, 2004

Sequential and evolutionary changes through time are recognizable in many, perhaps most major families of ore deposits and their geological environments. These changes are additional useful indicators of the evolutionary history of the earth and its tectonic processes. They are important in mineral exploration because they involve consideration of time as a fourth dimension, thereby indicating the most favorable ages, rather than types of rock for investigation. Many of the changes are analogous to those recognized in faunal evolution. Some primitive, unspecialized types of ore deposits occur nearly unchanged through rocks of widely differing age. Others diversify into several, more specialized variants, whereas still others become extinct. The place of these is taken by new, younger types, some of which undergo sudden proliferations and later diversifications of their own. In Archean greenstone belts irrlportant iron, nickel, gold, and base metal deposits occur co-regionally, but in different stratigraphic positions in the same, thick volcano-sedimentary successions. Here their close temporal and spatial associations suggest common genetic exhalative hydrothermal processes. The massive base metal sulfide family of ore deposits provides an excellent example of evolutionary changes, exhibiting distinct variations through both time and space. Deposits belonging to this family span the entire range of time, occurring in rocks of ancient Archean to Recent age, and specific types within the family also span the entire range of spatial environments from ensimatic to ensialic. Moreover there are possible evolutionary metallogenic links between certain types of massive base metal sulfide deposits and other important base metal ores, noteably Mississippi Valley-type and porphyry copper deposits.

Jan 1, 2013

By D. H. Diering

Definition of mineral resources and reserves forms the basis for effective mine planning and reliable public reporting of mineral assets. Historically, the mineral resource and reserves declaration process has been the domain of the geology and surveying disciplines, with the declaration of the reserves by the surveyor being based on the application of modifying factors to the declared resources available for mining. As part of an ongoing process to improve efficiency, reliability, and reproducibility of results, this approach has been revised and enhanced through the introduction of a revised process and reconciliation tools. The revised approach to reserve definition is based on the definition of scheduled resources, at an appropriate confidence estimate in the context of an approved business plan, over the anticipated life of the mineral asset being applied to define reserves. This planning and scheduling is developed, during the annual business planning process, by the mine planning department using tools such as CADSMine?. The scheduled area together with the application of revised modifying factors is tabulated in the BME (basic mine equation) and reflects the mine production plan over time. Simplification of the modifying factors to dilution and losses underpins the simple yet robust approach to improved definition of reserves in this process and in the basic resource to reserve equation (BR2RE). Dilution intrinsically affects grade but not metal content, whereas the losses reflect both the efficiency of mining and planning and are reflected in metal losses, area losses, or both. Reconciliation of the derived 'resource converted to reserve' area (which is based on the business plan from CADSMine?) versus the 'resource available for mining' (which is derived from Datamine?) underpins the robustness and auditability of the reserves declaration. This R&R accounting and reconciliation approach is transparent and facilitates interrogation of the logic and rationale of long-term business planning and project strategy. These numbers are processed and reported in the logic of the basic resource equation (BRE), which also addresses aspects such as white areas (future and historic), tail management, and partial extraction (non-scheduled pillars, etc.) in compliance with SAMREC definitions. Areas that do not have the necessary confidence and data support to be declared as resources find their space as pre-resource (outside the domain of public reporting), outlining existing potential for future extraction and reporting. Use of the BRE leads ultimately to a complete, refined accounting and reconciliation-oriented approach for all production entities. The revised resource and reserve process includes the discipline of mine planning as intrinsic to the definition and declaration of resources and reserves. Subsequent to the change in process, the resources and reserves have truly become the domain of the mineral resource management discipline. This paper defines the logic of the basic resource equations and outlines their application in the definition and reconciliation of mineral resources and reserves at Anglo American Platinum Limited.

