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By Michael Perch, Charles C. Russell

The fact that coal is a complex organic material and heterogeneous in composition has made its study extremely difficult, particularly in regard to obtaining a fundamental concept of the processes involved in the formation of coke. It has been stated1 recently that coals are natural polymers and that in a complex reaction such as occurs during carbonization the differences between coals are quantitative and not qualitative. Such being the case, it would be expected, therefore, that a series of coals subjected to exactly the same conditions of coking would produce results that should be related quantitatively to the chemical analyses of the individual coals. In the past, however, this fact was not generally recognized and consequently many empirical test methods were devised for testing coals. The interpretation of the results obtained depended upon comparing a set of data with other data on coals of known characteristics. The testing procedure had to be conducted in precisely the same manner each time and not the least requirement in making the interpretation was experience. The test methods varied from those utilizing a gram of coal to the plant-scale tests in which one or more ovens were charged with the test coal. The aim had been principally to find some simple, inexpensive means by which the coke-making and other properties of coal could be predicted. It is not necessary to emphasize the importance of these endeavors, for anyone acquainted with the problems involved in the selection of coals for making coke is well aware of the time and expense involved in making a series of definitive tests. Several attempts have been made to derive formulas for such predictions. The relations of both ultimate and proximate analyses to coke physical properties and byproduct yields have been studied. Lowry and co-workers1 correlated statistically the U. S. Bureau of Mines-American Gas Association assay test results with coal analyses, using 90 coals and coal blends. Parry,² Spooner,3 and Gabinskii and Krym4 made similar correlations. Lowry concluded that there were definite relationships between the proximate analyses of the coals and the yields and properties of the products. Although this statistical study was made on test results from carbonizing coal in a cylindrical steel retort, the conclusions are important and provided one of the first steps in the simplification of this complex subject. Studies should be made of other references on this subject just cited. Studies of the coking process reported in the literature frequently were confined to a small number of coals, and very few have included coals from various ranks. It would seem logical, however, that a program for studying factors involved in the formation of coke should be based on a number of coals selected from each of the various classes or types of coking coal. The possible use of the scheme of classifi-

Jan 1, 1950

By Roy A. Lindgren

Since the year 1643, when the first blast furnace in America for treating iron ore was built at Saugus, Mass., out of mica schist quarried in the neighboring district, the procurement of a suitable refractory for furnace lining has been a problem of concern to the operators of furnaces. The stacks built of mica schist continued to smelt iron ore until about 1836, when, according to F. H. Norton, the first firebrick were produced1, at Queens Run, Pa. Other writers speak of brick having been molded and burned in Massachusetts about the year 1834. In 1841, Andrew Russell began to produce medium refractory plastic clay brick near East Liverpool, Ohio, that were used for lining blast furnaces1. The well-known Kentucky clay-producing district was not opened up until the year 1871, but since then it has produced a large percentage of the linings for iron blast furnaces. While some strides have been made by the refractories industry during the 100 years that have passed since the first firebrick were produced, it has been only during the last two decades that any real progress has been made towards bettering the product, even though the method of production had improved. Perhaps the fault lies with the user of the brick rather than with the producer, for not sooner demanding a superior product. During the past 15 years the tonnage produced per lining has increased from 500,000 gross tons to 1,000,000 gross tons, and now some furnaces are producing 1,600,000 gross tons and better on a single lining. It is true that enlarged capacity of furnaces and improved practice have accounted for some of this increase in tonnage, nevertheless better quality in firebrick must be given credit for its share. However, we are not yet ready to say that we have reached a maximum life of furnace lining. We believe that a better product can be produced and that the refractories industries of America will, through their extensive research depart-

Jan 1, 1937

By H. F. Beeghly

UNTIL recently the only criteria by which steels were judged were their cost and their mechanical, chemical, and physical properties. The user was concerned with such properties as corrosion resistance, tensile strength, response to thermal treatment, hardness, ductility, and, to a growing extent in recent years, with behavior at high temperature. As plans were made to build power reactors, a new set of properties became important—the nuclear characteristics, which had to be considered by the designer and engineer in building his plant. The nuclear engineer developed methods for the rare and new metals and produced them in high purity, often at great expense. The pure metals then provided the raw materials for tailor-made alloys. For more common structural metals, such as steel, the nuclear industry depended on commercially available materials. Generally, the quantities required were small and specifications were rigid. It is not surprising, therefore, that difficulty was frequently encountered in procuring structural mate-

