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By Francisco Sena Leite, Thomas Palangio, Vinicius Miranda

With an increasing pressure to find efficiencies in the mining industry, operations are looking for continuous improvement tools to validate blasting procedures, a crucial and often overlooked area of the process. Using case studies completed at both small and large-scale mining operations, this technical paper proposes a practical methodology for pattern expansion studies, taking into account terrain parameters, rock quality and explosive strength. This technical paper will use a series of tools geared towards an economical continuous improvement procedure, using UAV particle size analysis to optimize blasting based on “generalized reduced gradient” for non-linear problems, with cost savings being the main objective. For the validation of this methodology, one scenario was created based on the operation’s budget: an economical continuous improvement plan that relied on manual data collection methods in order to baseline and optimize procedures.

Jan 1, 2018

By Roy A. White

The development of a fire and rot-resistant coating treatment for mine timbers, along with the associated processing technology, is described. Included are a literature search, laboratory studies of polyimide-fungicide coatings, and leaching and fungus growth studies on coated wood blocks. Finally, an economic analysis is performed tor various levels of production.

Jan 1, 1977

By John E. Lambert

Automatic control of drum head continuous mining machines was investigated as a means of reducing respirable dust generated and operator variabitity. Literature survey, manufacturer interviews and mine visits were the major information sources. Technically feasible automation concepts were Identified to control sump and shear rates, cutter head elevation limits and sumping distance. These are the elements of a programmed cutting cycle which maintains peak penetrating force on the cutter, to maximize depth of cut and therefore reduce dust generation. Based on the industry surveys, successful underground hardware demonstrations must be completed in order to stimulate the market demand for these advanced control features.

Jan 1, 1979

By F. H. McDowell

For more than two hundred years Mexico has been enriching the world from her inexhaustible wealth of precious metals. From this source alone, over three thousand five hundred millions of dollars have been poured into the coffers of Europe and America. During these centuries the wants of the country in manufactured goods have been supplied from the mills and machine-shop of the Old World. English, French and German merchants in Mexico have vied with each other in their efforts to control the importing of these goods from their respective countries. The overthrow of Maximilian, the departure of the French and the restoration of the Republic, largely influenced by the strong stand taken by the United States Government during our own civil war, established a new order of things. Americans were encouraged to visit the sister republic, examine into the needs of the country, as well as its resources, and interest themselves in the work of development. More recently, under Presidents Diaz and Gonzales, liberal inducements have been extended to American capitalists to build railroads, open mines, erect reduction-works, raise cattle and improve the crude systems of agriculture. The Mexican Central Railway has been pushed south from the Rio Grande to the Capital, and, by its branches and connections, makes the whole mineral belt of the country accessible.

Jan 1, 1885

By A. Vidyadhar

Printed circuit boards (PCBs) constitute a majorpart of electrical and electronic equipment containing valuable metals such as Cu, Ni, Au, Ag, Pd, Fe, Sn, Pb, etc. The concentration of base and precious metals in PCBs is observed to be several times more than those in their respective ores. Therefore, the recycling of PCBs is necessary to recover the valuable materials. However, the ultrafine particles pose a big challenge. Removal of them is suggested prior to processing by flotation. Froth flotation is observed to be a promising technique for rejecting the plastics from the comminution product. In the present work, enrichment of ground 1.0 mm PCB powder was investigated through flotation route by varying the operating variables such as frother dosage, pulp density, air flow rate and rotational speed of the impeller. The liberation studies indicate that excellent liberation of metal values is achieved from the non-metallic constituents at -1.0 mm size and below. The particulate system is quite rich in metal value with about 23% total metal content. The non-metallic constituents such as plastics are observed to possess strong hydrophobicity while the metal particles in the pulverized mass are hydrophilic in nature. Froth flotation kinetics is studied in depth with a view to facilitate high rejection of plastics and identify optimum operating conditions for the same. A number of experiments are performed to establish the influence of the operating variables on flotation performance. The conditions for achieving higher yield of the metal-rich fraction with respect to a specified grade are discussed in the light of the experimental results. It is found that the requirement of reagents is negligible which could be a very important factor from the commercial stand point. Single-stage flotation increases the metal content from 23% to over 32% with a mass yield of around 75% and over 90% recovery of metal values. 32% of the materials in the feed could be effectively rejected in the float fraction losing less than 4% metal values. The dependence of kinetics on the process variables is also discussed. It was concluded that a high rotor speed helps in efficiently rejecting the plastics. Frother should be added to help stabilize the froth and enhance the kinetics. A moderate air flow is required while pulp density must be kept low for efficient pre-concentration. It is established that the entire -1.0 mm comminution product could be treated by flotation for generating a pre-concentrate. Keywords: printed circuit boards, recycling, froth flotation, kinetics, recovery

