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By E. Hoek

INTRODUCTION Rock slope stability research has been in progress for the past four years at the Royal School of Mines in London under the sponsorship of a consortium of 23 companies* with interests in open pit mining. This paper reviews the principal aims and achievements of this research project. In order to assist the reader in following these details, the basic philosophy underlying the formulation and direction of this research project is discussed. DISTRIBUTION OF RESPONSIBILITY In open pit mining, the economic necessity of keeping waste rock removal to a minimum generally means that the mine slopes have to be excavated to the steepest possible slope angle. On the other hand, excessive steepening of these slopes can induce failures, which may negate the economic benefits that have been aimed at and which may also result in loss of life and damage to equipment. Consequently, where slope failures are likely to prove to be a problem, an evaluation of the stability of the slopes to be created should be included as part of the overall pit design. How is the stability of a rock slope evaluated? When this question was examined, during discussions on the research policy to be followed at the Royal School of Mines, it was clear that relatively few satisfactory techniques were available in a form that would be comprehensible and therefore useful to the practical mining engineer. It was recognised that the research project must be directed towards two distinct aims: a) The evaluation of existing techniques for rock slope stability analysis and the provision of new techniques where these existing methods were found to be inadequate and b) The presentation of the results of this evaluation and research in a form that would be useful to engineers without specialist training in rock mechanics. It was soon realized that a university based research team, however large and efficient, could not achieve these aims without the co-operation and assistance of mining engineers,

Jan 1, 1972

By K. Unrug, G. Herget, A. Smith

SUMMARY Statistics on roof falls indicate that the cost of just removing the unwanted waste from roof falls in US coal mines amounts to about $20 M per year. Almost 40 percent of fatal accidents occur under permanently supported roofs, indicating that the assessment of roof stability is still a very difficult task. In an effort to obtain a better understanding of roof fall occurrences, rock strength and ground stresses were determined in the roof of one mine each in Western Kentucky, northern West Virginia, and Eastern Kentucky. Triaxial ground stress determinations clearly show that horizontal stresses were higher than vertical stresses, and that maximum stresses in the horizontal plane were concentrated between the NE-SW to E-W direction, with the exception of the Eastern Kentucky site which was above the drainage. Magnitudes of stress components may vary considerably in one drlll hole. Strength tests of roof strata materials were done on core samples. Mapping of roof falls showed that the geometry of an opening or maximum span were not the overruling factor because in the same general area, a roof fall was observed in a room (entry) which connected two stable four-way intersections. It should be noted that, in very wet areas, the roof can break up to the bed where water is carried, and a very low ratio between extent of roof fall to height of roof, fall is observed. Geometry is, however, a contributing factor because nearly 70 percent of roof falls are intersection falls. The frequency of fractures parallel to bedding in failed roof strata is much higher than that observed in the original strata, indicating a significant amount of working in the roof before failure.

Jan 1, 1984

By Joseph Pogue

IN 1920, 531 million barrels of crude petroleum were consumed in the United States. As imposing as this figure is, the fact that the domestic consumption of crude petroleum has increased at an average rate of 10 per cent. a year for the past decade is more striking. Will this rate of increase in demand continue? If so, the year 1930 will call for 1260 million barrels of petroleum-a staggering volume. On the other hand, may we expect the demand for petroleum to grow as rapidly as it did when the automotive industry was having its most phenomenal expansion? If not, to what extent will the growth of oil requirements decrease? When and to what degree will the petroleum industry become affected by the economic law of diminishing returns? Obviously, this matter requires careful analysis, especially as both national and industrial planning must be predicated upon present estimates of the requirements of the future. The purpose of this paper, accordingly, is to project, as closely as present limitations of knowledge permit, the course of the demand for petroleum in the United States over the next ten years. At first, the problem of estimating the future of a demand as complex as that for petroleum might appear insoluble. Fortunately, however, there are several scientific methods of approaching the problem, centering around a study of rates of industrial growth, which lend considerable hope that the requirements of the immediate future in this field may be approximated with sufficient closeness to have practical value as a basis of action.