Jan 1, 1957

By A. T. Goldbeck

THE use of stone as a building material in relatively large blocks is recorded in ancient historical records but only within the past 200 years has broken stone in small sizes begun to have extensive use, principally in highway construction. Tresaguet, in 1764, describing his method for highway construction in France, required the top surface to be built of stone about the size of a walnut, broken by the use of a hammer. It is said that the Romans, in the top layer of their rather massive roads, used large stones bonded together with lime mortar and bedded in small stones mixed with mortar. Much of the early macadam as built by McAdam around 1815 in England was made with hand-sledged broken stone. In 1858, the use of crushed or broken stone received a great impetus from the invention in that year by Eli Whitney Blake of what is said to be the world's first stone crusher. As a consequence of that invention, stone could be crushed to small sizes with considerable ease and, as a natural result, the use of crushed stone in macadam roads and as railroad ballast increased at a great rate. Also, as portland cement came into use, machine-produced crushed stone furnished readily available aggregate. Rapidly, other uses developed, such as for fluxstone in the production of pig iron and for other metallurgical operations and chemical utilizations. These utilizations made for the rapid growth of the crushed-stone industry and this growth is still proceeding with the growth of population and the development of new uses, notably the employment of limestone for the improvement of soils for agricultural purposes. The industries of which the production of crushed stone is a part have a tonnage second only to that of mineral fuel in the mineral industries of this country.

Jan 1, 1949

By J. D. Hanawalt, W. H. Gross

Magnesium has long been known as the lightest of our engineering metals. This metal, silvery white in color, has a specific gravity of only 1.74. Aluminum, the next lightest structural metal, is 1 ½ times heavier; zinc is 4 times heavier; iron and steel are 4 ½ times heavier; and copper and nickel are 5 times heavier. Magnesium does not occur in the free state but is very abundant in nature, constituting 2.5 pct of the earth's crust in the form of various ores. It is the third most abundant structural metal, being exceeded only by iron and aluminum. Magnesium is unique, however, in that in the form of magnesium chloride it also exists in the oceans. Sea water is the source most widely used for production in the United States but magnesium is also commercially produced from magnesite, dolomite, and other ores as well as from certain inland brines. The vast quantity of magnesium existing in the waters of the oceans can be visualized when it is realized that the removal of one hundred million tons per year (the approximate annual steel production in the United States) for a million years would reduce the magnesium content of sea water only from 0.13 to 0.12 pct, providing no more magnesium had washed into the sea in the meantime. Not only is magnesium potentially very abundant but it is in addition a very versatile metal and can be shaped and worked by practically all methods known to the art of metal working. It can be cast by sand, die, and the various permanent-mold methods;

Jan 1, 1953

By P. Hazebroek, M. Prats, E. E. Allen

Well locations in water floods frequently do not coincide with the ideal well locations associated with the flood pattern which is used. A question of importance is. "How much oil is lost because of this?". This is the problem treated in this paper. It is assumed that each pattern in a five-spot flood has the proper number of production and injection wells but that the wells may be off-pattern. The distance by which a well is off-patern is given in terms of the pattern spacing, defined as the length of one side of a five-spot. The influence of off-pattern wells on the performance of a five-spot flood has been investigated mathematically for unit mobility ratio. All production and injection rates are assumed to remain equal. The loss in recovery resulting from pattern irregularitie: has been calculated at a cumulative water injection corresponding to a 98 per cent water-cut in a regular five-spot. Displacing a single production or injection well by about one-third the pattern distance reduces the total field recovery by 4.4/N per cent of the recovery obtainable with regular spacing, where N is the number of five-spots in the flood (assumed large). When off-pattern wells are separated by at least one regular five-spot and are displaced by less than one-third the pattern distance, the total loss in recovery in a large-scale flood is, at most, 1 per cent of the recovery obtainable from that field with a regular five-spot pattern. However, much higher losses may occur if the off-pattern wells are not separated by a regular five-spot, if the rates are imbalanced, or if the mobility of the injected water is higher than that of the crude. Although the loss in oil recovery due to pattern irregularity often may be low, the off-pattern case will always require injection of more water to reach the same final water-cut. The volume of water injected per unit volume of oil displaced has been calculated for each five-spot adjacent to a five-spot containing a single 08-pattern well. The cumulative water injection at the time of 98 per cent water-cut may be increased by as much as 37 per cent when a production well is displaced one-third the pattern distance toward an injection well. The existence of differences between actual subsurface locations and the idealized well patterns used in secondary recovery operations is well recognized. However, the methods commonly used for predicting waterflood behavior ignore such differences, even when subsurface locations are known. The reason for this is simple. The idealized well patterns are highly symmetrical and, as such, the production history of the pattern (and even of the field) can be determined from that of a few production wells—usually from only one. Consideration of the many irregular well spacings found in a specific field would entail a large amount of work, and then the results would be applicable only to that specific field. In an attempt to provide an answer to the more general problem, this paper considers a water flood having an idealized well pattern, except for one well which is not at its regular location. When several off-pattern wells are present, their contributions are assumed to be additive unless the off-pattern wells are close to each other. Only four positions of the off-center well (at x, y. of Fig. 1) are considered in this paper. These are shown

