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By B. T. Brady

Rock mechanics, like all engineering disciplines, must have a theoretical foundation. The subject of this chapter is the formulation of analytical methods that may aid in the rational design and determination of the stability of engineering structures in competent brittle rock materials. By an engineering structure in rock, we mean any (1) excavated sub- surface opening, (2) open surface structure, or (3) system of openings in rock that is virtually self-supporting-that is, not requiring artificial systems to carry structural stresses.

Jan 1, 1970

By Joseph E. Pogue

THAT the domestic consumption of gasoline displays a marked seasonal variation, with a low in the winter and a high in the summer, is well known. It is logical to expect that the nature of the variation has itself been undergoing a change as a result of improvement in roads, general employment of closed cars; and growth of mass haulage; but so far as I am aware the change in seasonal variation has never been investigated and measured. It is the purpose of this paper to present the method and results of such an investigation undertaken as a contribution to the technique of planning operating schedules now so prominent in connection with the functioning of the industry under a Federal quota system. For the method employed I am in-debted to the suggestions and help of Frederick R. Macaulay', who kindly looked over the work sheets; and credit is due Barnabas Bryan, Jr., for assisting in the computations and the graphic work. Ideas for the approach to the problem were also derived from an article by Aryness Joy, and Woodulief Thomas of the Division of Research and Statistics of the Federal Reserve Board*-.

Jan 1, 1934

By E. L. Vickers

Over the years, the pure theorist in economic analysis has accumulated a formidable array of facts in bringing his subject matter under control. Business managers and mining engineers are aware of the theorist's weapons, but the question of applying them to the mastery of practical problems seems hardly feasible, especially in view of the almost innumerable variables plaguing the everyday scene in the mining enterprise. One such sophisticated tool of long-standing in the theorist's arsenal is marginal analysis. Equally long-standing for the operating company and valuation engineer is the problem of defining the cut-off grade the point below which a mineral re- source ceases to be economically amenable to extraction. In other words, what part of a mineralized body of rock is ore and what is waste?

Jan 6, 1961

By Walter E. Mingramm

THE construction of rescue-apparatus on the principle of furnishing the wearer with air from a tank containing it under high pressure was given up by inventors about 20 years ago. Such an apparatus must supply continuously, for not less than two hours, nearly 50 liters of pure air at atmospheric pressure per minute, or a total of 6,000 liters (210 cu. ft.); and a cylinder containing this amount of air, under 2,000 lb. pressure, would weigh 180 lb. or more. Although apparatus has been recently constructed utilizing liquified air, no experiments have been made to determine the regularity with which the air is generated, nor has its chemical composition been determined. Moreover, the chief objection to such an apparatus is the' difficulty and cost of keeping on hand a large quantity of liquified air. The system of furnishing the wearer of a breathing-apparatus with air which has given the best results, and has found employment in all the devices now in practical use, is that in which the air contained in the human lungs at the beginning of the work is regenerated by the apparatus. By means of chemicals, such as caustic potash and caustic soda, the carbonic acid gas, CO., exhaled is absorbed, and the oxygen that has been consumed is replaced from a tank containing this gas under high pressure. The pressure of the oxygen (which is 1,875 lb. in the two cylinders at the beginning of the work) is automatically reduced to 75 lb., and is sufficient to keep the air inside of the apparatus in constant circulation, and to force it to pass through the chemicals provided for the absorption of the CO, gas. In the attempt to construct an apparatus which would (1) furnish the wearer with a sufficient supply of air; (2) replace the amount of oxygen used up by the lungs during the time of