Jan 3, 1922

By G. S. Hume

Activity in geological exploration and drilling continued in Canada in 1945 at about the same rate as in the previous year, but with disappointing results as far as new production is .concerned. Both in the foothills and on the Plains of Alberta, however, there are wildcat wells that have either given encouraging shows or some production, which are very important in relation to future developments. The normal decline of Turner Valley, the largest producing field in Canada, has continued, and this decrease has not been offset by new discoveries. In addition, the closing of the Canol pipe line on March 31, 1945, isolated the Norman Wells field in the Mackenzie River valley, and the outlet at present. is confined to supplying the relatively small local requirements. This

Jan 1, 1946

By L. G. Huntley

Introduction IN View of the recent advance made in the knowledge of the nature and conditions accompanying the occurrence of oil and gas, and of the recent activity in drilling in Wyoming, Montana, and western Canada, a discussion of the probabilities of obtaining production in such a reservoir as the Dakota sand in general, and in particular districts, is thought by the author to be timely and likely to result in more intelligent operating in certain parts of the territory underlain by this sand. In Canada particularly it is thought that these general considerations have equal if not more significance in a consideration of the oil and gas possibilities of the formations than have the various local conditions.

Jan 6, 1915

By J. Szekely, Robert G. Lee

Calculations are presented for the prediction of the combined radiative-convective heat loss from molten steel held in a ladle, covered by initially molten slag. A mathematical formulation is given and numerical solutions are presented of the resultant partial differential equation. It is shown that a slag layer of about 2 to 3 in. thick would prevent any significant heat loss from the top metal surface for Periods of up to 1 hr. For thinner slag layers (or in the absence of the protective slag) appreciable heat losses would occur; plots given in the paper allow the quantitative evaluation of the fall in the metal temperature due to this heat loss. The ironmaking-steel processing operation involves several intermediate steps where the molten metal is held or transfered in ladles. The quantitative assessment of the heat losses occurring under these conditions is of considerable importance in process design considerations since the temperature of the metal may have to meet rigid specifications in any given part of the processing sequence. While the metal is held in a ladle, heat is lost by two mechanisms: i) by conduction into the ladle walls; ii) by radiation and convection from the top surface. Calculations relating to the conductive heat loss, are readily made and information may be found in the literature both on data pertaining to metallurgical situations and on the techniques that are available for performing additional computations.'-3 The evaluation of the combined convective-radiative heat loss is less straightforward, especially when there exists a protective slag layer covering the metal. In this latter case, as the top slag surface loses heat partial solidification may occur and the latent heat thus given up by the slag may represent an effective barrier to the heat loss from the metal. A semiquantitative assessment of the role played by the slag in preventing heat loss from the metal has been made in a previous paper,4 where it was shown that a slag layer 6 in. thick would act as a near-perfect insulator for periods of up to 2 hr. However, this first paper reported on an essentially preliminary investigation that considered only one slag layer thickness; furthermore, the boundary conditions used for the calculations were somewhat restrictive since no allowance was made for changes in the metal temperature. The purpose of this second paper is to extend the scope of the preliminary investigation previously reported by: i) considering several slag layer thicknesses; ii) allowing for variations in the metal temperature; and finally iii) by performing calculations on the net loss from the metal rather than from the slag surface. FORMULATION Consider a slag phase extending from y = 0 to y = L1, covering a metal phase that occupies the region extending from y = Ll to y = L, as illustrated in Fig. 1. Denote the slag and metal temperatures by TS and Tm and assume that initially both slag and metal are molten, having a uniform temperature Ti. At time = zero the surface represented by the y = 0 plane (top slag surface) is brought into contact with cold air, the temperature of which is given as T Thus for time > zero, heat will be transfered from the slag to the air by natural convection and thermal radiation; as a result of this heat loss the slag temperature will fall and after some time a solid phase is formed and a solidification boundary (more realistically described as a zone) will move progressively from y = 0 toward y = L1. Once the region of temperature gradients, moving ahead of the solidification zone, reach the slag-metal interface (y = L1) there will be a net transfer of heat from the metal through the slag to the cold air, across the y = 0 plane. In the formulation of moving boundary problems, involving phase changes that require computer solution, it is convenient to represent both phases by a single equation, making allowance for the latent heat of solidification by assigning an appropriate temperature dependence to the specific heat content. Thus the energy equation for the whole of the slag may be written as follows:

