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By K. C. Ko, D. A. Pifer

The theory of probability with respect to the failure of structures is discussed. It is shown that the probability of safety, probability of failure, and factor of safety are directly related to each other and that as standard deviation approaches zero, the probability curves approach a unit step function which can be interpreted as the conventional factor of safety. The factor of safety is numerically the ratio of the load to the strength of the material at a particular point or plane in an engineering structure. Mathematically, it can be illustrated as a unit step function undefined at the point where the factor of safety is one (Fig. 1). The uncertainty of variation of soil and rock strengths require factors of safety much higher than those used in other engineering structures. The factors of safety used are generally determined from past experiences with similar structures. However, the factors thus determined do not have any theoretical meaning or do not indicate any relationship to actual safety.' It seems, therefore, logical to develop a system with a sound theoretical basis to obtain a more suitable factor of safety for structures. An application of elementary theory of probability indicates that it is possible to relate this number to theoretical and practical engineering facts.

Jan 1, 1971

Jan 1, 1967

By D. G. Westlake

Levine has concluded that prismatic slip in titanium is controlled by two distinct thermally activated processes in the temperature ranges O° to 220°K and 220" to 300°K. We feel that his evidence is not convincing. He has drawn a curve through the plot of activation volume u* vs temperature T with a break at 22WK, Fig. 2. We believe that considering the possible experimental error apd the fact that there are only four points between 4° and 196°K, one could be justified to represent these points by the smooth curve we show as a solid line in Fig. 12. Levine believes that (8rf/aT)+ is discontinuous at 220°K, but he hints that he recognizes the possible doubt. We doubt seriously that the results shown in Fig. 1 indicate a discontinuity at 220°K. Certainly if he were justified in drawing a straight line through only four points on Fig. 2, we are even more justified in drawing straight lines through the seven points between 77" and 297°K on Figs. 1 and 3, because a straight line touches all seven of his circles. If his measurements of t were so precise that his decision to draw two curves in Fig. 3 is valid, then the experimental technique is deserving of further mention. We have drawn a smooth curve through the results in Fig. 3 and used this and the curve in Fig. 12 to obtain the values of shown in Fig. 13. Finding continuous is a contradiction of Fig. 4, which deserves comment itself. Levine obtained the solid circles in Fig. 4 using Fig. 2 and a smooth curve through the points shown in Fig. 3. We have replotted these solid circles in Fig. 14. We submit that there is no basis for his two straight lines (dashed in Fig. 14), and therefore have superimposed the curve that we believe is indicated. Certainly, there is reasonable doubt that a discontinuity in dH/dT exists at 220°K, even when one accepts Fig, 2. Furthermore, if one draws the straight lines indicated by least-squares treatments of the results presented as open circles in Fig. 4, their intersection is at about 196°K, not at 220°K as shown. Thus the alleged agreement between Figs. 3 and 4 with respect to "break" temperatures is not apparent. In Fig. 9, Levine has drawn a straight line very much different from the one indicated by a least-squares treatment. Obviously, he has done this because he recognized that H = 0 when T = 0. He is consistent in drawing the low-temperature curves in

Jan 1, 1968

By R. S. Montgomery

Laboratory experiments simulating rock drilling were conducted on a number of commercial grades of tungsten carbide in order to determine their wear rates when they are used as inserts in percussive rock drill bits. The test rock was Barre granite and tests were made at conditions similar to those of the carbide buttons near the periphery of a large, down-hole, button bit. In addition, some wear rate measurements were made at a low blow energy. Wear rates of these carbide buttons were an extremely sensitive function of their cobalt contents and hardnesses and were proportional to e-°.57Hup to a hardness of about 91 RA. The point of minimum wear rate, which occurs at about 92 RA, corresponds to the point of maximum compressive strength. Modern percussive rock drill bits have inserts of cemented tungsten carbide on their wear faces. These inserts have drastically reduced bit wear in comparison to that of earlier all steel bits. The most common cemented carbide grade used in percussive rock drill bits contains about ten weight percent cobalt, although grades containing more or less cobalt are also used. Contrary to the case with carbide in metal-cutting tools, alloying materials are rarely used in mining grades. There are a number of designs of rock bits in current use. The most common form is an X bit which has four chisel-form radial wings. The button bit is another important design and one which has been recently developed. This design uses a flat steel face studded with relatively small hemispherically tipped carbide buttons. These types are illustrated in Fig. 1. Studies have been made of the sliding wear of cemented tungsten carbide on rock 1-4 and multiple-impact fracture', 5-6, b~t there has been comparatively little published on the percussive wear of this material although the wear of the impact face is the most important. There is some available data on the rate of dulling of rock bit inserts in actual drilling 7 but no laboratory studies. Sliding wear studies are useful for understanding the wear of coal and mineral cutting tools and gauge wear of percussive drill bits. but the