Jan 7, 1908

By E. W. Johnson, M. L. Hill

Cold working of iron-carbon alloys was found to increase greatly the hydrogen solubility and to decrease the diffusivity at temperatures up to 400° C. These effects are increasing functions of both the carbon content and the degree of deformation. The hydrogen behavior is consistent with the idea that cotd working creates "traps", which are concluded to be microcracks in which the hydrogen is chemisorbed. Hydrogen embrittlement is explained by the Petch theory of metal crack surface energy loss due to hydrogen adsorption. HYDROGEN embrittlement of steel has been studied for many years and has been the subject of an extensive literature, but the mechanism of the effect has not been completely understood. The embrittlement is unusual in that the ductility loss is not accompanied by an increase of the yield strength, being primarily a decrease of the fracture strength alone. The loss of fracture strength is usually most severe in the temperature range between 0°and 100°C. Here the solubility of hydrogen in the iron lattice at ordinary H2 pressures is extremely low while the diffusivity is still quite high. From the relationships between the ductility and the hydrogen content, test temperature and strain rate, it is apparent that the hydrogen atoms causing the ductility loss difbse to and concentrate in small regions of the metal which are especially susceptible to the initiation and propagation of fracture. This hydrogen segregation apparently occurs after plastic straining has begun. Below 0°C the ductility loss persists only at low strain rates in confirmation of the view that the embrittlement is diffusion .controlled. The tendency of the embrittlement to disappear above 100°C can be explained by the increasing lattice solubility of hydrogen with rising temperature. A common view of hydrogen embrittlement of steel is that the hydrogen initially dissolved in the metal lattice diffuses to structural discontinuities and there precipitates as H2 gas at very high pressures which assist the external stress in causing premature failure.1,2 The idea of a high H2 pressure in equilibrium with ordinary amounts of hydrogen in steel at room temperature is due to observations of hydrogen behavior in fully annealed material, for which the Sieverts' law constant relating solute concentration to H2 pressure is extremely small. Hydrogen-embrittled steel, however, is always plastically deformed to some extent, and therefore it is important that hydrogen embrittlement be explained primarily in terms of hydrogen behavior in plastically deformed material. Such an explanation is attempted in this paper. Previous studies of hydrogen in cold-worked steel have shown that both the solubility and the diffusion rate are significantly chaned when the steel is cold worked. Darken and Smith discovered that the amount of hydrogen absorbed from acid by cold-rolled steel at 35°C is many times greater than that absorbed by hot-rolled steel. They found also that the hydrogen permeability of the steel is unaffected by cold working. Keeler and Davis4 confirmed the high apparent solubility of hydrogen in cold-worked iron-carbon alloys at temperatures up to and even beyond the recrystallization temperature. They also found that this solubility increase accompanying cold work is a sensitive function of the carbon content, being absent when no carbon is present. The present experimental study was undertaken primarily to obtain an improved understanding of the behavior of hydrogen in cold-worked steel. Data were obtained on the effects of temperature, H, pressure, carbon content, and degree of cold work on the hydrogen solubility and diffusivity in iron-carbon alloys. These data have been helpful in elucidating the nature of the cold-worked steel structure as well as in providing information on the mechanism of hydrogen embrittlement of steel. EXPERIMENTAL Cylindrical specimens for hydrogen absorption and diffusion rate measurements were prepared from three iron-carbon binary alloys and a commercial SAE 1010 steel. The iron-carbon alloys were prepared by vacuum melting electrolytic iron with graphite in a magnesia crucible. The alloys were cast in vacuum as 2 1/2-in. sq ingots weighing about 20 lb each. The ingots were hot rolled (above 1900°F) to 5/8-in.-diam round bars and then cooled in air to room temperature. The resulting metallographic structure consisted of islands of fine pearlite surrounded by free ferrite. Chemical analyses of the materials are given in Table I. The 5/8-in. diam bars were turned to diameters such that cold reduction to the desired final specimen diameters would result in either 30 or 60 pct reduction in area (RA). The machined bars were then cold worked by swaging at room temperature

Jan 1, 1960

By J. J. Carrigan

IN all mining operations a considerable portion of the work performed, especially underground; is accomplished under artificial light, yeti this subject is often not given proper attention. Poor illumination decreases mining efficiency, impairs the sorting or grading of ores, and increases the risk of accidents. In the beginning, and for several years afterward in the metal-mining industry of Butte, Montana, candles placed in candlesticks were carried by the men. Sconces or holders for candles were also provided at stations and curves in drifts to furnish better light for men engaged in. hand tramming. It was also common practice to place clusters of candles on the ground, with no provision for guarding against an underground fire other than the exercise of sufficient care by the men themselves. An accumulation of candle grease from this source was the direct result of the first serious fire in the Anaconda mine, in 1889.

