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By R. V. Norris

IRving Ariel Stearns died at his home, 60 South River St., Wilkes-Barre, Pa., on Tuesday morning, Oct. 5, 1920, of pneumonia, after an illness of about a month. In his death, the Wyoming Valley loses one oflits most eminent and best loved citizens, and the loss of so strong a participant in the activities of the Valley will leave a gap most difficult to fill. Despite his more than three score and fifteen years, Mr. Stearns, at the time of his death, was president of the Wilkes-Barre City Hospital, Wyoming National Bank, and the Wyoming Historical and Geological Society, chairman of the Board of the Vulcan Iron Works, and a director of the Spring Brook Water Supply Co., and of the Wilkes-Barre Lace Manufacturing Co. Mr. Stearns came of New England stock, a descendant in the eighth generation of Charles Stearns who was admitted freeman in Watertown in 1646. Irving Ariel Stearns was born Sept. 12, 1845, in Rushville, N. Y., a son of George W. and Miranda (Tufts) Stearns. He was graduated from the Rensselaer Polytechnic Institute of Troy, N. Y., in the celebrated Class of 1868. After graduation, he was assistant professor of chemistry in charge of the analytical laboratory for a year, then went to Wilkes-Barre in 1869, as engineer in the office of R. P. Rothwell, at that time the leading mining engineer of the region. From 1871 to 1872, he was superintendent of the McNeal Coal & Iron Co. of Schuylkill County, Pa. and in 1872 succeeded to Mr. Rothwell's business when the latter became editor of the Engineering & Mining Journal of New York. From 1872 to 1885, Mr. stearns was in private practice as a mining engineer, handling a great amount of business in the anthracite region, including the building of the bridges at Shickshinny and Pittston, and the surveying and mapping of many of the individually operated mines. His practice extended throughout the country, with numerous examinations and reports upon mining properties in Pennsylvania, Virginia, West Virginia, Arkansas, Colorado, California, Wyoming, Idaho and Utah; he was responsible for the design and execution of the Lehigh Valley Railroad Co.'s great Tifft Farm improvements at Buffalo, N. Y. including canals, docks, coal stocking plant, etc. He was commissioned Quartermaster of the Ninth Regiment, N. G. P., March 29, 1880, was promoted to Major on May 15, 1884, and resigned Apr. 1, 1885. He always retained his interest in the National Guard and was trustee and president of the Ninth Regiment Armory Association.

Jan 1, 1922

U.S. Signs Pact With Miami Copper Miami Copper Co., of Arizona has agreed to mine lowgrade copper ores in an extension of its Globe-Miami mining district operations at a guaranteed price of 27.35[] per lb, under a contract signed with defense Materials Procurement Agency. Terms of the contract call for delivery of 230 million lb of refined copper between 1955 and 1962. DMPA said highgrade ore in the de posit will soon be exhausted and it is considered advisable to have Miami continue the operation. The Government has an option to buy 120 million lb of refined copper from present production at market prices. Miami will develop the new ore- body at its own expense-estimated at $3 million. If losses under the new contract reach a specified point, Miami may cancel the agreement. The company plans to use the block caving method in the underground operation.

Jan 4, 1953

By George Breyer

DURING the past 25 years the steelmaker has experienced some difficulty in producing steel to meet the standards established by the metallurgist. In contrast to the past, when a chemical specification of broad limits was the only requirement, he now has to employ such tests as microscopic, macroscopic, tensile, impact, Magnaflux and even X-ray and supersonic. The development of these tests has more than set the pace for a manufacturing process of which the exactness still hinges to an important degree on the ability of the furnace operator. In our efforts to produce steel, and especially alloy steel, to meet the exactness of modern engineering specification, many factors must be taken into account. It is not sufficient to make a good heat of steel in the furnace and then be satisfied that the job is done, since there are many pitfalls between the furnace and the finished product. The literature abounds with information on melting practices, deoxidation methods and slag control, but the lack of positive information about what happens when the steel is teemed into molds is quite evident. Such questions as what is the proper mold size, shape and thickness; which is the best mold coating; what is the best rate of pour for any given steel, and what is the effect of cooling rates on quality, are still answered by opinions. It is acknowledged that a poor heat of steel cannot be improved in the pouring pit. On the other hand, a good heat can be ruined by improper handling after it leaves the furnace.