Sep 1, 2012

"In response to needs created by intensive exploration and accelerating expansion of coal mining in the Western provinces, Canadian R & D on coal is progressively widening its scope. Principal interests continue to lie in coal geology, preparation and processing, carbonization, combustion and transportation, but much active work is also in progress with respect to mine environments, mined-land reclamation, and environmental consequences of coal mining, processing and use. Long-range 'basic' research, which characterized much of the R & D pattern in the fifties and early sixties and which was often no more than an attempt to prevent total extinction of a dying industry, has been somewhat de-emphasized, except insofar as it relates to 'safe' coal storage and to coal-based carbons (which are beginning to command attention as pollution control media).In this review, recent exploration, mine development and new preparation facilities are noted, and current R & D in transportation, processing, handling, carbonization and combustion is summarized. Reference is also made to investigations bearing on non-fuel uses of coal (notably as source-materials for carbons and agrobiological products)."

Jan 1, 1970

By R. M. Taylor

Lime addition to acid mine drainage (AMD) leads to precipitation, predominantly of metal hydroxides and calcium sulfate, and is the benchmark for remediation by precipitation. Geo2 Limited of Melbourne, Australia has developed and patented a novel alternative precipitation scheme based on the formation of mixed valency, M(I1)-M(III), hydroxide sulfate salts. When the composition of AMD is appropriate, the Green Precipitate Process provides a useful and more effective alternative to conventional liming. The characteristics and utility of the Green Precipitate Process are described in terms of the underlying chemistry, and a case study where the Green Precipitate process outperforms conventional liming. A mobile pilot pipe reactor rig which was built by Geo2 to demonstrate the process, and used successfully in both Australia and the United States, is described.

Jan 1, 1998

By J. R. Maxwell

Large capacity flotation cells with volumes ranging in size from 300 to 2000 cu ft are used in the Opemiska concentrator, Opemiska Copper Mines (Quebec), Canada. This paper gives a description of the flowsheet with metallurgical comparisons using Maxwell vs. conventional cells, total power consumption used, and estimated maintenance costs.

Jan 1, 1973

By C. A. Pierce

Studies of roof and floor movement are of interest to those actively engaged in mining. This is especially true in the case of an entirely new area where there is no precedent for guidance. The potash deposit being mined is in the southeast corner of New Mexico, about 20 miles east of Carlsbad. The deposit was formed by the land-locked, shallow, Permian Sea that extended through parts of western Texas, Oklahoma, Kansas, southeastern Colorado, and eastern New Mexico. The saline deposits vary from 500 to 4000 ft. thick. Neither of the companies operating in this area has delimited its commercial ore bodies. As all production so far has been from Federal and State leases, the Department of the Interior and the State of New Mexico have a direct interest in the development and extraction of these ore horizons. The ore is composed of an intimate mechanical mixture of sylvite (potassium chloride) and halite (sodium chloride). It lies generally in a horizontal bed varying from 5 to 12 ft, in thickness, and has a cover of approximately 1000 ft., consisting of about 500 ft. of salt beds and 500 ft. of sediments. The immediate mine roof for several feet is principally salt with some potash and clayey material. The next 500 ft. above, from the standpoint of structure, may be considered rock salt with a few inter-bedded potash members. The upper 500 ft. is of sedimentary (Permian and Triassic) origin and contains several water-bearing formations with flows varying from 10 to 500 gal. per minute. This water intensifies the interest in convergence problems as the ore and surrounding formations are water soluble. Potash salt (sylvite) and rock salt (halite) are plastic minerals. Plasticity is defined as a "property of solids by virtue of which they hold their shape permanently under the action of small shearing stresses but are readily deformed, worked, or molded under larger stresse."1