Jan 1, 1936

By R. L. Slobod, C. Gatlin

This .study defines the basic mechanism of the mis-cible displacerrzent of oil and writer from porous Medici by various water-driven alcohol .slugs. Three distinct alcohol slug processes were .studied. Considerable data concerning the quanity of alcohol required for oil recovery were also obtained. All data were obtained in a 1-in. diameter, 100-ft long, unconsolidated core. The porosity of this system was 35 per cent. and the permeability was approxitrlately 4 darcies. Total core pore volume wax 5,716 cc. All displacements were conducted at a constant injection rate of 5 to 6 cc//min, which corresponds to a frontal advance of 5 ro 6 ft/hr. The first portion of this paper is concerned with 111 use of one alcohol—isopropyl—a\. the slug material. Isopropyl alcohol (IPA) is completely miscible with both oil rind water; however, miscibility of the threc-component systems, oil-water-IPA, requires a relutively. high concentration of IPA. Hence, the displocement is not of the misoible type unless the IPA concentration is maintained above some critical value. A slug of IPA equal to only 13.5 per cent of the pore volume was jound to be sufficient to obtain complete recover?, of residua1 naphtha. In later studies two distinct process variations were developed. The firsr of these utilized methyl alcohol (MA) and IPA as slug materials. It was shown that methyl alcohol may he substituted for IPA at the front and rear of the slug with no loss of oil recovery. A .slug of 4 per cent MA-4 per cent IPA-4 per cent MA was sufficient for complere oil recovery. Because MA is considerably cheaper than IPA, this represents an important step toward economic application. A .second process variation used normal butyl alcohol (nBA) and MA as the composite slug, the nBA segnzent being injected first. This technique requires the smallest total slug size (approximately 10 per cent) of all processes studied. The high cost of nBA, however, precludes commercial application. It is possible that this basic process, subject to changes of alcohol type, may lead to a commrercicil process. INTRODUCTION Within the last 10 years, considerable study has been devoted to the general mechanics of miscible phase dis- placements in porous media. These studies have. in general, dealt with two-component displacernent. All reported field trials to date have been modified gas drives of one type or another. These utilize either lean gas at high pressure, rich gas at lower pressure or an LPG slug. The irreducible water content of the reservoir remains immobile during these processes. Although these techniques hold great promise. certain drawbacks do exist. Poor areal sweep efficiency, inherent in any displacement having a highly unfavorable mobility ratio, is one disadvantage. Furthermore, the miscibility of all processes which use gas is dependent on pressure. These pressure limitations may prohibit application to shallow reservoirs. There are also many areas where large quantities of LPG and natural gas are not readily available. These factors emphasize the need for improved techniques. The alcohol slug process is also a miscible-phase displacement process. It differs from the previously mentioned two-component techniques, however, in that both the reservoir oil and water are displaced by the slug. This behavior is a consequence of the miscibility of certain oil-water-alcohol systems. In the simplest case, a relatively small volume (slug) of an alcohol (such as isopropyl) is injected into the system. Water is then used to drive the slug through the medium. Thus. three components—-alcohol. oil and connate water-—exist at the front side of the slug. Miscibility is obtained at some alcohol concentration, this being dependent on the solubility of the particular system. Miscibility is maintained within the slug until the alcohol concentration falls below that value required to maintain miscibility. When miscibility is lost, the process reverts to a water flood. Certain inherent benefits of this technique are apparent. High pressures are not necessary to obtain miscibility in these liquid systems. Furthermore, water is a more desirable driving agent than gas because of the improved mobility ratio and the attendant improvement in areal sweep efficiency. The main disadvantage is, of course, the relatively high cost of alcohols. The use of an alcohol slug to recover reservoir oil is not a new idea." ' However, this process has received only limited study, presumably due to the lack of industrial interest caused by the seemingly prohibitive cost of alcohols. The main purpose of this study was to investigate the mechanism of the displacement of oil and water by various alcohol slugs and to develop process modifications aimed toward possible commercial application.

