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By R. G. Knickerbocker

A most important research and development item on ferroalloys in the calendar year of 1949 was the increase of interest in the recovery of secondary manganese. Owing to the importance of manganese to the nation's welfare, it is Ferroalloys most necessary that all possible avenues of research and development on the recovery of this vital metal be investigated. The principal objective of this new development is to recover manganese from steel furnace slags. Steel furnace slags contain a total of approximately 772,000 tons of metallic manganese which is compared to the 680,000 tons of metallic manganese as ferromanganese that is estimated to be used by the steel industry, annually, at this time.

Jan 6, 1950

By R. Malmstrom, H. Heden, K. Likin

Sublevel caving techniques at Luossavaara-Kiirunavaara AB (LKAB) in Sweden have undergone significant modification over the years as management strives to maintain mine viability amidst rising costs and erratic iron ore prices. LKAB, which is 96% state-owned, is Sweden's principal iron ore producer and operates three iron mines north of the Arctic Circle. By far, the largest of LKAB operations is the Kiirunavaara (Kiruna) underground iron mine which extracts an estimated 30 million t/y of ore, Other iron mines include the Malmberget underground nine, rated at 12 million t/y of ore, and the Svappavaara open-pit mine, rated at about 4.5 million t/y. Mined ores from Kiirunavaara and Svappavaara are shipped by rail to the northwestern harbor of Narvik, while Malmberget ores are sent to Lulea, located to the southeast. LKAB iron ores are marketed by Malmexport AB, which is owned jointly by LKAB and Granges, Sweden's base metal producer.

Jan 10, 1979

By H. Scott

Since Bohler discovered, in 1903, on cooling certain alloy steels, the phenomenon of a new and lower temperature transformation than the usual Ar 3-2-1 obtained by increasing the maximum temperature to which the material was heated, much has been published1 connecting this phenomenon with a large number of dissimilar steels of high alloy content. From the fact that the transformation divides itself, taking place at two widely separated temperatures, it has been called a "split transformation." The significant facts established by recent investigators2 are: that when the transformation occurs at the higher temperature Ar1, troostite or a decomposition product is formed, and that when the transformation occurs at the lower temperature Ar", the resulting structure is martensite. The terminology Ar' and Ar" adopted here is that of Portevin. Previous Investigations Reviewing the work on this subject published in a recent issue of Revue de Metallurgie and referring in particular to his statement that martensite is a solution of carbide in alpha iron, Le Chatelier says :4 "How then can a theory already 20 years old demand new investigations? The reason for it is that we have not succeeded in proving directly the real presence of the transformation of iron during the very short duration of the quenching. The fall of temperature takes place at the rate of several hundred degrees per second and the observation of

Jan 1, 1920

By C. W. Brown

In the author's experience and contact with engineering students the old form of recitations had grown into the lecture system in which the student was a passive receiver of digested material. Later, the tutorial system was developed because it was felt that the lecture system was breaking down. The student was too passive and was simply trying to absorb what was given him. The seminary method was then introduced and for the particular field the author believes that there is no better method, but that for 20 years he has been trying to change the attitude of the student in certain courses from a passive, almost noncommittal, to an active participation, to change him from a receiver to a doer. The student cannot look over the whole field. That must be presented by the instructor in charge. A topic such as structure or glaciation is taken up and from that standpoint are argued all the geologic problems that might confront the engineer. Problems relating to dams and foundations, and structures, tunnels and excavations, are particularly adaptable to the method. Usually, however, the problem comes to the engineer in more complicated form. By virtue of the character of the material the same topic cannot be assigned to the entire class. Different phases of the topic must be assigned. The greatest difficulty in after life comes in that the student cannot analyze the problem and has not the ability to see that there is a problem. He has had little or no training in the gathering of material and very little training in the arrangement of a report. Consequently, selecting different problems, putting them before small groups, and then starting the student on the way to make the knowledge of his particular topic an integral part of his own mentality, is something that will fix that part of the work firmly in his mind. Professor Brown has insisted on an introductory step in a great many classes, in that without the student knowning very much more than the general outline of the topic or problem, he is made in inductive fashion to take up the entire problem, look it over, and prepare an outline as far as he can; in other words, to expose the problem to his own mind. This preliminary outline is discussed with the student and if the arrangement or logic, with regard to the end in view, are faulty, he is shown where