Jan 1, 1947

By John B. Miles

THE present period of depression in the iron industry, with the resultant close approximation of the cost of production to the selling-price of pig-iron, should make the discussion of this subject at this time not only interesting but, profitable. It is possible that it may result, in the collection of data, which when added to those set forth in this paper will clearly indicate the influence of the rate. of driving a blast-furnace upon its fuel-economy. The question is not whether an excessive rate of driving (meaning a rate definitely in excess of the average rate in the United States) results in, an increase in the fuel-consumption, but rather whether a rate considerably less than the average does not result in a marked decrease in the fuel-consumption. The commercial and metallurgical sides of. this problem must be kept separate. With a large margin between the cost of production and the selling-price of pig-iron, and a plant already in operation, it is frequently profitable to sacrifice a couple of hundred pounds of fuel per ton of pig-iron in order to secure the greater gross profits resulting from a larger tonnage. When this margin decreases with a plant in operation, or when the determination of the size of a new furnace intended for a certain production . confronts the management, a clear understanding of the effect of the rate of driving upon fuel-economy becomes necessary. If it be granted that slow driving leads to low fuel-consumption, it should he borne in mind in the design of a new plant for the production of a certain tonnage that the adoption of an economical rate of driving increases only the size of the furnace proper, whereas, due to the decrease in quantity of blast required on account of the decrease in fuel burned, the stoves, the blowing-engines, the boilers and the piping may be de-

Sep 1, 1908

By A. C. Stevenson

THE hoisting equipment selected for use at the Hecla mine in 1907 was one of the first Ilgner type Ward-Leonard controlled hoists put into ser- vice. Development of the Hecla below the 2000-ft. level, which is the ultimate depth of the old equipment, and the additional service required by the "Star," necessitated additional hoisting capacity. It will be our endeavor to give j70u a brief summary of the engineering which determined the selection of the new equipment. The engineer in making his decision as to size, speed, etc., must .make a duty study approximating as closely &s possible the actual opePating conditions which will eventually result. Primarily, it is necessary to know what work must be done. The amount of material which must be hoisted under the maximum condition, as well as its distribution from the various levels of the mine was carefully studied by the mining engineering department, as the ore reserves, their relative-position and the probable method of working them had to be considered. The final figures reached, taking into consideration four different operating conditions, were, in tons per day, as follows:

Jan 1, 1930

By T. A. Rickard

"The chief aim in style ought to be absolute precision", said Flaubert. "There is only one noun that can express your idea, only one verb that can set that idea in motion, and only one adjective that is the proper epithet for that noun." Let this be your motto. The engineer tries to be exact in all his measurements; he should measure his language with similar exactness. The technical term is a word of precision. It is not only precise, it is a word-saver. To the unscientific the earth is "a ball slightly flattened at the poles, something like an orange". To the scientific it is "an oblate spheroid". A similar contrast between the precision of the technical term and the vagueness of common words is afforded by a conversation between Ivanhoe and Rebecca: "' What device does he bear on his shield?' asked Ivanhoe. 'Something resembling a bar of iron, and a padlock painted blue on a black shield.' 'A fetterlock and shacklebolt azure', said Ivanhoe "-using the technical terms of heraldry. It is good style in writing, however, to adapt your manner of expression to the intelligence and experience of the person or persons to whom the writing is addressed. The description of a mine should be worded differently according as it is intended to inform a mining engineer, a director, or a bishop. REMEMBER THE READER. It is as incorrect to write in a technical way for a non-technical reader as to write in a popular way for a technical or scientific reader. That style is best which enables the writer to place himself in the closest mental touch with his reader, to establish the maximum of sympathetic understanding. Let your precision be\ proportioned to your accuracy. You should not try to be precise in matters that do not admit of

