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By James C. M. Li, J. Weertman

James C. M. Li (United States Steel Covp.)—The author has discovered a single analytical relation between the minimum, or the steady-state, creep rate and the applied stress confirming a statement made earlier by orn" that such relation should exist and should reduce to the power law at low-stress levels and to the exponential law at high-stress levels. However, as pointed out by the author, all the available theories of creep are not adequate to explain such a single relation. Inspired by such a statement, I have made a suggestion concerning a possible explanation13 of the new relation. This is based on the concept that the rate-controlling step is the cooperative motion of a short dislocation segment. The nature of and the reason for the cooperation have been discussed13 as well as the reason why the motion of the dislocation could be controlled by the mobility of the short segments. A natural short segment has been proposed13 to be the node formed at the intersection of two dislocations. The reason why the node may contain only a few atoms has not been discussed and the application of the proposed model to all the metals and alloys reported in this paper has not been attempted. It seems appropriate to include these in this discussion. The model was partly inspired by the substructure recently observed in the electron microscope on creep specimens. One such example is shown in Fig. 48 in Darken's Campbell Memorial Lecture. The substructure is a collection of dislocation intersections and irregular networks. No pileups have ever been observed in such specimens. A closer look at the network indicates that one set of dislocations is more straight than the other set sug- gesting that the other set may be mobile in the plane of the net. Since, for the network to survive the creep deformation, some dislocation reaction has to take place at the intersection of the two sets of dislocations, the mobile dislocation, even if it can slip in the plane of the net, will have difficulty in moving at these intersections. To illustrate, an idealized network is shown in Fig. 9. The thin lines represent the set of dislocations which are mobile and can slip in the plane of the net except at the nodes which are formed at the intersection of the two sets of dislocations. The other set of dislocations, represented by the thick lines, may have a Burgers vector which is not parallel to the plane of the net, and therefore may be immobile. Because of this nonparallel Burgers vector, the Burgers vector of the node, which is avectorial sum of the Burgers vectors of the two sets of dislocations, will also be nonparallel to the plane of the net. Therefore, the node cannot slip in the plane of the net and the set of mobile dislocations will have to drag the node along as indicated in Fig. 9. Now the problem is how many atoms could be involved in the nodes. Exact calculation of the length of the node is a difficult task especially since the length should be a steady-state length and not an equilibrium length. An estimate of the equilibrium length can be made by balancing the line tension of all the dislocations. The results would be a small fraction of the length 1 between nodes as shown in Fig. 10. In some instances such a calculation shows that the node will not be formed. But, since the calculation is only approximate, it does not rule out the possibility of the formation of a short node. In other instances the equilibrium length of the node is an appreciable fraction of I. Such a node would

Jan 1, 1963

By U. N. Bhrany, N. Arbiter

Over the last one hundred years the problem of assessing the efficiency of energy consumption in producing rock breakage has been studied by many investigators from a variety of viewpoints. Their contributions fall into three main categories: (1) those characterized by a priori assumptions of a relation between the energy required for fracture and the degree of fragmentation produced (e.g. Rittinged(l), Kick(2) Bond(3)); (2) those studying simple systems with controlled energy applications (Gross(4)?(5) ); (3) those treating operating data to develop practical relative measures of efficiency (Coghill(6), Taggart(7)). Closely involved in the efficiency problem is the characterization of size distributions produced by comminution. Unless an experimental size distribution can be approximated by a distribution function and its constants, it becomes difficult if not impossible to develop quantitative energy-particle size relationships. While many such functions have been proposed, none are both completely adequate and convenient. The simpler fonns usually describe only a part of the sizing data, while those which apply to a greater extent are cumbersome(8). The thesis underlying the study here reported can be stated as follows: Size reduction in a tumbling mill subjects ore particles to a relatively constant fracture-producing environment. The intensity of the forces is determined by such factors as the mass of the breaking bodies (rods, balls, rock), and the speed and dimensions of the shell. For a particular ore the extent of size reduction will depend both on the intensity and on the duration of exposure. The latter is the residence time in a batch mill, or is determined by the effective volume and the flow rate in a continuous mill. Size reduction can thus be regarded as a rate process in which the weight of material in size intervals varies as a function of grinding time. Although both the rates of disappearance of coarser sizes and