Jan 1, 1969

By Eric J. Bradshaw

For several hundred years the petroleum industry has flourished in Burma and at the close of the eighteenth century there were over five hundred producing wells in the Yenangyaung field. These were laboriously dug by hand and were exceedingly primitive, yet even today a small part of India's total production is obtained from hand-dug wells. The Indian Empire, the cradle of the oil industry, today produces but an unimpressive fraction of the world's supply of petroleum, not because the size of her contribution has diminished, but because it has remained more or less stationary while other countries have far outstripped her during the prodigious increase in the world's production of petroleum in recent years. Though for the past 10 years the total production in India has been remarkably constant, it has become increasingly difficult to maintain this output and at any rate from the older fields a slow decline may be anticipated unless new productive horizons are discovered. Production figures for the 10 years 192&1929 (the last year for which figures are available) are given by fields in Table 1. Crudes of Burma and Assam The bulk of India's production comes from the Yenangyaung and Singu fields, from which the crudes are very similar, the only important difference being that the oil from the Singu-Yenangyat structure contains a higher percentage of lighter fractions. The Burma crudes resemble that of the Panhandle of Texas and have a high content of solid paraffin, though strictly speaking the oil is of mixed base with a low content of asphaltum. With the exception of the negligible production from Sabe, the Burma crudes do not require dehydration; the sulfur content is very low and is innocuous. A small amount of naphthenic acids occurs in the kerosene and intermediate oil fractions while the lubricating fraction is practically free from acid. The ash content is low and the average A.P.I. gravity of mixtures of Yenangyaung and Singu oil is 36.4. Burma crudes require only light refinery treatment and practically dl the fractions are merchantable. Part of the gasoline supply is stripped

Jan 1, 1931

Jan 1, 1954

By M. M. Austin

PURE metallic tantalum, from a practical standpoint, is one of the newer developments in the metal field. Although it was used as filament in incandescent lamps in 1906, only within the last five years has the metal been available in sufficient quantity and suitable form for more general application. In addition to corrosion-resisting properties and high melting point, the metal has an ability to withstand unusual amounts of cold working. It affords some striking demonstrations of block movement during plastic flow.

Jan 1, 1930

By J. M. Gaines

THE use of oxygen in electric furnaces is relatively old, and the practice has been employed by several steelmakers prior to the recent impetus given generally to the use of oxygen in steelmaking. This application has been described recently in several publications,1 and a number of patents relating to the application of oxygen in electric furnaces have been issued.2 An effort is made in this paper to assemble recent information relating to the use of oxygen in electric furnaces and to present this material from a practical viewpoint, to an extent consistent with the withholding of certain operating data which manufacturers consider to be confidential. The use of oxygen has been extended during the past months in a number of additional steel companies by incorporating oxygen practice into regular production and by much increased experimentation. Available records show that oxygen is used more or less regularly at present in 18 shops, of which six utilize the oxygen for production and the others for experimen¬tation. The number of furnaces per shop using oxygen varies from one to six. Many types of electric-furnace steel have been prepared with the assistance of pure oxygen, including low-carbon and medium-carbon killed steels, low-carbon rimming steel and low-carbon and medium-carbon stainless and alloy steels. Oxygen has been used in furnaces of all sizes up to 90 tons capacity for accelerating charge meltdown and for reduction of carbon.