By C. R. Holmgren

A large consolidated sand core was used in this investigation. Four groups of experiments including gas drives, water drives, and water drives combined with gas injection, were made. The results of the gas-drive experiments indicate that greater ultimate recovery may be obtained by higher pressure gradients. However, other considerations challenge the absolute veracity of this conclusion. Results indicate that with connate water present and a low pressure gradient during a gas drive, less gas is required to produce a given amount of oil. The saturation gradient determined during a gas drive is presented. Results of the water-drive experiments indicate that the recovery of oil is not a function of either gradient Or input rate. The presence of initial gas saturation resulted in a slightly lower final oil saturation. Injection of sufficient gas to maintain the initial gas saturation during a water drive resulted in lower final oil saturation. Introduction With the demand for petroleum products reaching an all-time record high and the location and exploitation of new reserves becoming more difficult and expensive, the oil industry must look to more thorough and efficient methods of producing the petroleum already located. Much of the previous work along these lines is exploratory and suggests a more complete investigation. For example, a great amount of laboratory work has been done on flooding sands initially saturated roo pct with oil. Since sands saturated roo pct with oil rarely, if ever, exist in nature, and because the water content is a vital factor in the ultimate recovery from the sand, laboratory investigations on cores without water must be supplemented by comparable work on cores with water present.1'2 Other investigators have done a considerable amount of laboratory work using gas and water drives.3 Krutter and Day4 have reported results of investigations using cores saturated IOO pct with oil and have concluded that " the ultimate recovery obtained, using air drive, from a completely oil-saturated core depends on the pressure gradients used. The higher the pressure gradient, the greater will be the recovery until a certain Pressure range is reached above which the reward of increased recovery is much smaller for similar increments in pressure." Yuster and Day6 conclude that less gas and less time are required to produce a given quantity of oil at high pressure gradients than at low pressure gradients; they also conclude that an increase in the viscosity of the oil requires a proportionate increase in the gas needed for recovery. Their results indicate that the gas required to produce a given quantity of oil is greatly reduced by the presence of connate water. R. C. Earlougher2 concluded, based on results of water-flooding a large number of

Jan 1, 1949

By Albert F. J. Bordeaux

INTRODUCTION. THE following general survey of the character and present condition of the silver-mines of Mexico, though not offered as a detailed treatise, has been prepared with care, is believed to he generally up-to-date, and is offered as a summary which may be found useful by mining engineers. Mexico has ranked for several centuries first among the silver-producing countries. It is now second as copper-producer, and seventh as gold-producer, with a fast-increasing output every year. The total amount of capital invested in its mining- and smelting-works is more than $250,000,000, while the yearly metallic production is $160,000,000. There are more than 20,000 recorded mining properties. The silver-mines of Mexico represent deposits of three principal classes: (1) veins and stock-works in eruptive rocks; (2) fissure-veins crossing the crystalline schists, granite, diorite, etc. ; and (3) veins and replacement-deposits in limestone. The true fissure-veins in some districts contain (in value) more gold than silver. In other deposits, the silver is decreasing in depth, leaving galena and zinc-blende as the principal ores.