Jan 1, 1961

By David R. Mitchell, Ernest M. Spokes

There is evidence that study of minerals now considered to have susceptibilities too low for magnetic separation should be continued. Present concepts may be false. INFORMATION on magnetic properties of minerals other than magnetite is scanty and sometimes erroneous. Often there is no information at all. W. R. Crane's table of tractive forces published in 1901 is still the best guide in the field, but Crane's data can be used as a guide only, since he ignored such important factors as impurities in the minerals, size, and packing effect. During the 1930's work by the U. S. Bureau of Mines added greatly to knowledge of the behavior of certain minerals in a magnetic field. The USBM bulletin gave for the first time complete magnetic characteristics for magnetite and fragmentary data for a few other minerals. The work reported here covers a study of the magnetic-susceptibility relationships of the wolframite series of minerals and sphalerites as related to their chemical compositions. Theories are proposed to explain divergences found from commonly accepted beliefs. Gouy Method for Determining Magnetic Susceptibility: The Gouy principle has been adequately described in the literature1-3 and applied in various ways.'- It may be summarized by stating that a body of material (gas, liquid, solid, or powder mixed with gas or liquid) of cylindrical shape changes in apparent weight if suspended with one end in a zone of higher magnetic field strength than is found in that portion of the field surrounding the other end of the cylinder. This may be expressed as K2 - K1 A (H2 - H2) - mg. [1] In determining the susceptibility of mineral specimens by the Gouy method, the mineral is reduced to a fine powder and packed in a glass weighing tube. Precise measurement of the bore and depth of the tube is made unnecessary by a calibration procedure. Using the basic expression of Eq. 1, Hoare"

Jan 1, 1959

By L. F. Pease, J. H. Brophy

A phase diagram for the Ta-Zr system is presented. The system is of the minimum-melting point type with the 0-zirconium phase decomposing monotectoidally at 785°C and 95.5 at. pct Zr. The minimum solidus temperature is 1875°C and the temperature of the top of the monotectoid loop is 1775°C. Techniques employed included X-ray diffraction and fluorescmce, electron microprobe analyses, diffusion couples, metallography, and melting-point measurements. Errors due to interstitial solutes and in melting observations are particularly common in this system, and their occurrence is discussed. SEVERAL versions of the Ta-Zr phase diagram have been reported in the literature.lm7 Williams et al.' report a diagram of the minimum-melting point type with a monotectoid reaction at 800°C and 12 wt pct Ta. The minimum in the solidus occurs at 1820°C and 25 wt pct Ta, while the top of the monotectoid gap is located at 1780°C and 80 wt pct Ta. The experimental techniques employed were metallography, electrical resistance variation with temperature, dilatometry, X-ray diffraction, and direct observation of melting by the technique of Pirani and ~lterthum.' Experience in the Nb-Zr phase diagram has shown that small changes in the interstitial content can cause large shifts in the positions of the phase boundaries. Small amounts of inter -stitials can cause similar changes in the Ta-Zr system and may be responsible for the wide variations in the phase diagrams previously reported.'-' The authors15 have found that alloys containing 0.75 wt pct 0 and 1.0 wt pct Ni with tantalum contents from 19 to 85 at. pct often contain a lamellar or cellular precipitate after annealing above 1400°C. This precipitate is very similar to that reported by pollack,12 Ralls," and Donlevy17 for the Ni-Zr system. In the present investigation, a wider variety of experimental techniques and improved alloy purity were applied to the resolution of errors in diagrams for this system as they now appear in the literature. New results have been obtained in the areas of alloy homogeneity and purity. Errors in the common techniques of direct melting observation in binary alloys have been demonstrated. In the commercially important high-tantalum region, the more accurate metallographic method of solidus determination has been employed. EXPERIMENTAL PROCEDURE Nominal analyses of the materials employed are given in Table I. The zirconium was low hafnium reactor grade iodide crystal bar, and the tantalum was in the form of high-purity sheet. Powders were impossible to use because of gas content. Alloys were melted on a water-cooled copper hearth, with a thoriated tungsten-tipped nonconsumable electrode in 2/3 atm of Zr "gettered" argon. Alloys were