By Alvinus Brown Wood

THE ancient copper-mines of Lake Superior, having been destroyed or covered by-modern mining-dumps, are not accessible to the present inhabitants of that region, and, since no more are likely to be found, some account of those already discovered, from one who has seen them, may be acceptable to the Institute. Early in May, 1855, 1 took a party of men to open an ancient pit on the Quincy mine-location. Mr. C. C. Douglas was the Agent.," as mine-managers were then called on Lake Superior. The Quincy Co. had previously done work on a fissure-vein, several hundred feet west of the Amygdaloid lode (afterwards called the Pewabic lode), on which was the ancient pit herein described. It was at this pit that the Quincy' main shaft was subsequently stink. The ancient pit showed an apparent depth of about 4 ft., but when cleaned out it was shown to be 14 ft. deep, having been filled up by the sliding-in of material composed largely of broken rock, taken out in sinking the ancient shaft, and left near its mouth. Midway of the shaft, and below water-level, was found a scaffolding, of white-birch poles,- which had been used as a landing, to assist in removing the excavated rock. The shaft was 7 ft. in diameter. The excavation had been done by first building fires in order to disintegrate the rock, as was proved by the abundance of charcoal found; then breaking the softened rock with hammers of diorite, such as is found in the greenstone range on Keweenaw point. These hammers had about. the size of large paving-stones. Only broken ones were found, the whole ones having been doubtless carried away for other work, such as could be traced on the lode for a hundred feet or more to the south. At the place where this shaft was stink, barrel-copper (i.e.,

Mar 1, 1906

By Betty L. Gibbs

A company must have an organized approach to effectively sort through the profusion of available software and hardware and find the programs and equipment which fit defined needs. The selection process must build a complete compatible system which includes hardware and software. The methodology presented in this paper helps identify some of the more important considerations. The steps needed for an organized approach to software/hardware selection are: •All involved staff should contribute to an assessment of current computer capabilities and projection of future needs. •Alternatives are analyzed to determine what software and hardware is available and how selections may possibly be merged into the existing computer system. The evaluation process focuses on details of program capability and hardware compatibility. Analysis must be done to determine how closely individual programs fit the established requirements. The final decision is often a balance of needs between program capabilities and hardware availability. Any programs selected must be able to run on existing and newly purchased hardware. Any additional hardware selected must be capable of meshing with the available computer system.

Jan 1, 1983

By Arthur C. Spencer

IN extension of a suggestion already made to account for certain features observed in the Juneau gold-belt in southeastern Alaska,' it is the object of the present paper to indicate in detail certain conditions in which deformation of rocks under their own weight might lead to the production of fractures in which veins could be deposited. A direct, uniformly-distributed pressure of sufficient intensity applied to an elastic brittle mass offering strong resistance to deformation produces rupture. In a material of ideal properties the surfaces of rupture under such pressure would be shearing planes inclined at 45° to the line of force, unless there be preliminary deformation, in which case this angle would be greater than 45°. This general conclusion, resting upon ana¬lytical mechanics, is completely supported by the results obtained by Daubrée in experiments upon the deformation of wax and resin prisms under compression. Let us then first con¬sider one of Daubrée's diagrams. In the case illustrated in Fig. 1, four sets of fractures in two appproximately right-angled pairs (that is to say, in conjugate sets) were produced by end-wise compression of the square cross-sectioned prisms. These fractures cut the axis of compression at approximately equal angles, not varying greatly from 45°. The location of the four sets of fractures is obviously determined by the shape of the prism, since the material in each corner acts in a way as a buttress, permitting the bulging to take place most readily on the sides. By limiting the directions in which bulging may take place, results of a more simple nature could be obtained. Take, for instance, a square prism and place it between two fixed and