Jan 1, 1929

By W. B. Mather

THE object of this paper is to record and interpret data collected during the examination of over 250 barite deposits in the Central Mineral District of Missouri. [ ] In the course of this study, the origin of the deposits, which the author believes to be hydrothermal, has been given particular attention. Economic barite deposits occur in two main areas in Missouri: (I) in the Washington County District of Southeast Missouri, from which over go pct of the state's production is derived; and (2) in the Central Mineral District, which includes portions of 15 counties in Central Missouri (Fig I). Barite in the smaller Washington County District is mined from widespread low grade, relatively shallow residual deposits, whereas in the Central District, it is mined

Jan 1, 1947

By Albert R. Ledoux

With the improvements in design and efficiency of machinery the element of danger in its use is becoming less, but it is a question whether the strain involved in operating modern plants is not increasing somewhat the danger of accident due to human fallibility. I propose to describe a somewhat uncommon casualty resulting from a not infrequent incident in the use of air-compressors. It is not necessary to state the location of the mine in which the accident occurred nor the makers of the compreseor, and the object of this brief paper is more to draw out suggestions from members more familiar than am I with the practical handling of mining machinery, than to point a moral. The compressor in question was a three-drill machine of standard make. At the time of the accident it was furnishing air to a single drill working in an upraise from a well-ventilated tunnel, and giving ventilation to a winze below the tnnnel where two men were hand-drilling. The compressor also furnished power to a small hoist in the winze, but the hoist was only operated occasionally, and never while the drills were working. The drills were located about 1200 ft. from the compressor. The engineer testified that he never had been short of air, and that there had been no complaillts that the

Jan 1, 1904

By Immo H. Redeker

Abstract-North Carolina is the leading state in the US in lithium mineral production. Spodumene is mined in open Pits and concentrated by flotation by the two companies, Lithium Corp. of America and Foote Mineral Co. North Carolina State University has a mineral research laboratory in Asheville, N. C., with trained personnel, batch and pilot plant facilities to assist in the state's mineral development. The NCSU Minerals Research Laboratory assisted both lithium-producing companies with spodumene concentration problems and has lately worked closely with Lithium Corp. of America to develop the best flowsheet for spodumene and byproduct recovery. The concentration of North Carolina spodumene and byproducts from pegmatites is presented and illustrated with figures.

Jan 4, 1979

By Immo H. Redeker

North Carolina is the leading state in the US in lithium mineral production. Spodumene is mined in open pits and concentrated by flotation by the two companies, Lithium Corp. of America and Foote Mineral Co. North Carolina State University has a mineral research laboratoy in Asheville, N. C., with trained personnel, batch and pilot plant facilities to assist in the state's mineral development. The NCSU Minerals Research Laboratory assisted both lithium-producing companies with spodumene concentration problems and has lately worked closely with Lithium Corp. of America to develop the best flowsheet for spodumene and byproduct recovery. The concentration of North Carolina spodumene and byproducts from pegmatites is presented and illustrated with figures.

Jan 1, 1980

By Richard D. Hagni

Although the ore microscopist routinely examines polished sections to determine the mineralogy and texture of ores, his importance to the solution of problems peripheral to geology is not always fully realized. The techniques which he uses can be applied with little modification to the solution of a wide variety of beneficiation problem. By extending his studies beyond those normally considered to be of interest to the geologist, he can include examinations of polished sections of selected mill products. This is a logical extension, because the minerals and textures in the polished sections of ores are the same as those in millproducts. The mill dressing engineer should be more aware of the types of beneficiation problem that can be solved by the ore microscopist and what the ore microscopist can do for him. A greater degree of cooperation between the ore microscopist and the mill dressing engineer can be of significant mutual benefit. Ore microscopy holds an advantage over chemical analysis, because the interrelations and combinations ofthe mineral constituents of an ore or mill product can be visually determined. This advantage provides solutions to many beneficiation problem. Locking is a type of beneficiation problem that is particularly amenable to ore microscopy. The percentage, type, and distribution of locked particles can be readily determined with the aid of an ore microscope and an estimate made of the extent of additional grinding required for liberation. The extent of intimately locked types, which no reasonable amount of grinding will liberate, can also be evaluated. Mineral coating conditions, free particles of a deleterious mineral, and free particles of a valuable mineral held in flocculated clusters of gangue are other features that can readily be observed. In some instances, visual examination may show that the problem is not one of locking. Photomicrographs illustrate the variety of beneficiation problems for which the ore microscope is applicable. These problems and their resolution demonstrate the importance of the instrument and show the value of close coordination between the mill dressing engineer and the ore microscopist.