Jan 1, 1963

By Milton H. Fies

THE writer wishes to acknowledge at the outset his great sense of obligation to those who contributed so broadly and expertly to the preparation of this paper: Dr. Albert DeSmaele, Chairman of the Board of Directors of Socogaz, Belgium; Dr. Julien Venter, Director of the National Institute of Coal Mining and Coal Utilization Industry, Belgium; Dr. Roger Loison, Chief Engineer, French National Coal Research Board, France; and Dr. Erich Sarapuu of the Sinclair Coal Co., Kansas City, Missouri. Liberal use has been made in this paper of a recent publication on Russian, Italian, Belgian, and French experiments prepared jointly by the Centre d'Etudes et Recherches des Charbonnages de France (Cerchar) and the Institut National de l'Industrie Charbonnière of Belgium (Inichar).1 The writer is particularly indebted to Dr. E. T. Wilkins, of the Fuel Re¬search Station, London, and to Mr. James L. Elder, of the Alabama Under¬ground Gasification Experiment at Gorgas, Alabama, for their unfailing patience and effective support. Not only did these experienced and capable men edit and revise this discussion, but much of its content is a direct con¬tribution quoted in full from their memoranda. Without the assistance of all these colleagues, this presentation would not have been possible. It has been a privilege to serve and work with them and to acknowledge repeatedly their loyal cooperation. The recovery of the energy inherent in coal beds throughout the world has been done through the years by methods that today may be justly regarded as primitive. While the techniques of coal mining through the application of machines and the enhancement of information and skills have advanced to an extraordinary extent, particularly during the past 20 years, the underlying means is essentially the same as when man first began to mine coal. Despite this progress in the manner of coal mining, it continues today as a hazardous, toilsome, grimy task. Coal mining per se has advanced at a greater and more rapid stride in the past 25 years than the mining of any: other mineral, but the basic method is fundamentally the same as it was the first day a miner took a pick into his hands many centuries ago. This situation presents a challenge to mining engineers everywhere, from

Jan 1, 1953

By Norman F. Schulz

The technical excellence of separation achieved in a mineral concentration process, or any other process where two constituents of any kind are physically separated from each other, is expressed uniquely and quantitatively by the separation efficiency (E,): E. = (R - R,), where R is the percentage of the valuable constituent and R, the percentage of the waste appearing in the concentrate. The separation efficiency meets all the usual requirements of a true efficiency and is independent of the nature of the process used. It can be visualized as the percentage of the feed material that, in effect, actually undergoes complete separation while the rest of the feed is distributed randomly and unchanged into the two separation products. The problem of quantitatively assessing the results of a mineral concentration process recurs whenever one tries to decide which of two similar test results is more desirable. Although economic factors may greatly influence the eventual choice of process, they usually have very little to do with the technical excellence of a separation and are, therefore, not a consideration at this point. Concentrate grade and recovery, used simultaneously are the most widely accepted measures of performance, and if both the grade and the recovery are greater for one case than for another, the choice is simple. However, when the results of closely competitive operations are compared, it often occurs that one set of test results shows a higher grade and a lower recovery than another and the choice is no longer obvious. Laboratory investigations of a mineral concentration process applied to a given feed material can often be designed to yield successive paired values of concentrate grade and recovery over the practical range of the course of a separation process.' These results may be plotted as some combination of the cumulative values of grade, weight recovery, or unit recovery in the concentrate. The resulting correlations for two slightly different sets of conditions can then be compared qualitatively, or even quantitatively in particular cases.2 Such comparisons are not applicable, however, to individual concentration test results. The reduction of a separation test result to a single efficiency figure, preferably as a percentage of ideality, would afford the simplest and most precise means for comparing the results of competitive tests. The effective proportion of feed material that undergoes complete separation in any real concentration process, hereafter referred to as "separation efficiency," is such a figure. It is essily calculated from the usual feed and product data and can even be evaluated, in many cases, from data in publications describing various concentration processes. Mineral Concentration Processes and Their Evaluation Mineral Concentration Processes: The overall concentration process may be subdivided into a liberation process which severs the bonds between unlike mineral species, and a separation process, which sorts the resulting liberated particles into two products—a concentrate rich in mineral A and a tailing lean in mineral A. A perfect mineral concentration process is represented by the idealized scheme shown in Fig. 1 in which liberation and separation are not differentiated. The feed mixture consists of two mineral types which are completely liberated early in the process and then sorted by type. All the mineral particles of type A which respond uniquely to the selection forces acting in the ideal separator, report to the concentrate, while all the mineral particles of type non-A report to the tail-