Nov 1, 1905

JOINT convention week has become a feature of the year with western mining men. The first was held at Denver in 1926, the second at Salt Lake City in 1927, and the third is about to take place at Los Angeles. Holding in the same city in one week the meetings of a number of related organizations has been .found to permit the development of a well-rounded program at the same time that it economizes time and money for the members, many of whom belong to several of the participating organizations. For the third time, the American Mining Congress, represented by its Western Division, of which Philip Wiseman is chairman, is taking the lead and assuming the main responsibility. The A.I.M.E. is furnishing the papers for two sessions and the California Development Association for one. The Southern California Section, Robert R. Boyd, chairman, is host for the Institute, but the Northern California, Nevada and Arizona sections have each contributed papers to the program, and will be represented at the meeting. It will be a real reunion of the mining men of the Southwest.

Sep 1, 1928

By AIME AIME

THE following brief description of the main features of the, engineering work was prepared for the use of members of the American Society of Civil Engineers and members of the American Institute of Mining Engineers on the occasion of their visits to the tunnels at the time-of their respective. annual meetings in New York, January and February, 1905. DESCRIPTION. Those portions. of the Pennsylvania Extension into Manhattan and Long Island, lying east of the Terminal Station and west of the East River, have been designated as the " Manhattan ?Cross-town:. Tunnels." They traverse a section of the city second in importance only to the financial district, and one that includes the larger hotels, retail shops and theaters and the residences of many of the best known citizens. Section "D," consisting of twin tunnels for west-bound express and local passenger traffic, lies under Thirty-third Street from a point 400 ft. west of the west line of Sixth Avenue, eastward to the river shaft, situated in the block between Thirty-third and Thirty-fourth Streets east of First Avenue. Beginning at the east end, the tunnels are in separate excavations, leading westward from the subaqueous tubes, on a curve of large radius, gradually closing together until it is found more appropriate to drive them in a single excavation. At a point just west of Second Avenue they reach the tangent, aid from there westward lie directly under Thirty-third Street. At a point about 180 ft. west of the west line of Sixth Avenue, the center concrete-wall between the twin tunnels is omitted, and the excavation somewhat widened to make room for a third storage-track, and the tunnel continues to tile station portal in three-track section. Here reprinted through the courtesy of The United Engineering and Contracting Co. The half-tone blocks used for the illustration of this paper have been kindly supplied by the Chasmer-Winchell Press of New York, Pittsburgh and Cleveland.

Mar 1, 1908

By Bauer, Alan

In considering blasting it is necessary to consider the drilling and explosives since one is generally concerned with the total cost of muck of a certain size in the pit or through the crusher. To get a current idea of the drilling situation in open pit mines plotted in Fig. 1 are the drilling costs per ton of material vs. hole diameter for rotary drill holes in large limestone, iron ore and taconite operations. The exception is the 2-in. diam hole which was drilled with a percussion drill in limestone.

Jan 1, 1968

By Lawrence Addicks

ONE of the properties of copper, which has done much to give it its present prominent place among the useful metals, is its electrical conductivity, a property which has now become the chief criterion of 'the value of the commerical product. In pursuance of that distinctively American principle that, 1' the best is none too good," metal of the highest conductivity is usually called for even where such extreme purity is of no advantage, for instance, in the making of brass and other alloys. The average brass-founder feels nervous unless his copper is so very pure that it shows a conductivity of 99 or 100 per cent., while the character of the zinc used is usually overlooked in his anxiety. Electrolytic refining has made it possible to produce copper of a' very high degree of purity, the metallic impurities averaging but a few thousandths of 1 per cent.; oxygen, usually present in the form of cuprous oxide, bringing the total up to about a tenth of 1 per cent. The published data bearing upon the relationship between chemical purity and electrical conductivity is, however, very scant,' nearly all the work that has been done having dealt with alloys carrying considerable quantities of the foreign elements. In this paper I have brought together the results of experiments extending over a period of several years that have been carried out with the idea of determining the amount of various elements which would lower the conductivity 3 or 4 per cent.-a series of impure coppers rather than alloys. There are many precautions necessary to keep the conditions