Jan 1, 1931

By G. B. Walker

THE sink-float methods designated by heavy-media separation processes were pioneered by C. Erb Weunsch for the treatment of base metal ores as an improvement over jigs. The work of Weunsch was further developed by Victor Rakowsky and The American Zinc, Lead and Smelting Co. Early in the development of the processes, the inherent unsuitability of galena as the solid constituent of the medium was recognized and ferrous media amenable to magnetic recovery and control were developed. The high efficiency and low cost of magnetic recovery and cleaning of ferrous media regardless of particle size, slime contamination, or surfacial oxidation had led to the adoption of ferrous media by all of the sink-float plants operating under the heavy-media separation processes patents controlled by American Zinc, Lead and Smelting Co. Approximately 2,000,000 tons of base metal and nonmetallic minerals are treated each month by these methods.

Jan 1, 1949

By Meissner, C. A.

THE tendency all over Europe, just as it is with us, is to go to the use of turbines for new construction or replacement of old steam or even gas engines. 'The lower construction cost and the lower operating cost, when they can have high steam temperatures and pressures, together with their efficiency, is the cause of this change to turbines, both high and low pressure. The present trend is to equip plants with modern, efficient steam boilers, turbines, etc., and gradually work into high-pressure superheated steam equipment to accomplish a saving. One company has just completed a 375 to 400 lb., 700 deg. superheated steam installation and turbo-blowers with this end in view. Some of our new steam plants are using 350 lb. working pressure.

Jan 1, 1928

By R. J. Charles

SEARCH for a consistent theory to explain the relationship between energy input and size reduction in a comminution process has accumulated, over the years, an enormous amount of plant and laboratory data. Although some correlation of these data has been possible for purposes of engineering design and for the advancement of research in fracture, there is still great need of a means of predicting behaviour of a solid when it is reduced in size by mechanical forces. The best known hypotheses proposed to describe the energy-size reduction relationships in crushing and grinding stem from a common origin. The present article analyzes problems of comminution in the light of the precepts of this origin. Its object is to reconcile points of difference between these well known hypotheses and to present relationships more widely applicable to comminution studies.

Jan 1, 1957

By Arthur Zentner

THE PAST YEAR saw important developments in all the main branches of zinc metallurgy, which can only be douched on briefly here. Vertical Retort Smelting-The New Jersey Zinc Co. reports their operations to be about as last year when the number of vertical retorts at the Palmerton plant was increased from 16 to 28. The first unit of eight vertical retorts at Oker, Germany, to treat the Rammelsburg complex ore was completed early in the year. A second unit has been under construction and is probably ready to start operations about this time. Each unit is rated for 10,000 metric tons of zinc per year. A plant of 40,000 metric tons annual capacity is the goal. A reflux plant was also built to make high-grade zinc. The plant program is being -carried forward with government finan¬cial assistance, as was the case with the electrolytic zinc plant at Magdeburg. Government subsidies cover mining and 'smelting, and allow for depreciation and reasonable return on invested capital, according to U. S. Bureau of Mines reports.

Jan 1, 1938

The papers presented at the International Congress, held in San Francisco, Cal., Sept. 20 to 25, 1915, are published in 11 volumes of Transactions. In addition, an index volume is published, containing .besides the author and title index, a report of the business meetings of the Congress, and a brief digest of each paper presented. The following is a schedule of the volumes: Index and Digest.-General proceedings, indexes and digests. Vol. I. Panama Canal. II. Waterways and Irrigation. III. Municipal Engineering. IV. Railway Engineering. V. Materials of Engineering Construction. VI. Mechanical Engineering. VII. Electrical Engineering and Hydro-electric Power Development. VIII. Mining Engineering. IX. Metallurgy. X. Naval Architecture and Marine Engineering. XI. Miscellaneous. Aeronautics; Refrigeration; Agricultural Engineering; Engineering Education; Heating and Ventilation. Remember the New York Meeting, Feb. 14 to 17, 1916.