Jan 1, 1979

By E. L. Davis

There have been many attempts to devise formulas for flowing efficiency and flow friction of oil-gas mixtures in oil-well flow tubes. Actually, however, flowing efficiency is rarely any real concern of the oil producer and flow-friction formulas contain so many unknown variables as to be of little, if any value. The production engineer is generally concerned with producing as much oil as possible with a minimum expense per barrel, and with the lowest possible net gas-oil ratio. These ends frequently are opposed to each other and the gas-oil ratio usually is sacrificed. In competitive operations, such as in town-lot fields, high current production is the sole interest. In conservative operation the greatest possible amount of oil obviously should be produced by natural flow unless the net formation gas-oil ratio can be improved by circulating gas. In practice this condition frequently exists. It would be a great advantage if the flowing condition of a well could be analyzed to determine the best possible producing status. Anticipating the death of a well so that gas-lift could be started immediately after the death, or preferably before, would save both production and expense. Frequently it happens that circulating gas fails to help a flowing well, or will not flow it after it has stopped flowing naturally. A knowledge of the laws governing flow would save considerable expense in testing such cases. A predetermination of probable pressures and amounts of circulating gas needed to flow wells and give best possible producing conditions would help in designing compressor installations. The optimum producing status of an oil well generally may be obtained by the conditions that subject the producing formations to the least possible back-pressure. This pressure is made up of the weight of the fluid column, frictional resistance to flow and the reaction from the acceleration of the fluid mass. A mathematical calculation of these components to arrive at a condition giving a minimum summation is impractical. Formulas would be complex and the results untrustworthy because it is impossible to assign proper values to the many variables involved.

Jan 1, 1931

By Charles E. Johnston

The haulage system at the International Minerals T & Chemical Corp. (IMC) potash mine near Carlsbad, N. M., reached a turning point in December 1956 with the introduction of rope suspended belt haulage. In fact, IMC pioneered the use of this type of belt in the potash industry. Since that time belt conveyance has been employed as an extension of the rail system but not as a replacement of the main rail haulage. IMC's potash mine is located in the Permian Basin, approximately 20 miles east of Carlsbad. From three levels, the 800-ft, 850-ft and 900-ft, over 60 million tons have been extracted. Langbeinite (K,SO,. 2MgS0,) is mined on the 850 level and sylvite (KCl) on the 900 level. The 800 level, with both langbeinite and sylvite mineralization, is idle. Mining heights vary from 54 in. to more than 10 ft. A room and pillar mining system is used.

Jan 3, 1963

By P. K. Chatterjee

The overall success of many strip coal mining operations depends primarily upon the efficient use of draglines to remove overburden. These machines require enormous capital investment and unless used efficiently the profitability of a venture is adversely affected. It is important that the dragline works continuously and it is imperative that the walking path and other facets of its operation be predetermined exactly so that the desired production rate is achieved with a minimum of non-productive time. Details of dragline operations which are of particular interest are walking path, prediction of best cut and positioning to maximize production, the angle of swing which produces the swiftest operation, optimum fill factor allowable for the type of material and conditions of ground, the maximum depth from which it can excavate and operating level with respect to the elevation of the high wall. The aims of the present paper are: 1. To establish a cut-off point in the cost-depth ratio. 2. Predict the most economic method of stripping in a given area using graphical plots of walking path implemented with information necessary to ensure optimum production. The optimum operating efficiency of the dragline in relation to the terrain and other conditions imposed on its operation will be evaluated. The model is based upon operating data which has been collected from site observations of a large strip coal mining operation in Central Queensland, Australia.