Mar 1, 1905

By G. S. Hume

RECENT developments in the Turner Valley gas and oil field, 40 mi. southwest of Calgary, Alberta, have indicated a large producing crude-oil area. Drilling be¬gan in Turner Valley in 1913 but no major developments took place until the fall of 1924, when Royalite No. 4 well at a depth of 3740 ft. in the upper part of the Paleozoic (Mississippian) limestone obtained a production - of 20,000 M cu. ft. of gas with a content of about one imperial gallon of naphtha (73° A.P.I.) per M cu. ft. This well produced as much as 600 bbl. of naphtha per day, and until abandonment in 1934 produced 911,313 bbl., which together with the gas sold was valued at about $5,000.000.

Jan 1, 1937

By AIME AIME

THE fall meeting at El Paso this year (Oct. 13¬15) will be of unusual interest due to the international atmosphere imparted by the many engineers from Mexico, who are making arrangements to attend this meeting. The meeting will be held jointly with the Western Division of the American Mining Congress. Cooperating in the program will be the representative society of Mexican engineers known as Centro National de Ingenieros of Mexico City, who are plan¬ning on sending many delegates and well known Mexican engineers to the convention. The cooperation of the West Texas Geological Society and the American Association of Petroleum Geologists has also been secured. Brent N. Rickard, manager of the El Paso Smelting Works of the American Smelting & Refining Co. at El Paso, Tex., is general chairman in charge of arrangements. He is receiving splendid cooperation from the Mining Department of the El Paso Chamber of Commerce and from the business people of El Paso, who feel highly honored in having these mining societies meet with them this year.

Jan 1, 1930

By John P. Cosgro

THE increasing use of internal furnace-boilers for mining power-plants (doubtless due to the facility with which they may be installed by reason of their portability; the fact that they require no masonry setting, cast-iron fronts, buck-stays, etc., and practically no foundation; and the successful maintenance of their claim to equal and even superior economy, as compared with boilers of other types) warrants this description of a method of remedying an injury which may occur, to such a furnace, even though it satisfies the requirements of the formula adopted by the U. S. Board of Supervising Inspectors of Steam Vessels.2 I refer to the sagging and deformation which may result from overloading the boilers for a considerable period-say, several days. This is sometimes unavoidable under the exacting conditions of continuous day-and-night service, and (in spite of all rules and precautions, the occasional careless or unskillful work of attendants. Such a trouble is by no means unknown on shipboard, where this type of boiler is so largely employed. In the case here described, two Morrison suspension-furnaces, of half-inch steel, 14 ft. long and 45 in. in mean diameter, with ? dry-back ? boilers, were necessarily operated somewhat beyond their rated -normal capacity for several months, while a third similar unit was -in process of installation, and during this period, though the boilers were kept perfectly clean, heat seems 'to have been generated slightly faster than it was absorbed by, the water in the boilers. The corrugations of this.

Mar 1, 1905

By E. P. Abrahamson, S. L. Lopata

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deforlnation gradient matrix, F - [axi/aXj/ where X and x refer lo the initial and final positions of a particle. This matrix is readily evaluated in termas of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip systena. In the case of deforma tion from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Göler and Sachs.4 Taylor and Elam1 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, ! terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(aN as N — m while a — 0 in such a way that the Product Na = a finite conslant designatzng the accumulated amount of shear. It turns out that this limit is simply eafF1, where F, is the matrix whose elements are the coefficients of a in the F(a) twatrzx. Application is made of the present treatment to a fcc crystal of Permalloy compressed on the (110) plane and contrained to elongate in the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to (xl,xz,x3), both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By F. C. Bond