Jan 9, 1908

By Donald F. Taylor

TANTALUM and columbium are newcomers in the world of metals. Many of the metals described in this volume had been known and used for centuries before either tantalum or columbium was known to exist. The scarcity of the ores and the comparative difficulty of extraction delayed their technology until specialized methods of processing could be developed. HISTORY Early in the nineteenth century, 1801, Hatchett discovered a new oxide, which he called columbium oxide, and a year later, Ekeberg announced that he had found a new element, which he named tantalum. The preparation of the metal tantalum in impure form was first announced by Berzelius in 1824, but the actual production of ductile metal did not occur until 1903, when von Bolton, of Siemens and Halske, developed a process for the production of tantalum pure enough to be drawn into electric-lamp filament wire. The use of tantalum as a filament wire began to decline when ductile tungsten was introduced in 1909. In 1921, C. W. sake, of Fansteel Metallurgical Corporation, produced the first ingot of tantalum metal in America. The first ingot of columbium was produced in 1927 in the laboratory of the same company. There are several good reasons why tantalum and columbium are often mentioned together. They occur together in their important minerals, are similar in many of their properties, and are

Jan 1, 1953

By C. H. Frick

BEFORE presenting the main topic, as indicated by the title, this paper will give some of the high-spot history of the anthracite industry. INTRODUCTION The earliest recorded use of anthracite was in the year 1762, when a company of Connecticut pioneers discovered anthracite near the present city of Wilkes-Barre, Pennsylvania. In the early days of the industry, the coal was used only in large pieces, the smaller pieces being discarded to waste piles. As the output of the industry increased during the nineteenth century, uses were developed for somewhat smaller sizes down to and including pea coal. Early in the twentieth century, sizes smaller than pea, such as No. I and No. 2 buckwheat, were developed and used. Accu¬mulations of piles from current mining operations were still increasing; that is, the smaller sizes were still being discarded. It was not until after World War I that preparation of the so-called steam sizes began commercially. This was largely No. 3 buckwheat, which is screened through a 3f 6-in. round-hole screen and over a 332-in. or a M 6-in. round-hole screen. USE OF SMALLER SIZES The earliest recorded experience in burning the small sizes of anthracite for steam production, other than in a previous small experiment, was in the year 1913, when a size known as "boiler fuel" was introduced-a mixture of rice and barley (No. 2 and No. 3 buckwheat). At that time, there was still no method known for burning the still smaller sizes. TABLE I.-Screen Sizes Used for Small Sizes of Anthracite [ ] At the present time, various sizes down to and including No. 5 buckwheat are being prepared (Table I) from current mining and bank-reclaiming operations. The sizes of No. 4 and No. 5 buckwheat and smaller are generally being used for steam production in large boilers. The Pennsylvania Power and Light Co., following World War I, used 680,000 tons of anthracite per year, burned largely on stokers for production of steam, whereas for the year 1943 it used 1,940,000 tons of stoker sizes and 400,000 tons of smaller sizes for grinding and burning in pulverized form. This company has taken a very large part in the research and development of ways and means of burning these smaller sizes of anthracite, including the grinding of the very small sizes. This paper is particularly concerned with the latter feature.

Jan 1, 1946

By Yap Chu-Phay

IN the previous paper, the writer showed how, on the basis of thermodynamic reasoning, it seems probable that when true equilibrium conditions obtain, carbon exists as Fe3C in the liquid state and as elementary carbon in the solid state (7 Fe), in which case the solidus would be a straight line from 0.18 to 1.70 per cent. carbon (Fig. 1). In the same paper he concluded that the solidus obtained by Honda 'and his co-workers1 probably does not represent the same conditions, insuring a complete equilibrium. Except for a downward temperature displacement, the solidus obtained by Gutowsky,2 using the Heycock and Neville method, practically coincides with Honda's solidus as shown in Fig. 1. The writer at first thought that perhaps in some way Gutowsky's thermocouple was improperly calibrated for high-temperature measurements, as his liquidus was also much lower than those obtained by Carpenter and Keeling3 and by Ruer and Goerens.4 However, the eutectic temperature obtained by Gutowsky agrees with the generally accepted value of 1130° C., so that the validity of the inference regarding improper temperature calibrations is to be strongly doubted. In Fig. 1, Gutowsky's solidus is shown both in the original and in the corrected form. In the latter, a correction of 29.2° C. is made for all temperatures above 1416° C. in accordance with-