Jan 1, 1970

By H. P. Willard, R. W. Gates

Basic Inc., has been mining magnesite and brucite for 27 years at Gabbs, Nev. This is a medium sized open-pit mine. The magnesite deposits are in north-western Nye County about 30 miles east of Luning, Nev., on the west slope of the Paradise Range, at an elevation between 5000 and 6000 ft. The magnesite and associated brucite is used to make magnesia refractories employed principally in the steel industry and magnesium oxide for various chemical uses.

Jan 10, 1963

By Paul H. Lu

Methods and results of measuring three basic parameters for ground stability control, ground pressure, strata movement, and geomechanical properties of mine rock are presented in this paper. It is found that these parameters can be measured in situ by simple and practical techniques with nonsophisticated and inexpensive instruments. Specifically, a drillhole dilation technique employing a cylindrical hydraulic borehole pressure cell (CPC) was used to determine the modulus of rigidity. Premining ground pressures were determined by pressure convergence tests with a combination of one CPC and two pre-encapsulated flat hydraulic borehole pressure cells (BPC) installed in a single drillhole. Abutment pressures and pillar loading were monitored with BPC's. Differential strata movements and bed separations were measured with self-recording 10-anchor-point extensometers. Roof-to-floor convergence was measured with self-recording convergence meters. Some applications of these in-situ-determined parameters to mine design and ground stability control are also discussed.

Jan 1, 1984

By H. F. Silliman, Daniel R. Hull, Earl W. Palmer

THE brass-rolling industry has not had a great deal of experience with antimony in its product. There have been some recent excursions with antimony as a corrosion inhibitor in tubes, but in sheet brass it has been regarded with apprehension and generally avoided. This is not to say that [ ] contaminations have never occurred, and probably a great many brass mill men have had their own ideas on the effect of such contamination. Our own views were based upon certain experiences some years ago with strip castings that split lengthwise in the early stages of rolling. The nature of this splitting is shown in Fig. I, from a photograph taken in 1922 as a record of 20 bars of 65-35 common brass made with an antimonial brand of copper. These bars were cast 6 ¾ in. wide by 1 in. thick by 45 in. long. In the first pass through the rolls, 19 of the 20 split lengthwise throughout their length, while each half curved outward in a wide arc as it emerged from the rolls. [ ] In those days, if splitting was not a frequent occurrence, it was not unfamiliar. One can recall periods of short duration when large amounts of common brass would behave in this way. There was nothing imaginary about these spells. The affected metal would split lengthwise in the breaking rolls, and no maneuvering of mill practice made any difference. The condition would descend like a plague, demoralize the mill for several days, and disappear. It is doubtful if anyone knew the cause-however many explanations may have been current. In 1921 a quantity of split brass was traced to the use of fired small-arms

Jan 1, 1943

By C. Dinis da Gama

Because of the growing importance of back analysis for the interpretation of rock slope failures, particularly in open pit mines, it is suggested a methodologic sequence of activities for dealing with those problems. The principal mathematical tools for the interpretation of the most common mechanisms of slope failures are reviewed, including methods of stress and strain analysis, which seem to be more powerful for parametrization studies, and for developing more realistic explanations of slope behaviour, such as the measurement of displacements. An application of those methods is described, using slope failures detected in a Brazilian uranium mine (Cercado), thus providing reliable shearing strength parameters for the rock mass discontinuites, which were used in the final pit design. The concept of using backanalysis results to supply input data for pit design was implemented by means of the excavation of an experimental trench within mine limits, where specific instruments were installed, and several slope failures were monitored and backanalysed, in order to yield information about sliding mechanisms in the future open pit.