Since the Third Theory of Comminution was presented eight years ago (I) it has found increasing use in crushing and grinding problems. The practical utility of its wok index equation is quite generally acknowledged (2). However, its theoretical basis has been questioned in at least three technical articles (3) (4) ('). The purpose of this paper is to present experimental proof that it is scientifically correct. Particles under compressive stress are strained and deformed. They absorb strain energy, and when this locally exceeds the breaking strength, a crack tip forms. The surrounding strain energy flows to the crack tip, which rapidly extends and splits the rock, releasing the strain energy as heat. The initial energy flow causes additional crack tips in highly strained areas. If the compression is rapidly applied by impact, crack tips may form before the strain energy has reached equilibrium in the particle, thus decreasing the total work input required for breakage. The energy necessary to break is essentially the energy necessary to produce crack tips, since the energy necessary to extend the cracks to breakage is already present as strain energy in the deformed particles. After breakage nearly all of this energy appears as heat. The crack length cannot be measured directly. However, in particles of regular and similar shape the crack tip length is considered as equal to the crack depth, or crack extension necessary to break, so that the crack length equals the square root of one-half of the surface area. The Third Theory states that the useful work done in crushing and grinding is directly proportional to the total length of the new cracks formed. It can be confirmed by showing that a constant work input produces a constant length of new cracks when reducing the same material to different product sizes. This is done in the present paper on a wide variety of material. The constant work input was supplied by one revolution of the 12" x 12" laboratory ball mill used in making grindability tests by the Allis-Chalmers method (12) (13) The new crack lengths produced per mill revolution were measured from all available grindability test results at 28, 35, 48, 65, and 100 mesh on fifteen different ores, and were found to remain substantially constant for each ore at all mesh sizes. A new technique is used for the measurement of crack lengths. Size distribution plots of the mill feed and product are made by the Third Theory method (9) and the crack lengths are obtained from these plots by the procedure described in the present paper. The energy input required to produce a unit length is of fundamental importance in the size reduction of brittle solids. The crack length Cr is expressed in centimeters per cubic centimeter of solid material. It bears a definite relationship to the external surface area of the crushed or ground solid. A uniform particle shape must be assumed before the surface area and crack length can be evaluated. In this paper it is assumed that the relationship between the surface area and the particle volume of a particle d microns in diameter is the same as that of cube d microns on a side. The external surface areas of particles with a cubical breakage probably agree approximately with this rule, and correction factors can be applied when physical measurements of the surface areas are available for comparison. However, the assumption of equivalent cubes has been found satisfactory for most calculation purposes. Assuming equivalent cubes, one cubic centimeter of particles d microns in diameter will have a crack length Cr of v30.000/d centimeters, and a surface area of 60,000/d square centimeters. The specific crack length is thus equal to the square root of one-half the specific surface area. Where Sa is the surface area in square centimeters per gram and Sg is the specific gravity of the ground solid, then Cr = vSg . Sa/2 = 173.2/ vd (1)

Jan 1, 1961

By JOSEPH MACDONALD

STRIPPED of its romantic possibilities, mining is a commercial business, carried on for the profit there is in it, and the business of the manager, in its ultimate analysis, is to make the profit as large as possible. The general manager of a mining company should keep himself personally familiar with all the details of its operations. If be fails to do so, chaos results, labor becomes inefficient, costs go up, and profits go down. Nowhere is this emphasized more than in Mexico. If the mining operations are extensive and complex, involving, besides the work of mining the ore, its transportation and treatment by various milling operations, and the marketing of the products, the business, to be carried on properly, must be divided into a number of main departments, which are subdivided into minor departments. Each main department should be under the immediate charge of a superintendent, or a foreman, and each minor department under a shift-boss. Organized in this way, and with all the principal centers of activity connected by telephone, the manager can keep in touch at all times with the details of every branch of the business, and be in a position to perform effectively the full duty of manager. The ?total cost of mining operations may be broadly divided under the heads of Labor, Supplies, and Marketing. Of these, it will be found, on averaging a number of cases, that the cost of labor will be about two-thirds of the total cost. The importance, therefore, of an efficient labor-department will be apparent. This department must be sub-divided and organized differently, according to the peculiar conditions at each mine, and no one system, however well suited for one particu-

Jan 1, 1909