Jan 1, 1971

By L. Adler

Two basic cases involved in the design of an opening in bedded rock are: 1) where the beds deflect from each other so as to be separated; and 2) where the beds deflect onto their lower neighbor, loading the latter while reducing their own load. Analysis of case 1 is relatively simple, while the interference of the original deflection curves in case 2 complicates analysis of the latter. Figures and formulae are presented for determination of interference loading in this situation. The design of an opening in bedded rock involves two basic alternatives.1'2 In one case the beds deflect away from each other, so as to be separated from their neighbors; in the other case the beds deflect onto their lower neighbor, loading it, while reducing their own load. This is shown in Fig. 1. The first case lends itself to a simple analysis, since the upper and lower boundaries of each beam remain a free surface. In the latter case, however, due to the interference of original deflection curves, the analysis is more complex. Earlier investigators of this interference problem solved it by making the tacit assumption that this type of loading was uniformly distributed along the beam's length. While there is no intuitive justification for this assumption, its use does lead to an approximate solution. Still, a more exact solution does not require this apparently unrealistic restriction. To achieve initial simplicity, the analysis will at first be limited to a two-bedded sequence, as in Fig. 2. Since both beams have identical end conditions and spans, the original deflections of their center lines are members of the same family of curves, as shown in Fig. 3. Therefore, if interference occurs at one point along their center lines, it will occur at every point. For convenience, the midspan point is that usually examined. Deflection at midspan for a uniformly loaded beam regardless of end conditions is: where c is a constant depending on end conditions; w is the body load and equals yh, lb per ft; y is the specific weight of rock, lb per ft'; L is the span, ft; E is Young's Modulus, lb per ft2; I is moment of inertia (for a rectangular section), I = bh3/12 = h3/12, (ft4); b is the width of beam and equals one; and h is the thickness of beam, ft; or 3U > yB an Substituting the appropriate values into Eq. lb, interference between the two beds can be predicted. Should it occur, the additional loads along the lower boundary of the upper bed and the upper boundary of the lower bed must be determined. From the principle of action and reaction, these added loads are known to be equal and opposite, as indicated in Fig. 4. Since the final deflection curves for both beds are identical (Fig. 3), their successive derivatives of y with respect tox must also be identical. That is:

Jan 1, 1961

By E. M. Norris

Phosphate deposits are distributed widely over the earth's surface. Of the known areas of deposit, eight fields are of particular interest because of their vast reserves of high grade phosphatic material and the volume of their production that goes to the world's great consuming areas. These fields, in the order of their present economic importance, are situated respectively in Florida, French Morocco, Kola Peninsula of U.S.S.R., Tunisia and Algeria, Tennessee, Montana-Idaho-Wyoming-Utah, Ocean and Naru Islands in the Gilbert group, and in Egypt. The Rocky Mountain deposits have a comparatively low ranking in the phosphate trade of today, but this field contains one of the largest known reserves of phosphatic material, associated with which are recoverable trace minerals, which are of increasing importance in our national economy. The first discoveries of phosphate rock in the western states were recorded in Cache1 and Rich2 counties in Utah, respectively in 1889 and 1897. Mining operations were begun on these deposits near Montpelier, Idaho, in 1906. During the latter year geological studies of the phosphate beds were started by Weeks and Ferrier of the U. S. Geological Survey. These studies have been continued to the present day by a distinguished roster of the Survey's technicians. As a result of this systematic exploratory program, the Survey has published a series of bulletins, papers, and maps, which provide the mining public with a comprehensive study of the exposed

Jan 1, 1949

By AIME AIME

The following abstract of the minutes of the final Adjourned Annual Business Meeting, held Nov. 12, 1912, in the office of the Institute, 29 West 39th Street, New York City, is here presented for the information of the membership at large. On the announcement by the Secretary that there was a quorum present, President James F. Kemp called the meeting to order. The minutes of the Adjourned Annual Business Meeting of Oct. 7, 1912, were read and approved. (Sec p. xi,Bulletin No. 71, November). Prof. Jos. W. Richards, in behalf of the Special Committee of the Board of Directors and the Council (Messrs. Richards, Kirchhoff, and Rand), withdrew the two proposed amendments to the Constitution offered by the said Committee at the Adjourned Annual Business Meeting of Oct. 7, 1912. (See Bulletin. No. 70, October, 1912, p. vi., and Circular Announcement No. 8, Oct. 15, 1912, p. 15.) Professor Richards presented a syllabus of the proposed amendments to the Constitution and By-Laws prepared by the Special Committee. Several members present discussed various sections of the proposed Constitution, and the Committee advised that the suggestions would he duly considered before submitting the final document, which would be duly presented and sent to the membership at large at least 30 days before the next Annual Business Meeting, Feb. 18, 1913. Professor Richards presented a resolution, seconded by Mr. Kirchhoff, making a change in the present Certificate of Incorporation, so that it would conform to the proposed changes in the Constitution and By-Laws; said resolution was unanimously adopted. Professor Richards presented another amendment to the Constitution, which had been purposely omitted from the printed list, but had been requested by many members, namely, the creation of a " Class of Fellows." This question was freely discussed at the Cleveland meeting (see Bulletin No. 71, November, 1912, p. 1348), and in view of the diversity of opinion it was-decided to present it in separate form for separate action of the membership at large at the Annual Business Meeting, Feb. 18, 1913. In answer to question, the President announced that the proposed amendments to the Constitution and By-Laws presented by Messrs. Corning and Stone at the Adjourned Annual Business Meeting, Oct. 7, 1912, and published in Circular Announcement No. 8, Oct. 15, 1912, were still on record. Professor Richards presented a syllabus of the proposed amendments to the By-Laws, and several sections were discused by members present, but no action of record was taken. Mr. Charles F. Rand read a letter from Mr. L. K. Armstrong, Sec-retary of the Spokane Local Section of the Institute, referring to the proposed amendments to the Constitution, and he announced that many of Mr. Armstrong's suggestions were, in one form or another, already incorporated in the proposed amendments submitted by the Special Committee. A special vote of thanks was passed to Dr. Albert R. Ledoux for the valuable assistance rendered by him to the Special Committee in the preparation of the proposed amendments to the Constitution and By-Laws.