Jan 1, 1942

By Simon D. Strauss

This paper discusses the ways in which the metals industries dealt with surplus capacity in the past, primarily the twenty years, 1950 - 1970. During this period, the bulk of metals production in the market-economy countries was controlled by private sector companies. Since then, public sector companies have played an increasingly important role in the metals industries of the market-economy countries. Of course, the change was not overnight. It occurred gradually over a period of many years. Indeed, by 1965, several developing nations had adopted policies of government control of metal operations previously in private hands. The metals industries are so many, so large and so diverse that the constraints of time make it impossible to deal with all segments. To illustrate the problems of surplus capacity in the metals industries during the period, this paper focusses primarily on three metals. One experienced rapid market expansion between 1950 and 1970; one had a growth more or less in line with the expansion of the world economy; and one lagged well behind the pace of industrial expansion. No one will be surprised if aluminum is identified as the metal with rapid growth; copper is identified as the metal that kept pace with the world economy; and tin is identified as the laggard. Individual computations of the rate of growth for these metals show some variations, but most estimates place the increase in aluminum consumption in the market economy countries between 1950 and 1970 at a compound annual rate of about 8%. The corresponding figure for copper is a compound rate of 4%. Tin consumption showed no growth. A widely accepted point of view is that sharply rising demand will force the price of a commodity to increase substantially in order to attract a necessary expansion of supply. The corollary to this is that stagnant demand will hold prices down, as there is no need to stimulate new supply and it may be necessary to force marginal producers out of the market. The experience with aluminum, copper and tin in the years 1950-1970 does not support this theory. In 1950, the average prices in the United States market as reported by the American Bureau of Metal Statistics were 17.74 a pound for aluminum, 21.24 a pound for copper, and 95.54 a pound for tin. The corresponding figures in 1970 were 28.74 a pound for aluminum, 57.74 a pound for copper and 174.24 a pound for tin. Aluminum, with the greatest market growth, rose by 60%, whereas tin rose 82% and copper by 172%. Clearly, other factors were a more important influence on price than was the trend of demand To revert now to the capacity issue, during the period under review aluminum demand was rising so sharply that that industry had no sustained problem with surplus capacity. Instead, if anything, capacity may at times have been a constraint on demand. The industry succeeded in attaining explosive market growth through imaginative research and promotion programs. Some of this growth was the result of substitution of aluminum for other commodities – steel, copper, wood and glass as examples. But much of the growth was the consequence of developing entirely new products through technological innovation. Prior to World War 11, the number of aluminum producers was extremely limited. Alcoa and Alcan in North American and Pechiney and Alusuisse in Europe were the dominant firms. The developing countries had virtually no production and in Japan and Germany production was only a small fraction of the North American output. During the War years the United States had financed the construction of many new facilities. After the war these plants were sold by the government to Reynolds and Kaiser in order to foster more competition in the market. Subsequently many other concerns became aluminum producers, both in the United States and elsewhere and competition for markets intensified.

Jan 1, 1989

By Weng Fu

In this study, Resin-in-Pulp (RIP) technology is used to separate Pb from a chalcopyrite slurry. Solvent-impregnated resin, Lewatit® VP OC 1026, which contains di(2-ethylhexyl) phosphoric acid (D2EHPA) in a macroporous polystyrene matrix was used, as the functional group exhibits selectivity for Pb over Cu. Adsorption pH, kinetics, as well as resin and CuSO4 concentrations were investigated. The results show that the kinetics of Pb and Cu loading are fast, reaching the adsorption equilibrium within 30 min. The equilibrium pH of 2 was chosen as optimum for operation in order to achieve a high Pb extraction rate and extent as well as selectivity for Pb over Cu. High Cu(II) concentration in solution results in Pb(II) requiring a larger amount of resin for the same degree of extraction. Regeneration and reuse tests show that the loss of adsorption capacity happens in the 1st and 2nd cycles and then the adsorption capacity stabilises for the 3rd cycle.