Jan 1, 1983

By JOHN W., E. C. SARCENT

The South Texas area discussed herein represents districts 2 and 4 of the Texas Railroad Commission. It extends from Jackson, Lavaca and Gonzales Counties on the northeast to the Rio Grande River, and comprises a total of 26 counties.

Jan 1, 1946

By Frederic Benard

PRIOR to 1936, the Ontario Refining Co. received all incoming blister copper from The International Nickel Company's smelter in the usual form of 460-lb. cakes, or slabs. These were received in open cars in lots of 250 pieces. At the refinery the cakes were unloaded onto narrow-gauge cars, for convenient handling and pickup by charging cranes. In March 1936, an investigation was started on the feasibility of transferring converter copper in the molten state from the smelter to the refinery anode furnaces, a distance of 1 ¼ miles. Although common in steel practice, the transportation of blister copper in this form had not previously been attempted and a preliminary study of the various factors involved was therefore necessary. For this purpose, a series of experiments was made in which molten copper, removed at different stages during the furnace cycle, was held in a small portable holding furnace. This vessel was essentially a refractory-lined steel cylinder provided with ports for filling and emptying, heated by an oil burner. Dimensions of the steel shell were 3 ft. 10 in. diameter by 7 ft. 3 in. long, and thickness of refractories depended on the design and combination used for the particular experiment. The vessel was filled with approximately 2 ½ tons of copper at a predetermined temperature, the lining having been preheated to a definite point by means of an oil burner. All openings were well luted and temperature readings were made every 15 min. by means of an immersion-type thermocouple. In this manner the rate of heat loss resulting with different refractory design could be developed. The ratio of exterior surface to weight of metal was taken into consideration in comparing the experimental results with what might be expected for a full-sized unit, and observations were also made on type and degree of slag accretion. It was not possible to get as much information on this latter point as desirable, but all evidence showed that the problem would be control of slag build-up rather than attack on refractories. From the information derived, and in consultation with the engineering staff of the supplying company, an order was placed for the first

Jan 1, 1938

By Enrique Touceda

FOR a number of years prior to the world war, the firm of Geo. H. Thacher & Co., of Albany, N. Y., was engaged in the manufacture of marine and other gray-iron castings. At -the outbreak of the war the firm decided to specialize in the manufacture f propeller wheels. It attacked the problem, therefore, from a foundry point of view, seeking to produce a casting that would be so accurate that no subsequent machining would be required on the blades, also from the point of view of the ship builder. There were two general methods f manufacture, the shortcomings of which have been freely acknowledged. In the sweep method, the nowel, or bottom half-mold, for each blade is swept up by a spindle beam and pitch race, while the top half-mold for each blade is built up individually. In the pattern method one individual blade, with the hub or hub portion, is mounted on a spindle and the individual -blade mold formed, the pattern is then rotated on the spindle to the position- for the next blade, etc. In rare cases wheels were made from a solid pattern. Owing to the cost of the pattern, its failure in many instances to be correctly made, and (when made of wood) its early and sure distortion the disadvantage of this practice is obvious, while metal patterns in most instances were prohibitive in cost. In these methods both green-sand and loam molding was practiced. The casting produced by either method can be considered only as a blank from which the propeller must be machined. The back surface f each blade must be chipped too the templet and through this procedure chipped to such accuracy, as will be required for a static balance. Inasmuch as the' work done by the machine tool is confined to the driving face of the blades, not only is perfection most difficult, but corrosion will be greater because of the removal of the dense skin f the casting and the local strains set up by the pneumatic tool in chipping. To produce a finished 9-ft. propeller for a Navy destroyer required from 8 to 21 days f foundry work and about the same length of, time for the machining. Through the use f the Thacher process, only as many hours are required, besides it is possible to produce a finished casting in perfect conformity, with any particular propeller-wheel design,