Dec 1, 1912

By Donald J. Knight

HEAT Treatment at 1500' F of a mild steel containing 0.1 pct C, in an atmosphere which is oxidizing to both carbon and iron, results in the progressive oxidation of the metal surface with little or no change in the carbon content of the underlying metal. Further heat treatment of the scaled metal in either a neutral atmosphere or in a vacuum may or may not result in the decarburization of the metal depending upon the physical nature of the scale. It is apparent that if a continuous layer of oxide is present on the steel surface, the reaction OScale + Cmetal Cogas cannot progress since the SO formed gas would be unable to leave the oxide/metal interface. Thus, in order for the reaction to progress, the oxide must be cracked or porous. Vacuum heat treatment at 1500" F of samples with a thick continuous oxide scale showed no decarburization of the steel. However, when cracks were introduced mechanically into the scale prior to the vacuum heat treatment notable decarburization of the metal resulted and a structure as shown by Fig. 1 obtained, i.e., reduction of the crack walls to ferrite. With reference to the diagram of Fig. 2, it would appear that a mechanism of the following type takes place. Carbon atoms arriving at an oxide/metal/void interface, such as 'A', Fig. 2(a), can combine with oxygen atoms from the scale and leave the reaction site as Cogas thereby reducing the oxide to metal. On a greatly magnified scale, Fig. 2(b),this will appear as a ferrite projection along the crack wall. Carbon atoms entering this projection can react with oxygen atoms at point 'C', which is a new interface, and so on leading to a progressive growth of the ferrite along the crack wall and to the surface, Figs. 2 (c) and 1. It would appear that the only means by which thickening of the ferrite film can take place is by a diffusion of oxygen through the ferrite film to react with carbon at the newly formed ferrite/ void interface. Since the diffusion rate of carbon is reportedly much greater than that of oxygen, and since there is a low probability factor of oxygen and carbon atoms arriving simultaneously at the same site on the ferritehoid interface, there will be a tendency for more rapid lengthening than thickening of the ferrite layer, as is observed.

Jan 1, 1962

By R. W. Heins, N. Street

An investigation was made of the Rehbinder-Kuznetsov pendulum as an instrument to aid in the study of rock drillability and of the effect of surface active agents on rock drillability. The "critical weight", i.e., the pendulum weight at greatest sensitivity, was determined for several solids and it was shown that a change in surface environment changed the maximum value of the apparent hardness but not the critical weight, and the critical weight increased with increase of hardness of the solid used. Using silver halides as the solid material, and solutions of either silver nitrate or the appropriate alkali halide, it was shown that there is a hardness maximum at the zero point of charge of the particular silver halide. INTRODUCTION The development of relative hardness measurement by the method of damped oscillations, or what has been called the pendulum sclerometer, is due largely to the Russian workers P. A. Rehbinder and V. D. Kuznetsov and their co-workers.1,2 The apparent simplicity of the method has led to its use in a number of fields, particularly those where relative hardness has to be determined on a brittle solid. As will be shown, the simplicity of the method belies its complexities. THEORY OF THE PENDULUM SCLEROMETER The operation of the pendulum is quite simple. Make a sharp point such as a diamond, hardened steel or tungsten carbide, as the fulcrum of a pendulum, with the center of gravity of the system below the point of support. The attenuation of this pendulum is a function only of air friction, provided no fragmentation, breakage or other work is performed by the point. However, when the solid surface breaks or disintegrates under the point, and the latter penetrates the solid, part of the energy of oscillation is absorbed in the work of creating new surface, and the rate of attenuation increases. In the case of brittle solids, the point of the pendulum produces fragmentary particles, whereas the point produces plastic deformation in a plastic solid; but in both cases damping occurs. This pendulum damping is a function of the hardness or strength of the solid. Whereas a pendulum oscillating on a hard material attenuates primarily by air friction, in the case of a soft material, the points penetrate the surface of the solid, producing new surface, and the pendulum damps much faster. Thus the attenuation rate is a function of the hardness or strength of a material in both plastic and brittle substances. Russian workers initially used a single support for the pendulum, but this created many problems because of oscillation of the pendulum in more than one plane. A revised version used two points, or sometimes a prism as support, successfully confining oscillation to one plane. The version using two points was constructed and used throughout this investigation, making the recording of the attenuation as a function of time relatively easy. That both points should be in contact with the solid during the damping is implied. Rehbinder (c.f. Kuznetsov2) proposed that the hardness H as measured by this method could be expressed by a quantity which is inversely proportional to the relative initial rate of attenuation of amplitude. where H = hardness parameter (arbitrary units) a, = initial amplitude da/dt = rate of attenuation of amplitude with time. In the simplest case of damping with a constant logarithmic decrement, H can be regarded as a constant for the duration of the whole damped oscillation process. That is