By John J. Dran

The elaborate analytical techniques for risk analysis used by the large mining companies in conjunction with the valuation of mineral reserve sites are totally inappropriate for the small miner. The small miner does not possess the financial and technical resources which are available to the large companies for such risk analysis. Even if these resources were available to him, the relatively small size of his investment would not justify a huge expenditure for risk analysis. What is required by the small miner is an improvement over the single point estimates provided by the valuation techniques that he currently uses. Such improvement should provide an indication of the extent to which the true value (known only after the fact) might differ from his estimated value of the mineral reserve site. In addition, a rough indication of the chance of occurrence of various differences between the true and estimated values would be helpful to him. These improvements must be obtained at low cost to be useful to the small miner. Such improvements would have to be based on a simple system requiring very few additional estimates by the miner. The small miner is not accustomed to dealing with sophisticated risk analysis techniques. Hence, any complex, time-consuming approach would be doomed to disuse or possible misuse. A simple, uncomplicated approach requiring a minimum of additional estimates by the miner can be based on a system devised by Frederick S. Hillier Although Hillier's method can be applied to various mineral reserve valuation methods used by the small miner, this note is specifically oriented to the discounted cash flow model. The basic discounted cash flow (DCF) approach provides a single point estimate of value and introduces the concept of risk (i.e. the possibility that the annual cash flows may differ from their estimated values and thus lead to an incorrect investment value) through the use of a risk-adjusted discount rate. This approach simply lowers the present value estimate with increases in the discount rate (i.e. increases in the risk assessment). The single point estimate still remains. Although the lower value estimate makes it less likely that the risky investment will be deemed profitable and undertaken, it provides no indication of risk that is suitable for examination and analysis. In addition to the "best guess" estimate of annual net cash flows required in the DCF model, application of the Hillier risk analysis model requires that the miner

Jan 1, 1976

By Kee Jeung Lee

In this study the characteristic factors and formation mechanisms for the hydrothermal preparation of a -quartz crystal powders were investigated to find the optimum synthetic conditions. The degree of Q -quartz crystal face development depended on the relative growth rate of a particular form that varies considerably with the degree of supersaturation, the reaction temperature, the concentration of mineralizers, and the presence of seed crystals in the feedstock. Alkali hydroxides and alkali halides were found to be effective in the reactions as mineralizers, which added in order to increase the solubility of the feedstock. The fine Q -quartz crystal powders were obtained in the temperature range of 250-450% and pressure range of 100-300atm. As the concentration of mineralizers increased, the particle size of crystalline powders became smaller at lower reaction temperatures. The fractional size distribution of synthetic crystal powders was depended on the hydrothermal conditions. As the reaction time and the amount of seed crystals increased, the width of particle size distribution became narrower. The weight mean particle size was in the range of 1 to 10m. The characterization of the products were carried out using XRD. SEM. PSA, FT-IR, Raman spectrometer.

Jan 1, 1997

The New England Fold Belt forms the easternmost and youngest section of the Tasman Fold Belt System of eastern Australia. From middle Palaeozoic to Early Cretaceous time it was the site of extensive episodic calc-alkaline magmatism related to W-dipping subduction. The oldest rocks may have formed at least partly in a volcanic island arc, but from the Late Devonian, the fold belt developed as a convergent Pacific-type continental margin. For Late Devonian-Carboniferous time, parallel belts representing continental margin volcanic arc, forearc basin and subduction complex assemblages can be recognised. Major dextral transform faulting may have offset parts of the fold belt in the Late Carboniferous. In addition, some structural blocks which appear to be out of place in the overall palaeogeographic setting are possible exotic or suspect terranes. A great variety of lode deposits ranging in age from middle Palaeozoic to Early Cretaceous is present in the New England Fold Belt. The vast majority of these are related to emplacement of extensive granite plutons and eruption of continental silicic volcanics in Late Permian-Late Triassic time. However, volcanogenic massive sulphides and volcanic hosted epithermal gold-silver deposits in older rock sequences include one major orebody (Mount Morgan) and several important ones (Mount Chalmers, Cracow, Silver Spur, Cangai and Halls Peak). Some problematical deposits are best classified as metamorphic-hydrothermal. These include gold-bearing quartz reefs and stockworks in sedimentary host rocks, the most important of which are at Gympie, and antimony-gold- tungsten mineralisation in the New England area, mainly at Hillgrove.