Jan 4, 1921

By P. O. Metz, E. L. Wiehe, J. S. Foster

BASED on their analyses of growth kinetics, ibbs' and Harris et al.' have recently proposed that the rate of subcritical graphitization of steel is controlled by the rate of diffusion of carbon in ferrite. illert has concluded that this is the rate controlling growth mechanism when the growing graphite particles are relatively large. Harris et al.' also propose that the matrix surrounding a growing graphite particle is plastically deformed to make room for the growing particle. If this plastic deformation does occur, then preferred recrystallization may be observed around the larger particles. If diffusion of carbon in ferrite is rate controlling, then a graphite particle growing in a matrix of, say, tempered martensite or pearlite, should be surrounded by a carbide depleted zone. Thus, the simple metallographic experiments reported here are sufficient to determine whether or not diffusion of carbon in ferrite is the dominant mechanism for the growth of graphite in steel. The present investigation considers graphitization in five alloys. The compositions are given in Table I. Graphitization was carried out at three temperatures: 900°K (627"C), 950°K (677"C), and 990°K ('717°C). Samples were reacted in both the martensitic and the pearlitic initial conditions. In the hypoeutectoid steels, Sets 7 and 8, .and in the hypereutectoid Fe-C binary, Set 6, graphitization was very limited after 1000 hr at temperature. In these samples graphite particles observed were less than 10 p in diam. In the hypereutectoid commercial steels, Sets 1 and 3, large graphite particles (100 p) did not appear until after 250 hr at temperature. The limited number of graphite particles observed and the range of sizes obtained prohibited measurement of growth rates in this investigation. However, in all samples showing graphitization, neithe a carbide depleted zone nor recrystallization was observed. illert's model predicts that diffusion of carbon in ferrite should become dominant for graphite particles larger than about 300 p in diam. The largest graphite particle observed in this investigation was approximately 450 p in diam. No evidence of carbide depletion was noted. Fig. 1 shows a typical graphite particle. This nodule is from an initially pearlitic sample from Set 3 after

Jan 1, 1970

By H. E. Biber

DURING the production of tin plate a thin layer of FeSn2, is formed at the interface between the steel sheet and the protective tin coating. Because excessive amounts of this alloy layer are undesirable, the kinetics of its formation is a subject of interest in the tin-plate industry. A recent study of this subject at our laboratory uncovered a relationship which should be of general interest to anyone studying kinetics of reactions in metallic systems. It had been previously concluded that, at any given temperature in the range 175" to 330°C, the Fe-Sn alloy layer would have a parabolic growth rate.1,2 However, our studies showed that this rule apparently holds only when the tin plate is heated very slowly to the "reaction" temperature; when the tin plate is rapidly heated, considerably different growth rates occur. An example of this effect of heating rate on growth behavior is contained in the accompanying results of alloy-layer growth measurements at 240°C in oil baths stirred at 10,500, 1800, and 0 rpm. The heating curves for these three conditions are given in Fig. 1, and the growth data are presented in Fig. 2. With the rapid heating rate, provided by the stirring at 10,500 rpm, the alloy layer had three distinct stages of growth. In the initial stage, which persisted well beyond the time required to heat the tin plate to bath temperature, the alloy layer formed very rapidly. The growth followed a rate law of the form w = ktn where n > 1. This initial stage was followed by a growth-retardation stage of about 50-sec duration in which little additional alloy was formed. In the third stage the growth again followed a rate law of the form w = ktn, but here « =0.3. With the intermediate heating rate provided by stirring at 1800 rpm, the three-stage nature was less pronounced and the slope of the third stage increased (i.e., n > 0.3). With the slow heating rate provided by the unstirred oil bath, the alloy layer grew in two stages. The initial rapid-growth stage persisted only until the specimen was heated to bath temperature, no growth retardation was observed, and the slope of the main portion of the plotted data was greater than in the stirred baths, having a value of almost 0.5. Similar results were obtained for other bath temperatures in the range 200" to 300°C. This effect of heating rate on growth behavior may be due to changes in the rate of nucleation of FeSn, crystallites. The iron and tin are in contact from the onset of heating. Thus the initial formation of FeSn, occurs not at the "reaction" temperature but rather while the tin plate is being heated to that temperature. Because nucleation is in general temperature-dependent, different heating rates could cause different over-all nucleation rates, which in turn could cause different growth behaviors. A more detailed discussion of the growth of Fe-Sn alloy layer and the effect of heating rate will be published shortly.