Jan 1, 2013

By D. Prince, G. Nollet

"Since 1994, Aur Ressources has operated Louvicourt mine, a zinc and copper mine close to Val d’Or, at a rate of 4300 t/d. Ever since the start-up of the plant, management has encouraged innovative approaches in reliability.The first of three papers will discuss the vibration monitoring program in place. The program will be described and two examples will be given: detection of a rolling bearing defect on a pinion driving the ball mill and identification of wear on the bearings of the flotation cells. Figures on the return on investment and the costs of a monitoring program will also be given.The second article will discuss the lubrication aspect. Since the establishment of a good monitoring and oil analyses, Louvicourt mine decreased its oil consumption by more than 38 000 L/yr. In addition, the company set up an oil regeneration system that restores the original properties of oil.The third article will cover the management aspect. Work organization as well as the management philosophy enabling the employees to push predictive technology to higher levels will be examined in detail. The key elements which made it possible for Louvicourt mine to position itself among world-class companies in the organization of maintenance will be discussed. IntroductionThis article is the second of three on predictive maintenance at the Louvicourt mine operated by Aur Resources Inc. The first article, published in the October 2002 issue, was about vibration analysis for rotating machines. This article describes how lubrication and oil analysis for stationary machines permitted Louvicourt to save more than $150,000 within two years and presents the evolution of the oil analysis program.Louvicourt mine, located near Val-d’Or, Quebec, is a copper and zinc mining and milling operation that processes 4300 t/d of ore and employs 289 people. Production began in 1994. Louvicourt mine is a partnership between Aur Ressources (30%), Teck Corp. (25%), and Novicourt (45%)."

Jan 1, 2003

By Gregory M. Molinda

The U.S. Bureau of Mines has developed a rock mass classification system for coal mine roof control. The Coal Mine Roof Rating System (CMRR) evaluates the structural competence of mine roof using simple field tests and observations obtained from underground exposures in roof falls or overcasts. The basis of the WRR is a weighing system which converts descriptive geologic roof rock data to a numerical value, facilitating its use in engineering design. A full suite of data collection and hand calculation sheets accompanies the CHRR A data base is currently being collected from all major coal basins in the United States to validate the CMW. To date, CHRR values are available from 96 roof exposures in 59 coal mines representing these basins. The system can be used to help solve many practical ground control problems, including longwall gate road design, roof support selection, and decisions regarding extended cut length.

Jan 1, 1993

E. G. WOODRUFF, Houston, Tex. (communication to the Secretary*). -Mr. Matteson has presented to us an idea worthy of our careful consideration. We have real troubles in the petroleum industry and as the supply of crude is exhausted our problems become more complicated and more numerous. Therefore, we who are engaged in field work are forced to consider all possible means which promise assistance in the location of prospective pools and the economic development of pools already located. In our country we are accustomed to turn to the. Government for relief in all our troubles. Do we want an Oil and Gas Bureau doctoring us? Will such a bureau do us practical good? The principal point Mr. Matteson suggests is that such a bureau should he authorized to receive and file all well logs. In analyzing such function, I am led to the following conclusions: If well logs are simply to be filed they would be useless. If they are to be filed and the files opened to the public, what benefit will be derived and can such action be taken justly? There is no doubt that if the record of all wells drilled in the United States were available the petroleum industry would be saved an immense amount of needless expense. Accumulating conditions would be better understood and prospecting more intelligently directed. Our other consideration is: can the oil companies be required to open well records to the public justly? I think all will agree that if any one should have the advantage of a well record it should be the company that drilled the well. If the oil companies are forced to file such record and open the files to the public, the company drilling the well cannot derive the exclusive benefit from the money expended. Would it be just for a small company to be compelled to reveal its records of a well it had recently completed, to its strong competitor who holds near or even adjacent leases? Would it have been just to the successful companies, in the Gulf Coast country to have been forced to display their hard-earned knowledge of 15 years to the host of younger competitors who have recently flocked to the Gulf Coast attracted by the success of those who have labored so long and learned of the conditions controlling the fields through the hazards of the industry.

Jan 10, 1917

By S. J. Davenport

The increased consumption and importation of fluorspar and cryolite (1)3/ in recent years, and especially the addition of fluorine compounds to drinking water in the United States, have aroused renewed interest in the properties of such compounds and possible health hazards incident to their use. It has been suggested that the issuance of a revision and elaboration of Information Circular 7311, The Hazards of Hydrogen Fluoride Poisoning in the Mineral and Allied Industries, which hay been out of print for some time, would be opportune. Fluorine minerals have been known since the Middle Ages. Fluorine was isolated in 1886 by Moisson (2).