Jan 1, 1987

By D. Burkhard, E. Herth

"Geologic structure and properties are the primary influences on ground control at San Juan Mine. Geotechnical properties of the coal seam and near seam strata, the presence of above seam sandstone paleochannels and water, are thought to be the leading contributors to ground control issues. It is the confluence of specific geologic conditions rather than isolated features that most often produce adverse conditions. Altering primary support installation and mining practices are done when unfavorable conditions appear during development. Installation of standing support is most often employed when adverse conditions develop at later dates. REGIONAL GEOLOGIC SETTING San Juan Mine is an underground coal mine located on the western flank of the San Juan Basin in northwest New Mexico. The San Juan Basin is contained within the south eastern region of the Colorado Plateau geographic province. The basin contains multiple coal bearing formations and is also a major producer of coalbed methane gas. San Juan Mine is stratigraphically located within the Fruitland Formation. From a prominent monocline marking the western boundary of the basin, the formation dips gently to the east towards the center of the basin. The primary driver for the deposition of coal bearing formations within the basin was the Cretaceous Inland Seaway. Multiple cycles of transgression and regression driven by sea level rise and tectonic subsidence deposited rock types from marine shale’s to terrestrial sandstones. The Sevier Mountains to the west of the seaway likely provided the sediment supply for the Fruitland Formation. During a major cycle of seaward regression, the Pictured Cliffs Sandstone Formation prograded over the marine Lewis Shale. The coal bearing Fruitland Formation followed, being deposited over the Pictured Cliffs. The Fruitland Formation contains numerous coal seams and is approximately 400 ft. thick at San Juan Mine. Fruitland Formation coal seams are numbered in order of superposition. San Juan mines the Fruitland number 8 seam. Dating has placed the age of the seam at approximately 73 to 75 million years [1]. LOCAL GEOLOGIC SETTING The Fruitland 8 coal seam dips approximately 1-3 degrees towards the E-NE. At San Juan Mine, the seam displays a mild plunging, synclinal structure, the axis roughly bisecting the mine from west to east. The number 8 seam consists of five coal benches and four volcanic ash band partings labeled sequentially based on superposition. The lowest portion of the seam is the 8-1 bench, the 8-2 through 8-5 benches following sequentially to the top of the minable seam. Ash band partings are labelled P1 through P4 from bottom to top respectively. The presence of distinctive partings and benches allows for seam definition and aids in identifying mining horizons."

Jan 1, 2016

By J. D. Warne

The ferberite district of Boulder County, Colo., has been an important producer of tungsten since 1900. During World War I, high prices for tungston concontrates resulted in a brief period of intense activity, and the production in 1917 was 2,707 tons of 60 percent W03 concentrates. Production declined thereafter, and in 19.2 the tungsten produced in Boulder County represented about 4 percent of the Nation's output, being exceeded only by the scheelite production in California, Nevada, and Idaho. Boulder County has boon an important source: of tungsten in the Korean emergency; the present report does not describe this recent activity, as it will be covered by a future publication. Tungsten occurs in small ore shoots of narrow and irregular veins. Most of the ore shoots have been found outcropping on the surface. Core drilling; has been used by the larger operators to explore for new veins and to locate extensions of known veins.