Jan 1, 1977

By Frank W. Harris

THE strength of hard drawn copper wire is a question of considerable importance to both manufacturer and consumer. Unlike steel and alloy wires, in which strength is governed by both chemical and physical considerations, the high conductivity required for copper wire in the electrical industry generally precludes the possibility of obtaining tensile strength through the use of alloys. Consequently, this strength is largely a matter of the physical structure, and all factors known to affect this structure, such as rolling temperature, die contours, lubricants, drawing speeds, etc., are matters of prime importance. The experiments described here have been carried out during the past year at the Baltimore plant of the American Smelting & Refining Co., in connection with a general investigation of some of the questions mentioned above, with the object of studying the physical structure of hard drawn copper wire and the influence of certain factors on that structure. The work has been of an exploratory nature, rather than comprehensive, but it was thought that the results might prove of sufficient general interest to warrant their publication. The bulk of the hard drawn copper wire used in places where strength is an important factor is manufactured to strict specification, based usually in the United States on that of the American Society for Testing Materials (B-1-23). This specification calls for almost as high a value of tensile strength, consistent with elongation, as it is possible practically to obtain, and only physically perfect material can be relied on to meet such a specification. Obvious defects, such as laminations produced through fins in the original rods or brittleness due to overdrawing, are usually recognized and need only passing reference. Laminations can be detected by twisting and untwisting the wire several times; they will show up on the surface in the form of fins. Fig. 1 shows a very bad example of this defect. The wire may be perfectly smooth before twisting but when such laminations are present they will readily show up under this treatment. This trouble is caused by similar defects in the original rod produced by overfills in rolling. Fig. 2 shows the cross-section of the rod from which the wire in Fig. 1 was drawn.

Jan 1, 1928

By Frank Harris

THE strength of hard drawn copper wire is a question of considerable importance to both manufacturer and consumer. Unlike steel and alloy wires, in which strength is governed by both chemical and physical considerations, the high conductivity required for copper wire in the electrical industry generally precludes the possibility of obtaining tensile strength through the use of alloys. Consequently, this strength is largely a matter of the physical structure, and all factors known to affect this structure, such as rolling temperature, die contours, lubricants, drawing speeds, etc., are matters of prime importance. The experiments described here have been carried out during the past year at the Baltimore plant of the American Smelting & Refining Co., in connection with a general investigation of some of the questions mentioned above, with the object of studying the physical structure of hard drawn copper, wire and the influence of certain factors on that structure. The work has been of an exploratory nature, rather than comprehensive, but it was thought that the results might prove of sufficient general interest to warrant their publication. The bulk of the hard drawn copper wire used in places where strength is an important factor is manufactured to strict specification, based usually in the United States on that of the American Society for Testing Materials (B-1-23). This specification calls for almost as high a value of tensile strength; consistent with elongation, as it is possible practically to obtain, and only physically perfect material can be relied on to meet such a specification. Obvious defects, such as laminations produced through fins in the original rods or brittleness due to overdrawing, are usually recognized and need only passing reference. Laminations can be detected by twisting and untwisting the wire several times; they will show up on the surface in the form of fins. Fig. 1 shows a very bad example of this defect. The wire may be perfectly smooth before twisting but when such laminations are present they will readily show up under this treatment. This trouble is caused by similar defects in the original rod produced by overfills in rolling. Fig. 2 shows the cross-section of the rod from which the wire in Fig.1 was drawn.

Jan 1, 1928

During the past 60 or 90 days, the metropolitan newspapers have published much concerning unemployment throughout the nation and the efforts of the Army and various other bureaus for finding work for the returning soldiers. The United States Employment Service has 2000 bureaus throughout the country, which Nathan A. Smyth, Assistant Federal Director, states have placed more than 2,400,000 persons in employment. The Engineering Societies Employment Bureau, which, since December, 1918, has been endeavoring to put all returning engineers in touch with employers who need efficient men, has produced results that are very gratifying to the Secretaries of the four Founder Societies under whose direct management the Bureau operates. During this period, 1615 men have registered at the Bureau's office in the Engineering Societies Building; not all of these, however, are unemployed. Many are ex-army and navy men, who in passing through New York on their way home, look over the field in the hope of making a change for their own benefit before returning to their former positions. During this period, 427 positions vacant have been filed, 2300 of which positions have been filled from the men registered. The letters mailed by this Bureau amount to about 1000 a month and the number of personal calls at the office, 1600. The lowest number of positions filled has been in mining, but the lowest number of registrations is also from mining men. While in February idleness throughout the nation was increasing at the rate of 35,000 a week, under date of Mar. 7, Arthur Woods, a special assistant to Secretary of War Baker, states that there is a material improvement in the unemployment situation and that the problem is no longer a serious one. It is recognized that' the improvement wrought in each individual by his military training and experience has so increased his value that it is 'not only unfair, to ask these men to accept their old jobs at the old wages, but it is probably very unlikely that they will be willing to do so. This plain statement of improvement may not carry conviction to everyone but a concrete example will show its validity. Take the example of a young man under 21, bright and intelligent, with only a high-school education who was employed, before being drafted, on purely manual labor. He shows up well under military training and is made a corporal; he makes good and is appointed a sergeant; and finally becomes top sergeant, which requires him in many ways to handle the entire company of 250 men. The result is; even if he has not been tried by the fire of battle, he comes out of the army with a feeling of self-confidence and capacity that was entirely lacking when he went in and he has had actual experience in handling a larger body of men than the average mine foreman at twice his age, and he has had twice the average amount of detail work to take care of.