Jan 1, 1931

By Thomas Cox

The following compilations are made from a series of investigations and are used to present the subject in an unbiased manner, as the writer does not represent any company or financial interest. The present situation is complex. The producers are hard pressed by reason of the low price of crude, while the independent refiner is little better off, because of the corresponding cut in price of refined products, except on occasional contracts. If the real costs are analyzed, it will be seen that the land speculators and the lessors—royalty owners—make the larger profits and not the struggling legitimate operator or independent refiner. The present-day (October, 1922) posted prices per barrel for crudes are Kansas, Oklahoma, Mexia, Gulf Coast, and Louisiana..... $1.25 Healdton............................................. 0.75 Northern Texas and Central Texas...................... 1 . 50 Pennsylvania......................................... 3.00 Wyoming, Elk Basin.................................. 1.25 Wyoming, Salt Creek................................ 0.70 California Base..................................... 0.60 These prices are at the well. In addition, crudes must be gathered and transported to refinery (by pipe line or tank cars), refined, and the refined products marketed. These crudes are of various gravities, ranging within a narrow margin for each field or district, so that averages are not difficult to deduce, and it is these averages that really determine the average operating conditions. In order to show the present realizations, the prices and costs now obtaining are listed against the average yields; the figures are also adjusted VOL. urn.----71

Jan 1, 1923

By Thomas Cox

The following compilations are made from a series of investigations and are used to present the subject in an unbiased manner, as the writer does not represent any company or financial interest. The present situation is complex. The producers are hard pressed by reason of the low price of crude, while the independent refiner is little better off, because of the corresponding cut in price of refined products, except on occasional contracts. If the real costs are analyzed, it will be seen that the land speculators and the lessors—royalty owners—make the larger profits and not the struggling legitimate operator or independent refiner. The present-day (October, 1922) posted prices per barrel for crudes are Kansas, Oklahoma, Mexia, Gulf Coast, and Louisiana..... $1.25 Healdton............................................. 0.75 Northern Texas and Central Texas...................... 1 . 50 Pennsylvania......................................... 3.00 Wyoming, Elk Basin.................................. 1.25 Wyoming, Salt Creek................................ 0.70 California Base..................................... 0.60 These prices are at the well. In addition, crudes must be gathered and transported to refinery (by pipe line or tank cars), refined, and the refined products marketed. These crudes are of various gravities, ranging within a narrow margin for each field or district, so that averages are not difficult to deduce, and it is these averages that really determine the average operating conditions. In order to show the present realizations, the prices and costs now obtaining are listed against the average yields; the figures are also adjusted VOL. urn.----71

Jan 1, 1923

By Douglas Bunting

The first presentation of this paper was before the Pennsylvania Anthracite Section of the Institute in May, 1914, after which a committee was selected to verify and add to the data contained in the original paper. The author is indebted to G. W. Engel, H. W. Montz, R. V. Norris, and H. H. Otto, of this committee, for additional information. I also wish to acknowledge the courtesies extended me by a number of the mining companies for information relative to accidents, systems of proving, and mining practice. The paper should bring forth additional criticism and recommendations, which will be of value in establishing future practice relative to this subject. Throughout the northern anthracite field of Pennsylvania glacial and alluvial deposits of sand, gravel, and clay exist in varying quantities. The extent and character of these deposits are described by N. H. Darton in Bulletin 45 of the U. S. Bureau of Mines, entitled, Sand Available for Filling Mine Workings in the Northern Anthracite Basin. It is estimated that the northern field contains 10,000,000,000 tons of these deposits, or a sufficient quantity to cover the 176 square miles of coal area to a depth of about 25 ft. These deposits of sand, etc., overlying the coal measures attain a maximum depth of more than 300 ft., and are usually saturated to such an extent as to render them semi-fluid. It is this condition of fluidity that limits the mining of coal seams cropping in or in close proximity to these deposits, and it is in the interest of safer and more efficient mining methods under these conditions that the study of this subject is here presented. The dangers incident to mining under deep deposits of sand have long been realized by operators in the northern anthracite field, and much has been done to prove the contour of the rock and vein croppings underlying these water-bearing deposits of sand and gravel. Although, as far as we know, the accidents of the past have not resulted in the loss of life, except in two instances, yet nearly all were attended with more or less miraculous escapes of men working in the vicinity of the breaks, so that the probable existence of pot holes, etc.,