Jan 1, 1953

By Noble AC

Ore reserve reporting practices in the United States may be broken into four general categories as follows: ò Reserve reports, often of an unofficial and preliminary nature, which are made through the news media. These are often based on exploratory drilling or sampling results. ò Reserve reports made for the purpose of raising public funds by issuing securities on the stock market, or as part of other filings to the United States Securities and Exchange Commission. ò Reserve reports to obtain private funds from banks, financial institutions, or other investors. ò Reserve reports for internal use and planning by companies operating or evaluating mineral properties. This paper discusses current practices for each of these types of ore reserves reports and reviews recent changes which have affected those practices.

Jan 1, 1987

By B. S. Crocker

Introduction Pebble mill grinding can be defined as wet or dry grinding in a tumbling mill with pebbles used as grinding media instead of metal balls. To clarify the terminology, which may differ in the various mineral industries, it is essential to point out the differences between grinding with partially sized and carefully sized grinding media. When grinding with partially sized media (limited top size only), sizing is usually the setting of the primary crusher and there is no bottom sizing-all fines, chips, sand, and small sizes are included. This is often called run-of-mine or primary autogenous grinding. In this case the entire crusher discharge is fed into the mill and part of it becomes "charge" and the rest is "sand feed." When grinding with carefully sized media (i.e., media that is sized both at the top and bottom of the size range), no fines or chips should be present in the charge to the mill. This is pebble milling and the grinding media consists of ore, rock, Danish pebbles, gravel pebbles, or ceramic pebbles-media that is appreciably lighter than steel balls. The grind¬ing charge is fed to the mill to maintain a load and it does the grinding usually on a classified sand product of suitable size. If the grinding media is the same as the raw material being ground, this type of grinding is also called secondary autogenous grinding. Pebble milling was in common use in the gold mines of South Africa in the early 1900s. It is by far the oldest form of autogenous grinding. It may be used to grind crushed ores from a maximum size of about -% in. to all -10 µm. Pebble milling differs from "run of mine" grinding in many ways, but two big differences are: I) The ore itself is crushed to approximately t/4 in., or it may be further reduced to 8 or 10 mesh in a rod mill or fine crusher. 2) Then carefully screened ore of the correct size is placed in one or more stages of pebble mills to grind the ore to its desired final size. The media size is carefully selected to be the most efficient for the particular size reduction required in each stage. This is a precise practice, and pebble mills can be designed as easily and accu¬rately as can rod mills or ball mills by those skilled in the art. A pebble mill is a rotating cylinder in which the grinding media has been carefully sized for the job in hand. If the mill is doing coarse grinding, the media will be correspondingly large and the mill might be called a primary (or intermediate) pebble mill or a lump mill. If it is to do fine grinding, the media selected is proportionately smaller and the mill would be called a secondary or tertiary pebble mill. The media itself is normally rounded pebbles made from screened ore from the primary-crusher discharge. The charge could be rounded pebbles of the correct size removed from a primary autogenous mill, or the pebbles could be carefully sized gravel, sized beach pebbles, or sized flint pebbles. Usually the specific gravity of a pebble is from 35 to 55% of that of steel balls. It commonly varies from 2.66 to 4.2, depending on the specific gravity of the ore. Primary pebble mills, or lump mills, would be charged with pieces of rock up to 10 in. maximum and 5 in. minimum and would grind crusher discharge with a maximum size of 1/4 in. on hard ores and 3/8 in. on softer ores. Secondary pebble mills could be charged with pieces of rock screened on 4 x 4-in. square mesh and retained on 1 1/2 x 1 1/2 in. These mills would grind material with a top size of 8 to 10 mesh. Tertiary pebble mills could be charged with screened rock that would pass 3 x 3 in. and be retained on 1 x 1 in. and grind 35 to 48 mesh sands. Principles of Operation Media Size To operate a pebble mill efficiently it is imperative that great care be taken in screening the rock feed that is fed into the mill to round up into a range of pebble sizes that are suitable for grinding of the sands that are also being fed into the mill, having regard to the top size and the average size of such sands. Since most mill operators know from experience the correct size of steel balls to be used in a mill to handle different sizes of sand feed, it is convenient to relate the pebble size to a ball size. If the correct ball size is not known, it is relatively simple to conduct batch laboratory tests in 12- to 18-in. laboratory mills to determine the optimum size of steel ball. Also, Bond and others have published formulas for calculating the optimum ball size. When the correct size of the individual steel ball is known, then a pebble of the same weight will perform the same grinding if used in the proper size of mill and under the proper conditions, which will be defined later. This media size, as defined by the average weight of the individual pieces, is most important. The following tests will serve to clarify this point. Laboratory Tests Using Steel Balls or Pebbles. Several labora¬tory grinds were made to compare a given size and weight of steel ball with a pebble of the same weight but larger size, and of the same size but lighter weight. The following loads were used in the 12-in. laboratory mill: All 1 1/4-in. steel balls weighing 122 ± 10 g. All 1 3/4-in. pebbles weighing 123 ± 5 g. All 1 1/4-in. pebbles weighing 45 ± 3 g. To equalize capacity, the test with the steel balls was run only 34% as long as the tests with pebbles. In each case, 2,500 g of primary sands were ground at the optimum gravity for the media being tested at a speed 78 1/2 % of critical speed, and for 170, 340, and 680 revolu¬tions for the steel balls, and 500, 1,000, and 2,000 revolutions for the pebbles. The first test is summarized in Table 74 by showing the 80% passing size in microns for the feed and for each of the grinds. Two other tests are summarized in Table 75 showing the screen analyses