Jan 1, 1966

By E. C. Olsen

This paper describes the unusual hazardous conditions encountered in mining thick, inclined coal beds under heavy cover in Carbon County, Utah. This description includes heavy roof conditions, sloughing ribs, steep pitches, and severe bouncing experience. Emphasis is placed on the top bench system of mining and development in the top half of a 16-ft seam, under the roof rock, which is bolted, and the recovery of the bottom coal on retreat; success of bolted roof and ribs; and shuttle car haulage on pitches up to 25%. The use of protective cages for operators of face equipment, the guarding of belt conveyor systems to prevent injury associated with deliberate entry, and the positive lockout of electrical equipment is described and illustrated. Most coal mining areas of the Western United States are characterized either by thick beds, steep pitches or heavy cover. Individually, each of these may present inherent safety hazards that in- fluence mining. When all are met at one location, the combined effect is to make the safe operation of the mining property a challenge to management. These combined conditions are met in the coal mines of the Columbia-Geneva Steel Div. of the United States Steel Corp., in southeastern Utah. This coal bed measures up to 16 ft in thickness, the pitch is as much as 25% and mining is under a cover approaching 3000 ft. The Sunnyside coal bed is found in the Book Cliff Mountains, a great escarpment extending from west of Castle Gate, Utah, some 180 miles to Grand Junction, Colo. West of Green River, Utah, the Book Cliffs swing sharply to the north because of the domelike uplift of the San Rafael Swell to the southwest. It is in this northerly extension of the Book Cliffs that the Sunnyside coal in the Blackhawk Formation of the Mesa Verde Group, Upper Cretaceous Age is found. The strata are transected by numerous faults with from a few inches to as much as a hundred feet of displacement. All of these faults have had some effect on the mining operation, either in roof control or, in the case of major faulting, the pattern of mine development. MINING PRACTICES Mining has generally been confined to the Lower Sunnyside Seam which measures from 7 to 16 ft in

Jan 1, 1963

By F. W. Bowdish

A theoretical and experimental laboratory study has shown that the rate of breaking of oversized particles in a ball mill is proportional to 1) the concentration of such particles, and 2) the area of the balls, provided that the balls are larger than a certain size relative to the particles. If all undersized material were removed as formed, the rate of breaking would be almost independent of the quantity in the mill. Rate equations are given which are similar to those for zero, first, and second order reactions. Deviations of small balls from the equation for a second order phenomena are quantified by a factor called "nipping efficiency." Some data are correlated by a dimension-less equation, which is used to estimate nipping efficiencies from data not in the correlation. The investigation described here was undertaken after a literature survey revealed that little was known concerning the mechanism of breaking of particles within a ball mill and the effect of this mechanism upon grinding rates. One paper, by Roberts1 , offered a theory concerning the mechanism of breaking, and a rate equation for the breaking of particles larger than some size to particles smaller than that size. That paper provided the starting point for a theoretical and experimental investigation of grinding under carefully controlled conditions. THEORETICAL CONSIDERATIONS In his paper on the probability theory of ball mill grinding, Roberts theorized that "... a given expenditure of power leads either to a certain number of point to point blows per bp-hr or to a certain distance of line contact per hp-hr ..." He assumed that the balls touch each other during each blow or during moving contact. Then he said that a volume of pulp, dependent upon the size being considered, would be covered per minute within which all oversized particles would be crushed to particles smaller than that size. Naturally, the higher the concentration of oversized particles in the pulp, the higher the rate of which they would be broken. From this reasoning Roberts obtained the differential equation -dC/dt = k hp/ton C (1) where k is a constant for any size of particle, density of particle, and moisture content of pulp. C is the percentage of oversize in the material to be ground, t is the time, and hp/ton is the power input per ton of material in the mill. He then integrated the equation to log Co/Ct = k/2.3 hp/ton t , where Co and Ct are the percentage of oversize at time zero and t respectively. By always using the same quantity of material in a mill and assuming that it required constant power to run the mill, he was able to combine the horsepower per ton factor with the other constants to give an equation for a first order rate.