Jan 1, 1947

By W. K. Lewis

During the last decade the petroleum refinery engineer has made great progress in achieving a better understanding of the physical behavior of hydrocarbon mixtures, with particular reference to their pressure-temperature-volume relationships, the mechanism of the evaporation of liquids, the condensation of vapors, including the changes in composition, and the heat effects accompanying them. With the new insight into the mechanism of movement of oil and gas through the formations in which they occur, achieved by the production engineer, it is clear that the latter will need to utilize in the solution of his own problems much of the information outlined above. It is the purpose of this paper to outline the portions of that information that seem most certain to prove of importance in production work. Properties of Pure Hydrocarbons While it is true that petroleum always consists of highly complex mixtures of hydrocarbons, none the less understanding of the behavior of the mixture must be based upon a knowledge of the properties of the pure components. However, in view of the tremendous number of hydrocarbons existing in petroleum, the determination and formulation of the properties of all of them would seem a discouraging task. The difficulty of the situation is increased by the undoubted facts that the overwhelming majority of chemical individuals in petroleum have never been isolated as pure compounds, none of their physical properties have been determined and even their chemical constitution is unknown. The situation would be hopeless were it not for the fact that certain extraordinary correlations of important properties of various hydrocarbons have been discovered which make it possible to predict those properties for a given chemical individual on the basis of a very limited characterization of it. Thus one can predict the vapor-pressure curve of an unknown hydrocarbon over a considerable range from the knowledge of a

Jan 1, 1934

Jan 1, 1915

By L. A. Bromley, R. L. McKisson

A high temperature calorimeter designed for use up to 1500°K is described and the theory of its operation presented. This calorimeter was used to measure the heats of formation of Na-Sn alloys ranging in composition from tin to Na2Sn. The values tend to support those reported by Kubaschewski and Seith. ONE method of obtaining the heat of formation of an alloy is to measure the heat of mixing of the elements at high temperature. The principal advantage of this method is that the desired quantity is measured directly, while in conventional room temperature methods the differences of the heats of solution of the elements and the alloy in a suitable solvent are measured. A method of improving the accuracy of the high temperature measurements, when the precision of the measurement is lower than that of the heat capacity values for the elements, is to add one component at room temperature to the other at the high temperature, so that part of the heat of reaction is dissipated in heating the cold component to the high temperature. Thus, only a fraction of the heat of reaction is measured, and a result of higher precision is obtained. The limitations of the high temperature technique are that volatile systems cannot be studied, and that many alloys melt at temperatures higher than those at which the calorimetric apparatus operates readily. Nevertheless, a calorimeter operating at 1500°K would be useful in investigating many of the lower melting alloy systems and the low melting mixed oxide systems. A unit designed for these applications was built and is described here. The Na-Sn system was chosen for investigation because the temperature involved, 880°K, would adequately test the operation of the calorimeter. Further, the data reported in the literature for the various alloys of sodium and tin differ markedly, and it was hoped that this investigation would help to fix the values of the heats of formation in this system. Design of Apparatus A detailed discussion of the considerations involved in the calorimeter design is given by Mc-Kisson and Bromley,' and a brief summary follows. Fig. 1 shows a sectional view of the calorimeter. The inner graphite chamber is maintained at constant temperature by means of the circulating molten tin bath in which it is submerged. The tin is contained in a graphite vat. This unit comprises a thermostat whose heat capacity is about 7000 cal per "C. The main heating element consists of a machined graphite spiral with a room temperature resistance of about 1/2 ohm. These parts are separated from the powdered carbon external insulation by the cage, a cylindrical graphite chamber. The electrical insulators and separators, the auxiliary heater spool, and the loading tube liner are made of sintered alumina. The tin vat stirrers, the sample stir-rer, the melt thermocouple well, and the power leads are made of molybdenum. The auxiliary heater is wound with molybdenum wire and serves to compensate for the heat loss up the loading tube. All of the individual components in the high temperature region of the calorimeter will withstand at least 2000°K, and the various contacting materials should easily withstand 1500°K. The external container for the insulating carbon powder is a copper shell upon which copper tubes are soldered to serve as cooling coils.