Jan 4, 1919

By Richard P. Schoemaker

Introduction In underground mining operations the effects of economic and mechanical factors on costs and profits can readily be appreciated and can perhaps be expressed in exact figures and percentages. Less apparent, but frequently more important, is the influence of physical stress. Stress causes failure of supports, collapse of openings, rockbursts, and other damage which directly affects the costs of maintenance, and also to a certain extent the accident rate. Stress can, however, if properly directed, be an aid to mining operations. The caving methods in metal mining and the long-wall method in coal mining are well-known examples. In large-scale mining operations it is almost impossible to neglect stress-control. A better understanding of the mechanism of rock pressure and the application of its principles to practical mining will inevitably lead to a reduction in operating costs. Many theories have been advanced to give the mining engineer a practical outline for stress-control but, although today most experts agree upon the principles of stress distribution around underground openings, there is still no generally accepted theory that explains all phenomena. The main reasons for this incomplete understanding of the problem are the lack of accurate knowledge of the physical properties of rocks under field conditions, and the great complexity of these conditions due to in-homogeneity of the rock, stratification, tectonic disturbances, and many other unknown factors. The research on the rock pressure problems has, however, yielded some valuable facts which, expressed in practical terms, and adapted to local conditions, may become a valuable aid for mining operations. The purpose of this paper is to give a review of the most important accomplishments of this research with respect to the stress phenomena around small underground openings, such as tunnels and shafts, so as to arrive at an outline of the problem as it stands today. Special emphasis is placed on a new theory by the German mining engineer, Rudolf Fenner, which has never before been published or discussed in English. The Pressure Dome Theory The formation of a dome-shaped space around underground openings is well known from field observations. When openings are made in rock under stress, the rock in the top of the openings will often fail, and caving will continue until the openings have assumed a dome-shaped form, after which equilibrium apparently is re-established. The oldest theory which attempted to explain the phenomenon is the "beam" theory, which postulates that the hanging wall consists of stratified measures that behave as independent beams with fixed ends and a uniformly distributed load. When failure of the beam occurs, inward shearing at the ends will cause the formation of a dome-shaped space. The pressure dome theory, which more or less evolved from the beam theory, merely

Jan 1, 1949

By James A. Barr

Phosphate rock is a natural rock containing one or more phosphate minerals usually calcium phosphate, of sufficient purity and quantity to permit its use, either directly or after beneficiation in the manufacture of commercial products.1 The principal minerals in phosphate rock have the apatite structure which may be represented by the type formula: Ca10(X2) (PO4)6 where X represents the hydroxyl group (OH), chlorine or fluorine, either singly or collectively. The calcium may be partly replaced by sodium, magnesium, and other positive ions such as manganese, strontium, lead, uranium, cerium, yttrium and other rare earths. The PO4 radical may be partly replaced by small quantities of UO4, AsO4, SiO4, CO3, SO4, or Vo4. A typical commercial rock is usually a calcium phosphate containing 3 to 4 pct fluorine, the major impurities being limonite or other iron oxides, clay, aluminum phosphates and silica as quartz sand. A little vanadium is present in most of the domestic rock deposits (except the Tennessee Brown Rock), according to Jacob, Hill, Marshall and Reynolds! A little uranium occurs in the Florida leached zone, as will be brought out later. The chemical analyses are reported as P205, or tricalcium phosphate Ca3(PO4)2, the latter often designated by the trade name BPL (bone phosphate of lime). Commercial analyses usually report iron and alumina as oxides, lime as CaO and silica or insoluble. Colony3 examined many samples of apatite, staffelite, dahlite and American phosphorites and concluded that all have identical X-ray diffraction patterns. The phosphates in the phosphate rock have very minute crystalline structures. The mineral apatite Ca3(F.Cl) (PO4) 3 is the principal primary source of the element phosphorus, and occurs widely distributed in igneous rocks but rarely in a minable mass. Only about 12 pct of the world production of phosphate rock comes from primary apatites; the remainder is derived from secondary phosphorites. These phosphorites have been formed by the alteration of sediments by solutions containing phosphoric acid. Such solutions have come from the weathering or leaching of igneous rock containing apatite, bone deposits of prehistoric animals, marine life or guano deposits. These phosphorites are mostly alterations of phosphatic limestones. The sedimentary phosphate deposits are of marine origin and may have been enriched by subsequent solution of the more soluble calcium carbonate by waters containing carbon dioxide, by physical concentration by wave action, and by redeposition of the dissolved phosphate ions. Uses of Phosphate Phosphorus is the spark of life and is the structure builder and one of the main elements of plant food (fertilizer). Without phosphorus, life cannot exist. A "complete" plant food[t] in addition to phosphorus compounds contains potash, which acts as a catalyst to convert nutrients to useful forms, nitrogen to supply the growth element and many minor elements. The cycle of supply of phosphorus is from the apatite to solution and soil, absorption of plant life, decay and return to the soil or by animal life feeding on the plants. With insufficient supply of phosphorus in vegetation, life is not prolific. If crops are removed from