Jan 1, 1915

By T. S. Fuller

VARIOUS phases of the embrittlement of solid copper containing oxygen by the action of reducing gases at high temperatures through the work of many experimenters are familiar to readers of metallurgical literature. In 1900, Heyn1 recorded observations of copper being heated in hydrogen with the development of fine cracks, the result of the formation of steam within the metal through the action of hydrogen on the copper oxide usually found in copper. Archbutt,2 in 1905, published the results of experiments, showing that all oxygen can be removed from copper by heating to redness, for several hours, in hydrogen. Intercrystalline cracks and extreme brittleness developed. Archbutt attributed the brittleness to the reduction of oxides present in the copper. Bengough and Hill,3 in 1910, encountered the now well-known embrittlement at the outset of their investigation and stated in their paper: It soon became evident that the effect of any heat treatment depended largely on the presence or absence of reducing gases in the atmosphere of the furnace, as well as on its temperature. Hence it became necessary to adopt a somewhat elaborate scheme of heat treatment. The authors found embrittlement in separate experiments due to both hydrogen and carbon monoxide and concluded that: "The gases ruin the alloys after being heated to about 650° C. in their presence."

Jan 2, 1926

By Stanley D. Michaelson

Stanley D. Michaelson retired in 1976 as chief engineer, Metal Mining Div. and director of the Engineering Center for Kennecott Copper Corp. An active consultant on mining and metallurgical assignments, Mr. Michaelson is also currently adjunct professor of mining engineering at the University of Utah. He received his B.S. degree in mining engineering from Lehigh University in 1934 and an honorary E.M. degree from the Montana School of Mines in 1961. Mr. Michaelson received AIME's Robert H. Richards Award in 1962 and was named a Distinguished Member of the Society of Mining Engineers of AIME in 1975. He has served as a Director and as a Vice-President on the AIME Board of Directors and is a Past President of the Society of Mining Engineers. He became an Honorary Member of AIME in 1978.

Jan 1, 1979

By O. W. Ellis

CERTAIN alloys1 that, as a result of quenching, are retained in the form of homogeneous solid solution are known to increase in hardness and strength on standing at room temperature or on heating at slightly elevated temperatures. Other alloys" that, on rapid cooling, are held in the form of homogeneous solid solution (as, for example, certain steels) behave in like manner on heating to somewhat higher temperatures. The observed increase in the hardness and strength of these alloys, referred to as "aging" or as "secondary hardness," is widely accepted as being occasioned, either in whole or in part, by the precipitation in submicroscopic form of such constituents as were held in supersaturated solid solution as a result of cooling in excess of a certain critical rate. In earlier discussions of the cause of age hardening or secondary hardness, the question of the hardness of the precipitated particles does not appear to have been raised. At present, however, the general opinion appears to be that age hardening and secondary hardness are occasioned by the precipitation of hard particles within the supersaturated solid substance.3 The authors may be wrong in their belief that the last is a prevailing opinion. Nevertheless, it is thought that the following experiments,

Jan 7, 1924

By T. S. Fuller

The work of D. J. McAdam, Jr.1,2 at the U. S. Naval Engineering Experiment Station, Annapolis, Md., on what has been called by him "corrosion-fatigue" has focussed the attention of the engineering profession in general, and of those interested especially in the study of corrosion in particular, on the importance of making tests which will indicate as nearly as possible what can be expected from a given material in service. Pitting is unquestionably the chief agent operating so tremendously to reduce fatigue limits, but in the light of previous work3, 4, 5, 6, 7, 8 it is fair to assume that absorbed hydrogen resulting from the action of the corroding medium upon steel may, under certain conditions, have a perceptible influence. The experiments described in this paper deal more precisely with stressless corrosion, or "prior-corrosion fatigue,"9 and have been carried out to test such an assumption, to segregate, if possible, the effect of pitting from that of absorbed hydrogen, and although very preliminary in nature they indicate results which are striking.