Jan 1, 1965

This consolidated index covers all publications of the Institute for the years 1926 through 1935. The following list indicates subjects of volumes and gives numbers or abbreviations used to designate them. TRANSACTIONS VOLUME *G26. Petroleum Development and Technology in 1925 (Published in 1926). *G26. Petroleum Development and Technology in 1926. *E27. Institute of Metals Proceedings. 73. Nonferrous Metallurgy, Milling and Concentration, Nonmetallic Minerals, Institute of Metals and Iron and Steel. [ ]

Jan 1, 1936

By B. W. Prof. Frazier

I PROPOSE in this paper to treat of the chimney merely as a heat engine, as one of the devices resorted to in practice for the conversion of heat into mechanical work. For the sake of simplicity and clearness in the discussion, let us consider the subject in its simplest form. Conceive a chamber, heated from without, in free communicatioH at one end with the external atmosphere, and at the other end opening into a vertical chimney. Let the. cross-section of the chamber be so great, relatively to that of the chimney, that we can neglect the actual energy of the air passing through the chamber. We will neglect, also, all passive resistances to the passage of the air. We will assume that the cross-section of the chimney is constant, and that the air in passing through it neither gains nor loses heat. The following symbols will be employed in the discussion : Po = the normal pressure of the atmosphere, which, it is assumed, is the pressure existing at the level of the chamber. Po = 10332.96 kilograms per square meter. P2 = the pressure of the external atmosphere at the top of the chimney. To = the, absolute temperature of melting ice by the centigrade scale. This is assumed to be the temperature of the external air at the level of the chamber. To = 273°. T2 =the absolute temperature of the air as it passes from the chamber to the chimney. T3 =the absolute temperature of the air as it issues from the chimney. to, t2, t3 are the temperatures, as recorded on the centigrade ther¬mometer, corresponding to the absolute temperatures To, T2, T3 re-spectively to = 0° C. In general, t = T- 273. Io, I2, I3, represent the intrinsic energy of the air at the temperatures To, T2, T3 respectively.

Jan 1, 1882

By E. Northcott, I. M. LeBaron

Before describing the electrostatic processing of feldspar, it might be well to review some of the basic definitions and terminology of feldspars. The feldspar minerals constitute a group of alumino-silicates of potassium, sodium, and calcium. Barium feldspar sometimes occurs naturally but is very rare. Hardness varies between 6 and 6.5 and specific gravity between 2.5 and 2.8. Color is generally white or pale shades of red, yellow, or green. The approximate chemical composition of the principal feldspars is given in Table I. The albite (sodium aluminum silicate) and an-