Jan 1, 1985

By Paul Levin

A coal preparation plant built with conventional materials only might be able to do an efficient job of preparing coal, but its maintenance costs would be high and emergency shutdowns frequent. To remedy this situation special materials are being used, either in original plant construction or for replacement of conventional materials. The special materials vary from high-strength and abrasion-resisting steels and stainless steel alloys to ceramics. They include hard surfacing welding rods, rubber refractories and some of the newer plastics, the merits of which are cited by the author. A coal preparation plant, limited strictly to the use of conventional materials-for example, mild steel, cast iron and ordinary rubber-could, no doubt, do an efficient job of preparing coal, but the high cost of maintenance and increasingly frequent emergency outages would soon force the operator to seek relief by introducing special materials such as alloyed steels, oil-resistant rubbers and hard-surfacing welding rods.

Jan 6, 1964

By L. G. Austin, R. R. Klimpel

This article demonstrates that the Gilvarry and Klimpel-Austin equations for the random fracture of solids are incorrect by deriving intuitively correct expressions for simple cases and showing that the foregoing equations do not reduce to right answers. It is the purpose of this article to point out serious errors in some existing treatments of the random fracture of solids. Gilvarry ' gives the equation where B(y,x) is the cumulative fraction by weight of particles which fall below size y when particles of size x are broken. The constants i, j, k contain shape factors and densities of flaws leading to propagating fracture surfaces. The authors believe this equation to be incorrect. Klimpel and usttin' give where r~ is the number of fracture planes originating from edge flaws (per L where L is the edge length of the original particle), rs is the number of fracture planes originating from flaws on the particle surface (per S where S is the surface of the original particle) and rv is the number of fracture planes originating from flaws within the particle volume. This equation is also incorrect. The failures of these equations will be demonstrated by deriving intuitively correct expressions for simple cases and showing that the Eqs. 1 and 2 do not reduce to the correct answer. In this process, the flaws in statistical reasoning inherent in the derivations of Eqs. 1 and 2 become apparent. THE KLIMPEL-AUSTIN EQUATION Eq. 2 was derived by considering a set number of fracture planes occurring spatially at random within a given particle. This case will be treated here in its simplest form: a line with 1, 2, 3, etc., fractures occurring at random. This is illustrated in Fig. 1, with the original length of the line as Vo. The breakage of a long, thin, brittle fiber is a corresponding physical case, with the volume of a fragment proportional to its length. Assuming independence of the occurrence of the fractures, the probability of any one fracture occurring in length dV is dV/V0. The probability of the first fracture occurring at a length V to V + dV is dV/Vo. For the case of only one fracture per particle, formation of a number-size distribution of the left-

Jan 1, 1969