Jan 1, 1953

By S. Harries Daddow

THE INSUFFICIENCY OF PILLARS OF COAL FOR THE PURPOSES DESIGNED-THE FRUITFUL CAUSE OF DANGER, EXPENSE, AND WASTE-THE PROOF OF INSECURITY-SUBSTITUTE FOR PILLARS OF COAL-PILLARS AND PANELS COMPARED. PILLARS of coal, which are designed and left in our mines as the means of supporting the overlying strata of our coal-beds, and securing protection to the miner, are not only insufficient for these purposes, but the most objectionable means of providing the desired security to life and property. Though such pillars are left at a great sacrifice to the owners of collieries and mineral lands, loss to the resources of the commonwealth, and ultimate privation to the public, they defeat the very ends for which they are designed, and not only do not secure life and property, but are as fatal to the one as ruinous to the other. Propositions.-It is eminently desirable that the resources of the commonwealth-particularly our mineral wealth in anthracite coal, which is limited-should be carefully utilized and made available, not only to ourselves but our posterity. Yet, speaking as an anthracite miner, we are wasting our resources of coal with a recklessness which will bring ruin in the end, unless checked, not only to the iron manufacturing interests of the East, whose chief protection, in competition with the iron-masters of the interior, lies in a cheap and abundant supply of anthracite furnace fuel, but to the best interests of the State. It is, consequently, not only desirable, but necessary, that we should realize every ton of coal from each colliery, and every acre of coal area, in order that our resources may not be wasted at present, to breed want in the future, and to realize the greatest present benefit to the mine, the miner, and the public. It is not possible, however, to secure these ends, if we continue to leave, as we do at present, from one-third to one-half our resources in anthracite as pillars in our mines. But our sad bills of mortality, our abandoned collieries, and our yawning mountain-sides, present ample evidence that even this enormous waste of coal, though left for the purpose of protecting life and property, is as totally inade-

Jan 1, 1873

By I. L. Barker

ALTHOUGH valuable information has been pub-lished on the important problems of slag losses with which every copper metallurgist has to contend, a great deal of money is still being wasted in copper smelters all over the world, through metal being irretrievably lost in reverberatory slags. When smelting a relatively low-grade pyritic concentrate together with a proportion of direct-smelting oxi- dized ore, as is done in Oroya, slag volumes are of necessity high, and even a relatively clean slag, say of 0.5 pct Cu, means a loss of almost 4 pct of all the copper charged, or over $1,000,000 annually at present output and prices. While it is known that such losses can often be reduced by allowing the slag time to settle, with or without addition of a reducing agent such as coal or pyrite, the facilities for such treatment are not always available in a plant of old design working to capacity under severe space limitations. Nor is it easy under such conditions to run large scale tests which may endanger the smooth flow of production for considerable periods without yielding

Jan 1, 1958

By J. L. Bray

Lead has often been suggested as a protective coating for iron and steel. Such a protective coating should possess: (1) good adhesion, (2) durability, (3) ease of application, (4) freedom from pinholes, (5) good appearance and (6) low cost, but, unfortunately, lead coatings so far produced do not have all of these characteristics. Because of the necessity of carrying out the coating process cheaply, and because lead solutions have poor plating characteristics, most of the efforts have been directed toward the hot-dipping process rather than electroplating. The hot-dipping processes using lead have not been successful chiefly because of the lack of adherence between iron and lead. In any coating process involving iron a bond can be obtained only by the formation of an intermetallic compound, the formation of a solid solution, or mechanical means. Lead forms with iron two immiscible liquid solutions, and in the solid state no intermetallic compounds or solutions. It is necessary, therefore, to employ some other element or elements as a binding agent. Tin may be used as in terneplate, or copper in the form of a thin film of electrolytically deposited metal to which the lead will adhere. Because of its physical and chemical properties, lead as a coakkg medium would undoubtedly be limited in its use to sheet and wire and then only when the article is not subject to abrasion or wear. A very large tonnage of these products is being used under such conditions and a successful lead-coating process should be a valuable contribution to the science. Two other difficulties stand in the way of successful lead coating—that of poor appearance of the weathered surface and the tendency of the lead to form pinholes during solidification. Since lead is commonly accepted as cathodic to iron, these exposed areas are ones of accelerated corrosion. Use of Zinc.—The method under consideration involves zinc as a binding agent on both the steel sheet and in the molten bath. This