Jan 12, 1915

By Thomas T., Read

E DUCATION for the mineral industry was at first a single comprehensive curriculum, but it was early recognized that the main basis of mining is physics, while that of metallurgy is chemistry. The first school to offer curricula leading to degrees in mineral industry education in the United States (1853) had separate ones in mining and metallurgy. The Columbia School of Mines (the first really successful one) had only a single curriculum when it opened in 1864, but within a few years had so reorganized its work that it offered curricula in mining, metallurgy, geology, chemistry, and civil engineering. Interest in the metallurgy or geology curricula was slight at first, and for the next 30 years the great majority of Columbia students took the mining curriculum, probably partly because it contained nearly as much geology as the geology curriculum, practically all the metallurgy, and most of the chemistry, and partly because of the degree awarded for it. Other schools kept their mining curricula equally broad, and as late as 1900-1910 men were graduating as mining engineers who were practically as well prepared to make geology or metallurgy their life work, as they were for mining. Gradually, however, the subject matter of mining geology and metallurgy became so enriched through research and development that separate curricula in them became worth while; their progressive development is the subject of another chapter. Mining curricula also began to be somewhat diversified, and schools in areas where coal mining was of outstanding importance began to offer options in coal mining, the earlier curricula having been chiefly aimed at metal mining. The petroleum industry began its meteoric rise about the same time as mineral instruction in this country, but little more of applied science attended its birth than had attended such ancient practical arts as copper and iron

Jan 1, 1941

By L. A. Rapport, J. R. McCord, W. P. Drews, K. H. Coats

Water movement about an oil or gas reservoir can be predicted provided an aquifer influence function is known. This function is generally determined from an electric analyzer study or by fitting an idealized mathematical model to field data. A prohlem arises in determining that influence function which best reproduces field data and satisfies certain smoothness requirements, without making any idealizations concerning aquifer geometry and heterogeneity. This study shows the problem to be solvable through the linear programming technique and presents applications to one oil reservoir and two gas storage reservoirs. In addition, a theorem is stated and proven which confirms influence junction smoothness requirements heretofore accepted on physical intuition and establishes additiotzal smoothness constraints formerly not recognized. INTRODUCTION The pressure decline accompanying production results in water encroachment into oil and gas reservoirs situated adjacent to aquifers. The importance of this water movement derives from the significant dependence of production rate upon reservoir pressure and of pressure, in turn, upon water encroachment. Pressure and rate of water movement are uniquely related through an "influence" function which may be in the form of reservoir pressure response to a unit water encroachment rate or of water movement caused by a unit reservoir pressure drop. This influence function reflects the heterogeneity and geometry of the aquifer and is therefore particular to each reservoir. If the influence function is known, then reservoir pressure may be predicted from a production rate schedule, or vice-versa, with the aid of the material balance equation which relates water influx to reservoir production and pressure. The problem of determining this influence function for a given reservoir has been approached in three different ways. Van Everdingen and Hurst calculated and tabulated certain influence functions pertinent to idealized mathematical models which satisfy simplifying assumptions such as aquifer homogeneity and elementary reservoir-aquifer geometries.' Other studies developed additional tables for a variety of elementary reservoir-aquifer geometrical con- figurations and demonstrated their validity and utility.:' Hicks, et al. described the use of an electrical network to determine an influence function giving "best" match of field history and allowing prediction of future performance.' Finally, Hutchinson and Sikora5 and Katz, Tek and Jones attempted to develop a calculation method for deriving the influence function directly from field data with no idealizing assumptions concerning aquifer geometry and homogeneity. They encountered difficulties with inaccuracies in field data and with satisfaction of well-known smoothness requirements of the influence function. This study is concerned with the determination of influence functions from field data and, more specifically, treats the following problem: given field pressure-production data of arbitrary accuracy, how does one determine the influence function which, subject to satisfaction of known smoothness requirements, gives best agreement with field history? A rigorous solution to this problem is ohtained through linear programming as described below. Example applications to one oil and two gas storage reservoirs are presented. In addition, a theorem is proved which confirms influence function smoothness requirements heretofore accepted on physical intuition and establishes additional smoothness requirements formerly not recognized.