Jan 1, 1959

By P. B. Baxendell

The appraial of producing properties and profitability ntzalysis of a proposed capital expenditure are based on the same principles. In both problems a projection of future cash income is. cornpared to one or more capital expenditures. Several different methods have been in use either to compute a price to obtain a given earning power on the investment or to compute the earning power which will result from a given capital expenditure. One of these, the "Average Annual Rate of Return" method, computes in a simple manner the ratio of the present value of the future earnings after amortization to the present value of the undepreciated balances of the investment over the life of a project. This method, not well known generally, appears to have some rather unique advantages in reducing the computation work required, eliminating trial-and-error solutions, and providing a more accurate answer when applied to oil industry investments subject to the unit-of-production basis of amortization. Its derivation is given and its versatility demonstrated in the solution of certain everyday investment problems. A number of charts, useful in applying this method to profitability analysis and appraisal work, are provided. The current trend in the market values of producing properties is shown. INTRODUCTION Making sound capital expenditure decisions requires an objective means of measuring the productivity of individual investment proposals. Since the best measure of the economic worth of such proposals is their ability to produce profits, it is common practice to grade proposed capital expenditures according to their annual earning power as a percentage of the outstanding capital. The same principles which govern the determination of the rate of return of proposed capital expenditures also apply generally to the problem of determining the appraisal value or purchase price of income-producing oil and gas properties. Both problems are of prime importance in the producing phase of the oil business, where management is faced daily with decisions to drill or not to drill certain development wells, or with the determination of the appraisal value of producing properties. The common feature in both problems is that a projection of future cash income is compared with a known or estimated capital investment to determine itsiearning power or annual rate of return. In the case of development drilling, the cost of the proposed well can usually be estimated with a fair degree of accuracy and the problem consists of finding the rate of return on the invested capital. In the case of appraising producing properties, on the other hand, the desired rate of return is usually known in advance and the problem consists of determining the purchase price which, for the given income projection, results in the fequired rate of return. Certain accounting procedures common to the oil and gas producing business make these two problems and their solutions somewhat different from corresponding problems in other industries, and, in certain ways, simpler. The main difference is in the amortization policy which, for oil and gas production, is frequently on a unit-of-production basis, compared to the amortization on a time basis used in many other industries. The purpose of this paper is to discuss briefly the various methods currently in use for the measurement of productivity of invested capital in producing properties and, in more detail, the derivation and application of what will be called the "Average Annual Rate of Return Method". This rather interesting and not too well known method has some very definite advantages in the solution of many problems common to the oil industry. For the sake of simplicity, federal income tax considerations have been disregarded in the examples used, since they do not affect the principles involved. The use of the production payment route in the sale or purchase of producing properties, which has been amply covered in many other publications, has also not been included in this analysis. METHODS FOK MEASUKING THE EARNING POWER OF INVESTED CAPITAL, Of the many different methods used to measure the earning power of invested capital, four are applicable to oil or gas production ventures. Depending on whether these four methods utilize one or two interest rates, and whether a fixed amortization pattern is used, they may be classified as follows.

By L. F. Bishop

THE ore bodies of the Butte district1 are found in many different vein systems having many different structural characteristics; some are narrow with self-supporting ore but with weak walls; some are wide with weak or strong ore and weak walls; some of the veins dip steeply and others do not; some have well defined walls, and others, in the "horsetail" area, are mined to sample limits. Consequently, many types of stoping methods are used in mining these ores. The stoping methods used in the Anaconda Copper Mining Company's properties are the square-set and cut-and-fill. The square-set method is the principal stoping method used because, generally speaking, the ore and walls are weak, the ore is high grade, and good extraction is required. These square-set stopes may be classified as conventional, vertical slice, slot, timber rill, and Mitchell slice types. The conventional type square-sets are those of various shapes and sizes, mined by horizontal slicing to the boundaries of the stopes. The rock is slid to the chute and the filling is moved by gravity. The ore and waste may be handled with a scraper when local conditions require it. The vertical-slice square-set system is the type used in narrow veins that are mined in vertical panels. The slot stopes are stopes in wide veins that employ a slot across the vein instead of a con- ventional chute to handle the ore. The timber rill fs a type of square set in which the ore is mined as in inclined cut and fill but the square-set timber is used. The Mitchell slice is the type used for some broken or heavy ore blocks, or for pillar extraction between two converging slot stopes. The cut-and-fill method is used where the ore will stand without much support although the walls may be weak. The principal type of this method is the horizontal cut-and-fill, with mechanical scraping. The inclined cut-and-fill, or rill, stopes are used in some veins too narrow for scraping. The production from the various meth: ods in use for the second six months of 1944 are shown in Table I. [ ] This paper deals mainly with the vertical slice and slot types of square-set stoping, because of their effect on production locally and their potential possibilities here and in other districts, with sufficient reference to conventional square-setting for comparison.

Jan 1, 1945