Jan 1, 1937

By Luiz C. Correa da Silva, Robert F. Mehl

An experimental study of the movement of markers in the systems Cu/a-brass, Cu/Sna-solid solution, Cu/Ala-solid solution, Cu/Ni, Cu/Au, Ag/Au, employing many types of markers and a variety of temperatures. Marker movement is confirmed and undoubtedly associated with the manner in which atoms move during diffusion. EVERAL years ago Smigelskas and Kirkendall' •S reported measurements on the interdiffusion of copper and a-brass and on the movement of inert markers placed at the original join. These markers were observed to move toward the a-brass side of the join, and from this it was inferred that zinc diffuses in a-brass more rapidly than copper. Similar results were reported a little earlier for the diffusion of solvents into high polymer solids.' This has attracted much attention, particularly from those interested in the mechanism and the theory of diffusion: Seitz3 has employed it in supporting the vacancy theory of diffusion; from the data Darken4 has calculated separate diffusion coefficients for copper and zinc, developing a "phenomenological" theory of diffusion; and Bardeen5 has employed it in constructing a general theory, including therein the work of Seitz and Darken, as has Le Claire. These matters have recently been reconsidered in a sympo~ium.7 Some reason has existed for questioning the work of Smigelskas and Kirkendall.' Their technique consisted in electroplating copper on a-brass, upon the surface of which Mo-wires had been secured, and then diffusing, measuring the extent of diffusion along the normal to the join, and measuring the marker displacement in the same direction by a comparator determination of the distance between Mo-wires on opposite sides of the electroplated brass sample. It has been suspected that the copper plate might have been porous, and that the original interface might have been an imperfect join, both contributing to the transfer of the volatile zinc by vapor transfer;' it has also been questioned whether the marker movement might not in a measure be a property of the marker itself; etc. These legitimate questions require experimental answers; the present paper offers such answers. Moreover, Smigelskas and Kirkendall studied the effect only in the Cu-Zn system and at one temperature; the attention which the work of Smigelskas and Kirkendall has commanded recommends similar

Jan 1, 1952

By James H. Gardner

It is a striking fact in the domestic oil statistics of 1926 that with an increase in production of 13,000,000 bbl., there was nevertheless a lowering of both crude and gasoline stocks. It was the first reduction in the last eight years. In 1918, the last year of the war, stocks of crude and refined products were lowered 16,000,000 bbl., but in the following seven years stocks were increased 350,000,000 bbl., due largely to the phenomenal crop of major pools discovered in 1923. The big pools of that year coming as they did through some curious coincidence unprecedented in the oil industry, not only piled up a sudden increase of stocks at a time of large imports but they continued to add their quota to an increase of storage until 1926. With an increase in crude production, according to the Oil and Gas Journal, from 760,000,000 bbl. in 1925 to 773,000,000 bbl. in 1926, and an increase in cracking facilities of about 30 per cent., there was a draft on storage of 22,300,000 bbl. of crude and 1,000,000 bbl. of refined. Crude and refined changed from a stock surplus of 29,130,000 bbl. in 1925, to a deficit of 23,300,000 bbl. in 1926, or a differential total of 52,430,000 bbl. With a stock reserve of 541,700,000 bbl. of crude and refined oil in 1925, the amount drawn from storage was not large in percentage but it marked an important contrast with previous years. It meant a year of stability in prices and a sound condition in the industry. The indicated domestic demand increased from 695,120,000 in 1925 to 743,360,000 in 1926, (7 per cent.), 1 per cent. of which was due to California fires. Most of the gain in consumption was due to the increased demand for gasoline. There was little comparative change in the combined imports of crude and refined oil. There was an increase in exports of 17,200,000 bbl. (1.5 per cent). A petroleum balance sheet for 1926 and a comparativl sheet for the last two years, production in the United States by major districts and pools, and a list of imports are given in Tables 1 to 5, inclusive.