Jan 1, 1954

By Betty L. Gibbs

The ultimate objective of mine design is to determine the development and untilization of mining resources. Computer Aided Design (CAD) and automated mapping are becoming very popular in engineering and in mining. Any computer program which produces a design or model with the interaction of an engineer can be considered computer-aided design (CAD), but' the term CAD is often associated with interactive graphic design and mapping capabilities. Graphics can be effectively used to describe and model two-or-three dimensional mine workings, orebodies, and geologic structures. Interactive computer graphics is applied to mine design with a combination of deposit modeling techniques and the use of AutoCAD for interactive graphics and mapping. The combined system can perform a large part of the calculations and drafting work for geologic and mining design. Using computer calculation and graphics techniques, comparisons of alternatives, can be made quickly.

Jan 1, 1989

By J. A. Herbst, D. W. Fuerstenau

This paper examines the zero order production phenomenon in the context of the size discretized batch grinding model. A restrictive interrelationship between the selection and breakage parameters of the model, which is mathematically sufficient to ensure zero order behavior, is delineated. Based on this interrelationship, a scheme is developed for predicting the values of the selection and breakage parameters for all size fractions from a minimum of experimental data. To test this scheme, dolomite was ground in a laboratory batch ball mill. Successful simulation of the comminution behavior of this system was achieved using the batch grinding model with the parameter values obtained from the proposed scheme. Historically, a preponderance of comminution research has centered on attempts to relate breakage energy to the performance of comminution machines. Concomitantly, grinding data were interpreted almost exclusively in terms of inherently empirical energy-size reduction relationships1-3 or "laws of comminution"4- 6 which were based on highly oversimplified descriptions of the fracture process. In some instances, these relationships provide a crude basis for the correlation of experimental data, but, invariably, this approach is inadequate for meaningful process simulation. The control and optimum design of comminution circuits require a mathematical model capable of depicting the size reduction behavior of every size fraction for grinding conditions of technological importance. Energy-size relationships do not provide this detailed information. For example, an energy-size analysis for batch ball-milled dolomite has recently been completed in the authors' laboratories.7 This analysis provided a satisfactory correlation between the hypothetical size modulus, which characterizes only the finer portion of the size distribution, and the input energy. However, this relation did not constitute an adequate description of the complete system. In general, one of two distinct viewpoints toward simulation has been adopted in recent comminution research. The first approach focuses on the fracture of single mineral specimens, with the essential aim of representing the over-all process in terms of the breakage characteristics of individual particles and the characteristics of the stress field which the particles experience within the particular size reduction device. As illustrated by Harris's review,' the actual incorporation of single-specimen fracture information into a description of the behavior of a multiparticle comminution system has seldom been attempted. The only model to accomplish this incorporation was the one developed by Schönert.8 The Schonert model treats single-passage grinding machines in terms of a distribution of effective loads acting on a particle, a distribution of required particle breakage energies, and the breakage product distribution. However, the use of single-particle fracture behavior to derive models of the size reduction process is at present limited to machines in which the particle residence time is approximately equal to the time required to apply stress. As a result, Schönert's analysis cannot be used to advantage to simulate the complex environment which prevails within a tumbling mill. For multiple-passage systems a second approach to the description of comminution processes has been more fruitful. This approach entails the formulation of a mathematical model which is phenomenological in nature in that it lumps together the entire spectrum of stress-application events which prevail in a system under a given set of operating conditions. The appropriately defined average of these individual events is then considered to characterize the over-all breakage properties of the device. Thus, to analyze the performance of a tumbling mill, the manner in which the particles of a particular size (or size fraction) are stressed need not be distinguished. Instead, a single parameter is assumed to represent the resistance of that size to fracture, given the average grinding environment which exists in the mill. The isolation of such a parameter and a related set of quantities, which constitute the breakage product size distribution for the average event in this size fraction, allows the formulation of physically meaningful descriptive equations capable of yielding precise and detailed information for simulation.

Jan 1, 1969