Jan 1, 1965

By Thomas T., Read

T HE preceding chapter has recorded the initiation of mineral industry education during the period 1890-1910 in numerous institutions that had not previously offered it. It should also be emphasized that in many institutions where instruction had begun before 1890, as recorded in earlier chapters, but had not yet become firmly established,, this period was one of marked growth and development. This was not universally true, however, for at the Universities of Pennsylvania, Michigan, Illinois, Wisconsin, Washington (St. Louis), Iowa, Vanderbilt and Tennessee, and at the Polytechnic College of Pennsylvania, mineral industry instruction was being dropped during this period, instead of gaining in strength. It is necessary to emphasize this, because writers on the subject have not infrequently , attempted to make a much too simple correlation between mineral -discovery or production and the intensity of student interest in mineral industry curricula. It would naturally be true that periods of large mineral production would, in general, coincide with cycles of business prosperity, and the latter are conducive to starting new ventures, educational as well as business. It should be equally evident that opportunities for business and professional success might, in such periods, appear to increase at a more rapid rate in industries other than mineral, or in the utilization of minerals rather than in their production. The author has not been able to perceive any simple and clear relation between interest in mineral industry education and mineral discovery, production, and utilization, or general business prosperity. On the contrary, the more the problem is studied the more complex the factors involved in it appear to be. In a later chapter an attempt will be made to analyze them in more detail.

Jan 1, 1941

By E. A. Holbrook

AS A whole, engineering schools have not awakened A to the fact that the workmen compensation laws passed in most of our states between 1914 and 1917 effected a quiet but none the less real revolution in. the relations between labor and management; no longer are industrial accidents unfortunate or careless happenings over which we feel a humanitarian interest and sorrow, they are a cost of the process and the finished product, as vital as improved design and increased efficiency. Last year the writer and others made a committee report to. the American Institute of Mining and Metallurgical Engineers on the cost of accidents in the coal industry of Pennsylvania. Comparatively the accident record in Pennsylvania coal industry is not high, yet the direct compensation cost plus the interference with operation cost of accidents was over 5 per cent. of the total cost of producing the coal. This stands out more vividly -if you realize that about 70 per cent. of the' cost of producing the coal is for payment of labor, wages that are fixed and over which engineering efficiency and management skill have little or no direct effect. This leaves 30 per cent. of the cost chargeable .to hoisting, haulage, overhead 'and other items subject to engineering control. One sixth of this is due to cost of accidents. Surely a direct place 'for an engineering attack.

Jan 1, 1925

By E. D. Gardner

The tide of increasing demand for metals turned during early 1949, with resultant lower prices. The production of the principal metals was less than in 1948. The problem of high unit costs, however, was held over from 1948. With the lower prices for metals, greater efforts are being made to reduce operating costs. The labor supply was adequate during the latter half of the year in most districts. The force has been reduced at most mines; some mines were idle during part of the year because of strikes, and others ceased operations on their own account. In the main, labor efficiency increased during the year in underground metal mines. Efforts are being made generally to improve labor relations. Green men hired in the time of the scarcity of skilled miners are becoming better trained. The supervisory personnel of most mines is cost conscious, and the planning of operations has been improved. Overhead costs are being scrutinized. The trend toward mechanization underground continued strong. Mining technology rapidly is becoming a problem of handling materials. Surface miners, underground miners and miners of metals, nonmetallics, and coal can learn much Gardner from each other. A mine, however, may become overmechanized. The capital charges against new equipment may exceed the saving in labor costs where sufficient daily tonnage is not handled.