Jan 1, 1961

By K. G. Gorling, S. J. Wallden, N. B. Lindvall

It is the policy of The Metollurgical Society to provide, in the TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME, a prompt and accurate medium for publication of reports of significant new research in both the scientific and engineering aspects of metallurgy. Papers submitted to the Society are judged by competent reviewers according to established criteria for technical merit, accuracy, originality, and presentation. STAFF: Editorial Director, Rixford A. Beals; Associate Editor, James J. Burke; Assistants, L. Capria and R. K. Larkin. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: A. W. Thornton, Choirmon; Dennis Carney, John Chipman, J. C. Fulton, J. H. Hollomon, H. tl. Kellogg, A. E. Lee, R. Maddin, J. D. Sullivan, and O. Swan. Review and selection of manuscripts is under the supervision of the following Publications Committees: Extractive Metallurgy Division T. B. King. Cha~rmon; S. J. Dickenson, R. P. Hermsdorf, R. Schuhmann, Jr.. and P. T. Stroup. Institute of Metals Division: Robert Maddin, Chairman. F. Lincoln Vogel, Jr., Vice-chairman, W. A. Backofen, R. W. Balluffi, J. H. Bechtold, M. B. Bever, R. S. Busk, C. G. Goetzel, Paul Gordon, C. D. Graham. Jr., Robert F. Hehe-mann, R. I. Jaffee, F. E. Jaumot, Jr., lrving R. Kramer, A. J. Leno, Horold Margolin, C. J. McHorgue, Russell A. Meussner, J. 6. Newkirk, H. W. Paxton, G. E. Pell~ssier, I. S. Servi, Alan U. Seybolt, A. J. Sholer, and Sack Wahsburn. Iron and Steel Division: J. C. Fulton, Chairman; T. B King, F. C. Langenberg, W. O. Philbrook, and T. B. Winkler. Published bimonthly by the American Institute of Mining Metallurgical and Petroleum Engineers Inc., 29 West 39th Street, New York 18, N. Y. Telephonne pennsylvania 6-9220.Petroleum Subscription Engineers$20 per year for non-AIME members in United States and North South and Central 6-9220.SubscriptionAmerica $25 toreign; $5 for AIME members. Single copies, $4.00, iinalo copies Southfpr;ign,andCentral $5 00. The AIME 'is $25not responsible for any statement made or opinion expressed in its publications Copyright 1958 1958 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . Registered coble address, AIME New York . . . Indexed in Engineering Index, Industrial Arts Index, ...and Chemical Abstracts . . . Application for second class mail privileges IS pending at New Yark, N. Y. Volume 212, Number 2.

Jan 1, 1959

By S. A. Falconer

The benefication of non-sulfide or non-metallic minerals by froth flotation has been practiced commercially for at least 30 years. In the pioneer stages of development of this flotation art, most of the promoters investigated were fatty acids or soaps that had been found to float sulfide minerals. When commercial application of froth flotation started to assume importance in the late 1920' s and 1930's, a great deal of fundamental research work was done in the laboratory (11-14, 19, 22, 23, 26, 29, 32). Among other subjects, this work included studies of the relative effectiveness of the different fatty acids and their salts on the flotability of various non-sulfide and non-metallic minerals. The successful present-day use of fatty acid and petroleum sulfonate type promoters results from better understanding of the principles of non-sulfide flotation plus the developnent of effective selectivity modifying agents. Many investigators have contributed to a greater appreciation of the numerous interrelated factors involved in fatty acid and soap flotation of non-sulfide minerals. Of these, mention should be made of recent fundamental studies by Tagart and Arbiter (31); Wolstenholme and Schulman (35); Schulman and Smith (28); Wark and his co-workers(3,4) Du FIietz(l5); and J. Leja(24). According to J. Rogers, K. L. Sutherland and E. E. and I. W. Wark(27), "the basic requirements for a 'collector' in flotation are that it shall form a film over the surface of the mineral to be floated and that this film should be oriented so that hydrocarbon (non-polar) groups form the effective surface." When modified in that way, the mineral surface possesses some degree of air avidity. All investigators would agree with Taggart, Taylor and Ince (33)that such a film can be produced only if the collector compound contains an active (polar) group to be attracted to the mineral surface, as well as the non-polar group. The commonly used anionic-type promoters for non-sulfide, non-metallic and metallic oxide ores include: 1. Fatty acids, and their soaps and emulsions. 2. Fatty acids residues — "pitches" and "foots." 3. Sulfonated and sulfated fatty acids and so-called "petroleum sulfonates." 4. Paraffin chain salts — sulfonated and sulfated higher alcohols. 5. Cyclic organic acids or salts, such as naph-thenic acid and naphthenates. Certain fatty acids are more effective than others as promoters for particular minerals under certain specified conditions. Some of the more costly fatty acids or collectors of the paraffin chain salt type may give improved selectivity in some instances and are being used commercially in a limited number of operations. Local availability may dictate the choice of the fatty acid used — for example, the use of palmoil fatty acid for flotation of copper carbonate ores in the Belgian Congo. Coconut oil fatty acids have also found limited use.