Jan 1, 1927

By W. J. Houk, F. C. Hull

To clarify interpretations of grain structures and to assist in calculations of spatial grain size distributions, plane distribution curves have been determined for random sections through four regular polyhedrons approximating the shapes of metal grains. The characteristics of the distribution curve for the average metal grain are predicted. IT was realized early in the history of metallurgy that metals are polycrystalline aggregates and that the size and shape of crystals affects the properties of the material. Reaumur1 in 1722 employed the microscope to examine the fractured surfaces of steel and of white and gray cast iron and suggested a polyhedral arrangement of the crystals. The first extensive investigation of the form of crystal grains was carried out by Desch.2 He examined the disintegrated grains from a ß brass sample and noted that the number of faces per grain ranged from eleven to twenty and that the number of edges per face varied from three to eight and the maximum occurred at five. While it has been found practical to examine isolated grains only in exceptional cases, it is always possible to make a plane section through the metal and examine the shape of the grain sections on the plane of polish. Desch2 tried to determine the relation between the form of a polyhedron and that of its plane sections for comparison with distribution curves of numbers of sides per grain section of actual metal samples. The polyhedrons investigated were the rhombic and pentagonal dodecahedrons and the orthic tetrakaidecahedron. However, the frequency distributions of the number of sides of plane intersections were not sufficiently characteristic to decide which polyhedron most closely approximated the average grain in a metal. Determination of Statistical Shape of Grain in Space Scheil3 was interested in the problem of calculating the distribution of grain sizes in space from the easily measured distribution of grain section sizes on the plane of polish. Assuming that the grains were spheres and using the plane distribution curve for a sphere shown in Fig. 1, he employed a successive subtraction method to calculate the spatial distribution. In order to evaluate the accuracy of these calculations, Scheil and Wurst4 determined the actual distribution of grain sizes in space in their sample of ingot iron by polishing off successive layers and following every individual grain in a series of micrographs. From curves of mean radius of intersection of a given grain vs thickness of metal removed in polishing, Scheil and Wurst attempted to derive the statistical shape of a grain in space. Their calculated plane distribution curve for this shape is compared with the distribution curve for a sphere in Fig. 1. A table of values based on this curve was prepared for calculating spatial distributions of grains. The calculated and measured spatial distributions of their sample then agreed much better than when a spherical shape had been assumed. In the present paper, an attempt has been made to learn something about the average metal grain by studying in detail the effect of the shape of regular polyhedrons on the plane distribution of areas and shapes of areas produced by random sections through them. From the data presented below, it can be concluded that the plane distribution curve for the average metal grain differs in three fundamental respects from the curve derived by Scheil and Wurst. Polyhedrons Selected for Study The polyhedrons selected for the statistical study are illustrated in Fig. 2 and consisted of a cube, a figure formed by cutting off the corners of a cube at the midpoints of the original edges, a tetrakaidecahedron, and a pentagonal dodecahedron. The length of edge on any one figure is a constant. For the above models the edge lengths were 3.50, 4.00, 2.00, and 2.08 in., respectively. A cube was selected for one of the polyhedrons because of its simple geometry, because it is a form that by repetition can completely fill space, and because it represents a convenient degree of departure from compactness beyond which the shape of

Jan 1, 1954

By D. W. Fuerstenau, G. D. Gumtz

Use of the discretized batch-grinding model for the simulation of locked-cycle grinding tests from batch-grinding data is illustrated. The simulated results were compared with actual locked-cycle experimental data for the dry grinding of dolomite. To illustrate the utility of this simulation method, a number of relationships between operating and performance parameters were generated, including relations between batch grinding and the Bond test, the production rate and the circulating load, and the production rate and the product size. A large amount of testing is done each year in the mineral industry for use with grinding unit cperations, and much of the experimental test data is obtained by the tedious locked-cycle testing procedure. In addition to being experimentally complex and requiring large amounts of sample, the very nature of the locked-cycle experiment yields results that cannot readily be interpreted. The attempts that have been made to model comminution systems during the last few years may provide a better and simpler way to obtain and analyze grinding test data; these models involve elements of both fitting to "model equations" and deterministic representations.1-1 The traditional engineering design techniques for comminution systems have relied mainly upon large amounts of industrial operating data that have been correlated with locked-cycle grinding data.',' Bond's empirical mill-design procedure involving locked cycle testing remains the most generally available method to this day. The purpose of the present paper is to show how much more useful data can be obtained from a simple batch-grinding experiment that provides information which subsequently can be utilized with population balance models of the grinding process to simulate locked-cycle behavior. These simulation results can, of course, be used in Bond's general design scheme. However, the combination of batch-grinding tests and the population balance model allows many more conditions to be considered than do single laboratory tests under specific locked-cycle conditions. The use of these simulation techniques for prediction of locked-cycle behavior represents one of the first practical applications for the simulation method in comminution.

Jan 1, 1971