Jan 1, 1960

By R. L. Fullman

IN the investigation of metallurgical transformations and the relationships between microstructure and properties of metals, it frequently is desirable to obtain a measurement of the relative amounts of the various phases present and of the mean size of particles into which each phase is dispersed. The relative amounts of the phases can be measured by the classical methods of area, lineal, and point analysis,1-5 in accordance with the principle that the volume fraction of a phase, the fraction of a polished cross section occupied by the phase, the fraction of a random line occupied by the phase, and the fraction of randomly arrayed points occupied by the phase are all equal. The validity of this relationship depends only on the attainment of a truly random sample of area, length, or points, and not on the size, shape, or distribution of the particles constituting the phase. Smith and Guttman8 have derived a relationship between the interface area per unit volume S, and the measurable quantities L., the interface length per unit area on a cross section, and NL, the number of interfaces per unit length intersected by a random line. Their equation, Sv = — L8 = 2NL is also valid regardless of the distribution of particle sizes and shapes. In contrast to the situation concerning measurement of relative fractions of phases and of interface area, the measurement of particle sizes in opaque samples has not been subjected to a complete analysis. It has been common to measure some lineal or area dimension of particles on a polished cross section and to use the mean value as a qualitative measure of particle size. In the present paper, quantitative relationships are established among the various mean dimensions on a polished cross section and the actual dimensions of the particles present. Particles of Uniform Size Spheres: If a metal sample contains particles of a phase a dispersed in the form of spheres of uniform size, a polished cross section through the sample will reveal circular areas of phase a with radii from 0 to ?, the radius of the spheres. Consider a cube of unit dimensions to be cut from the sample. If a cross section parallel to one of the cube faces is examined, the average number of particles per unit area (N,) equals the number of particles per unit volume (Nv) times the probability p1 that the plane would intersect a single sphere positioned at random within the unit cube. Since, of the various possible positions for the cross-sectional plane over the unit length from top to bottom of the cube, only those positions existing over the length 2r would lead to the plane intersecting the sphere, the probability of intersecting a single sphere is just 2r. N8= Nvp1 = Nd-2r [1] Applying the equality of area and volume fractions, the relationship is found between sphere size and average area s of uniform spheres intersected by a random cross section, 4 - f = NV V = Nr . — pra = N s = Nd . 2rs S = —pr2 [2] A similar analysis reveals the average traverse length across spheres of uniform size when random lines are passed through the sample. If a randomly oriented unit cube is cut from the sample and a randomly positioned line is passed through the cube parallel to a cube edge, the number of spheres intersected by the line (Nl) equals the number of spheres per unit volume times the probability p1 of the line hitting a single randomly placed sphere in the cube. Since possible positions of the line occupy unit area, and possible positions for which it will pass through the sphere occupy an area of pr2, the probability of the line hitting a randomly placed single sphere is pr2. NL = Nv p1 = Nvpr2 [3] Combining this relationship with the equality of volume and lineal fraction, the desired relationship is obtained between radius and mean lineal traverse length -i, for spheres of uniform size. 4 - - 3 l=4/3r [4] Circular Plates: Consider a sample containing particles of a phase a in the form of circular plates of uniform radius r and thickness t, where r >> t. If the plates are randomly oriented, as in a sufficiently large sample of a fine grained polycrystalline material, area and lineal analysis may be carried out with parallel cross-sectional planes and lineal traverses. If the plates are not randomly oriented, it is necessary to randomize the orientation of the cross-sectional planes and traverse directions. Let a unit cube be cut from the sample, and a cross-section plane be passed through the cube parallel to one of the cube faces. The number of plates cut by the cross-sectional plane per unit area is equal to the number of plates per unit volume times the probability of a plate intersecting a single randomly positioned and randomly oriented plate in the cube. If J is the component of the plate diameter in the direction normal to the cross-sectional planes, the probability of a plane cutting a single randomly oriented plate is equal to J, the mean value of J for all possible orientations of the plate. Let 4 be the dihedral angle between a plate and the cross-sectional plane, and let p?, d? be the probability that a plate makes an angle between 4 and ? + d? with the cross-sectional plane. Then for ran-