Jan 1, 1961

By Westwater, J. S.

The Mather mine of The Negaunee Mine Co. embraces nearly all of Sections 1 and 2, T47N, R27W. within the limits of the cities of Negaunee and Ishpeming on the Marquette iron range of Michigan's Upper Peninsula. Operations of the Negaunee Mine Co., the stock of which is jointly owned by Bethlehem Steel Co. and The Cleveland-Cliffs Iron Co., are under the direction of the latter company. The opening of the Mather mine was described by C. W. A1len. Mather "A" shaft was completed to an initial depth of 2352 ft in early 1943. The shaft capacity of over one million tons yearly is in prospect of being realized by orderly development and mining, and sinking of the second or "B" shaft then started in accordance with previous planning. Mather " B, " also a vertical shaft, was designed as a twin to Mather "A" shaft and the sinking technique developed at Mather "A" was utilized in "B" shaft operation.

Jan 1, 1949

By Edna A. Dancy, Gerhard J. Derge

Jan 1, 1963

By B. A. Eaton

The subject of many discussions and technical papers in the last 20 years has been the prediction of the well-bore pressure gradients that are required to induce or extend fractures in subsurface formations. The subject merits this attention because of the frequently recurring problems that arise from an inability to predict fracture pressure gradients. Encountered in several common types of operations in the oil industry are problems associated with the prediction of formation fracture pressure gradients. When wells are being drilled in both new and old fields, lost circulation is often a very troublesome and expensive problem. Complete loss of circulation has been disastrous in some cases. Many times, such disasters could have been avoided if techniques for calculating fracture pressure gradient had been employed in the well plans, and if casing strings had been set, and mud weight plans had been followed accordingly. In areas of abnormally pressured formations, the prediction of fracture gradients during the well-planning stage is extremely important. In fact, it is as important as the prediction of formation pressure gradients, which has received a great deal of attention in recent years. There are several published methods used to determine fracture pressure gradients. However, none of these methods appears to be general enough to be used with much reliability in all areas. In 1957, Hub-bert and Willis published a classical paper that included the development of an equation used to predict the fracture extension pressure gradient in areas of incipient normal fau1ting.l Overburden stress gradient, formation pore pressure gradient and Poisson's ratio of rocks were the independent variables that were shown to control fracture pressure gradient, the dependent variable. In 1967, Matthews and Kelly published another fracture pressure gradient equation that is different from that of Hubbert and Willis in that a variable "matrix stress coefficient" concept was utilized.3 Later the same year, Costley wrote about a similar idea.5 Goldsmith and Wilson used a least-squares curve-fitting technique and field data from the Gulf Coast area to correlate fracture pressure gradient with formation pore pressure gradient and formation depth.' They noted that the fracture pressure gradient increased with increasing depth while the pore pressure gradient remained constant. In each of these cases, the problem for which a solution was sought was to determine the bottom-hole pressure gradient required to initiate or extend a fracture. Results of the previous work show that fracture pressure gradient is a function primarily of overburden stress gradient, pore pressure gradient, and the ratio of horizontal to vertical stress. There is argument for a fourth variable in that in many cases breakdown fracture pressure gradient is greater than the fracture extension pressure gradient. However, if the fracturing fluid is able to penetrate the formation through the pores or existing cracks, there is very little

Jan 1, 1970

By Thomas Leonard Watson

Jan 1, 1906