Jan 1, 1950

By Fred J. Miller

FRED J. MILLER was born in Ohio, in 1857. He had a common and high school education, supplemented by personal study and special instruction. After serving a 4-year apprenticeship and working in various capacities in machine shops, he became a contributor to mechanical journals and finally a member of the editorial staff of The American Machinist, where he remained for twenty years, the last ten years as editor-in-chief of the magazine, and vice-president of the publishing company. On retiring from journalism, he was for nine years general manager of a group of typewriter factories, and was then commissioned Major of Ordnance in the U. S. Army, being stationed during most of his service at Rock Island Arsenal, where he organized the Civilian Service Division of the Arsenal. He is now a member of the Technical Advisory Committee of the War Claims Board at Washington. Major Miller became a member of the American Society of Mechanical Engineers in 1890, and has always taken an active interest in its affairs, having served on a number of important committees, and as a member of Council from 1904 to 1907, inclusive. He was elected President in December, 1919.

Jan 1, 1920

By Stephen Zorn

INTRODUCTION The process of financing mining projects in developing countries has changed greatly in the past 15 years. New methods of financing, notably the use of syndicated Eurocurrency project loans, have appeared, and direct equity financing by transnational mining corporations has become less significant. These changes are of particular importance to developing countries which have many mineral deposits still awaiting development, or even discovery. If major new mines are to be financed, host governments will need to obtain more sophisticated information than has hitherto been widely available as to the various sources of finance currently available and as to possibilities for innovative approaches to financing, such as the combination of several different kinds of financing in a single package. This paper reviews the major sources of mining finance potentially available to developing countries and highlights those problems in obtaining adequate financing that developing country producers have begun to experience in the last few years and that are likely to persist through the 1980s. Section I surveys the major types of mining finance; section II reviews specific financing problems, including (a) the withdrawal of the transnational corporations from developing countries, (b) inflation and the size of new projects; (c) developing country indebtedness, and (d) competition among projects in different countries. SOURCES OF DEVELOPING COUNTRY MINING CAPITAL1/ There is a wide range of financing mechanisms which are potentially available to developing countries with economically viable mining projects., Moreover, these financing mechanisms have not been fully exploited by developing countries, and more aggressive pursuit of financing by the governments of these countries may well reveal greater possibilities in respect of any particular project than may initially have appeared. However, virtually all the funds available from these sources are available only to projects which meet the standards of viability acceptable to lenders and others in the business community. If a project does not, for example, promise to generate a discounted cash flow rate of return of at least 15 per cent on total funds employed, or if it does not appear likely to generate sufficient cash flow in the early years of production to cover debt service requirements with a comfortable margin in reserve, most of the sources of financing will not be available. Only where a government has its own financial surplus (as in the case, for example, of the industrialization program of the Saudi Arabian government) can it effectively undertake projects which do not satisfy the definition of economic viability that is accepted at any given time by the worldwide financial community. Internal Sources In Developing Countries Internal financing capacity in developing countries is restricted to a relatively small number of countries - typically those large enough to support a well-rounded industrial sector, in which mining is only one of a number of dynamic industries. While there are large mining companies in certain other countries, the ability of such companies to finance new projects (or even, in some cases, to generate the cash necessary to maintain existing levels of production) is highly problematical. Within developing countries, the possible sources of internally-generated mining finance are the following: (1) state-owned enterprises; (2) private capital; (3) the banking system, and in particular those financing agencies that have a special involvement with the mining sector; and (4) direct budgetary appropriations.

Jan 1, 1985

By AIME AIME

A SYMPOSIUM on current. conditions in Mexico, particularly in the oil and mining industries, was a most successful feature of the May meeting of the New York Section of the A.I.M.E. Heath Steele, vice-president of The American Metal Co.. Ltd., with an intimate knowledge of Mexico gave the principal address, and asked that his analysis of the present situation he regarded neither as an endorsement of Mexico's policy nor as the criticism of a disgruntled operator. To explain the .attitude of the great mass of the Mexican people towards recent developments, he first described briefly the political, social, and religious beliefs and customs of tile Mexican Indian. In spite of their contact with foreigners these beliefs and customs have remained unchanged throughout many generations. The old communal spirit and the idea of common ownership of the land still persist especially in the rural districts and villages; the old custom of a council for local self-government is reflected in the present-day labor committee. Mr. Steele discussed in order land oil, and mines.

Jan 1, 1938

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