Jan 1, 1954

By Richard P. Schoemaker

INTRODUCTION IN underground mining operations the effects of economic and mechanical factors on costs and profits can readily be appreciated and can perhaps be expressed in exact figures and percentages. Less apparent, but frequently more important, is the influence of physical stress. Stress causes failure of supports, collapse of openings, rockbursts, and other damage which directly affects the costs of maintenance, and also to a certain extent the accident rate. Stress can, however, if properly directed, be an aid to mining operations. The caving methods in metal mining and the long-wall method in coal mining are well-known examples. In large-scale mining operations it is almost impossible to neglect stress-control. A better understanding of the mechanism of rock pressure and the application of its principles to practical mining will inevitably lead to a reduction in operating costs. Many theories have been advanced to give the mining engineer a practical outline for stress-control but, although today most experts agree upon the principles of stress distribution around underground openings, there is still no generally accepted theory that explains all phenomena. The main reasons for this incomplete understanding of the problem are the lack of accurate knowledge of the physical properties of rocks under field conditions, and the great complexity of these conditions due to inhomogeneity of the rock, stratification, tectonic disturbances, and many other unknown factors. The research on the rock pressure problems has, however, yielded some valuable facts which, expressed in practical terms, and adapted to local conditions, may become a valuable aid for mining operations. The purpose of this paper is to give a review of the most important accomplishments of this research with respect to the stress phenomena around small underground openings, such as tunnels and shafts, so as to arrive at an outline of the problem as it stands today. Special emphasis is placed on a new theory by the German mining engineer, Rudolf Fenner, which has never before been published or discussed in English. THE PRESSURE DOME THEORY The formation of a dome-shaped space around underground openings is well known from field observations. When openings are made in rock under stress, the rock in the top of the openings will often fail, and caving will continue until the openings have assumed a dome-shaped form, after which equilibrium apparently is re-established. The oldest theory which attempted to explain the phenomenon is the "beam" theory, which postulates that the hanging wall consists of stratified measures that behave as independent beams with fixed ends and a uniformly distributed load. When failure of the beam occurs, inward shearing at the ends will cause the formation of a dome-shaped space. The pressure dome theory, which more or less evolved from the beam theory, merely

Jan 1, 1947

By G. L. Coleman, D. S. Hutton, W. C. Leslie

The occurrence of twins in a iron, generated during cooling through the ?-a transformation, is well established,1-8 but this phenomenon has been nearly ignored during the past 20 years. It is the purpose of this note to call attention to the prevalence of such twins and to illustrate their appearance. The work of paxton7 and Kelly8 has demonstrated beyond reasonable doubt that for Neumann bands (mechanical twins) in a iron the twinning plane is (112) and the twinning direction <III>. The agreement with McKeehan&apos;s earlier work4 on transformation twins indicates that both types of twins in ferrite follow the same twinning law. There is little doubt of this conclusion, but it could be strengthened by a microbeam X-ray determination of the orientation relationship between a single ferrite grain and a transformation twin within that grain, as in the technique used by Kelly8 on Neumann bands. RESULTS AND DISCUSSION Transformation twins, identified by their appearance on a polished and etched section, were found in

Jan 1, 1960