Jan 1, 1929

By T. S. Fuller

The work of D. J. McAdam, Jr.1,2 at the U. S. Naval Engineering Experiment Station, Annapolis, Md., on what has been called by him "corrosion-fatigue" has focussed the attention of the engineering profession in general, and of those interested especially in the study of corrosion in particular, on the importance of making tests which will indicate as nearly as possible what can be expected from a given material in service. Pitting is unquestionably the chief agent operating so tremendously to reduce fatigue limits, but in the light of previous work3, 4, 5, 6, 7, 8 it is fair to assume that absorbed hydrogen resulting from the action of the corroding medium upon steel may, under certain conditions, have a perceptible influence. The experiments described in this paper deal more precisely with stressless corrosion, or "prior-corrosion fatigue,"9 and have been carried out to test such an assumption, to segregate, if possible, the effect of pitting from that of absorbed hydrogen, and although very preliminary in nature they indicate results which are striking.

Jan 1, 1929

By Tuncel M. Yegulalp, Malcolm T. Wane

In general, many problems relating to the exploitation of mineral deposits are probabilistic in nature. This derives from the fact that the geologic universe is inherently random. Probability theory and statistics have been found useful for forecasting the behavior of natural events that occur in the geologic universe. The objective of this paper is to illustrate the application of the theory of extremes to this fore-casting problem. For example, it is customary for design purposes to determine the rupture strength of geologic materials. The theory of extremes is exceedingly useful in describing that portion of the frequency distribution of rupture strength which contains the least strengths. Parameters describing the distribution of the least strengths are more important to the designer of mining excavations than parameters describing the total distribution. The basic principles of the theory of extremes will be detailed and illustrated. Any person required to work in the laboratory of nature is aware that uncertainty is a salient feature of all mining enterprises. A mining engineer required to plan the most efficient, practicable, profitable, and safe mine finds himself face to face with numerous ill-understood and often unquantifiable states of nature. Basic information necessary for adequate planning is often lacking or derived from incomplete tests on samples or experience of doubtful validity. The planning procedure usually takes the form of determining a feasible layout with the intent of determining an optimal layout when and if the necessary details and information become available. The crux of the entire procedure is the choosing of numbers to put into the operational and structural models which encompass the plan. Many times these numbers must be assigned qualitatively from past experiences and are called the "most probable ones." At other times, load records, performance records and material tests provide a basis for extrapolation. In any event, the numbers are chosen from a distribution or set of all numbers. Since each number in the distribution represents a possible state, the choice of any particular value is based upon a decision rule. To illustrate, consider the design of an underground structure or the design of a rock slope. The initial step is the formulation of the various possible structural actions which result from the geometry of the layout. For a given structural model various intensities of behavior are possible depending upon the load, deformation, and material characteristic spec-trums, respectively. Of particular interest to mining people is the failure behavior or condition, i.e., when there is a complete collapse of structural resistance by either structural instability or fracture. A necessary feature of the analysis is the "rupture strength" of the material. Information on the rupture strength is derived from testing either in situ or in the laboratory and the usual outcome is a variation in the test results. The methodology used to overcome this variation is to construct a frequency distribution of rupture strengths, and then determine a measure of central tendency and variability. The main idea involved is that the central tendency number will be used in the failure calculations and the measure of dispersion will be used to estimate the probability of failure. In particular if the distribution of rupture strength is normal, the mean rupture strength is the central tendency number and the standard deviation of the rupture strength is the measure of variability. Suppose the mean value of rupture strength is 1000 psi and the standard deviation is 200 psi. Insertion of 1000 psi into the failure calculation produces results that are unsafe, hence a common decision rule is to reduce the mean value by a "factor of ignorance" so that the failure calculation will produce a "safe result." If two is chosen as a factor of ignorance, this means the value inserted in the calculation is 500 psi or 2.5 times the standard deviation. The next step is to determine the percentage chance that failure will occur from a design created on this basis. Tables on the normal distribution function show that this percentage chance is 0.621% or approximately 7 times out of 1000. In practice, however, the situation is more complicated than represented by the foregoing illustration. The laboratory or field testing program usually constitutes a pathetically small sample of the geologic universe of interest and not enough testing is carried out to determine the exact form of the distribution of the test results. The normal, Cauchy and Student's T distributions are strikingly similar, and it becomes a matter of mathematical convenience to assume the normal law for phenomena which follow other laws.

Jan 1, 1969