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By Edward L. Wilson, Keshavan Nair, Ranbir S. Sandhu

In planning and designing of underground excavations and construction, it is of considerable importance that the stresses and displacements in the rock mass subjected to arbitrary sequences of unloading and loading be within allowable limits. For determination of the stress and displacement fields, the usual approach is to treat the rock as an elastic material and to apply the principles of the theory of elasticity. However, analytic solutions are available only for a limited class of problems of simple geometry and idealized material properties. Nonhomogeneity and anisotropy of material coupled with complex geometrical configuration and initial stress fields that are almost always preexistent in rock masses at great depths, render the problem intractable by analytical methods. Approximate solution techniques using numerical procedures have, therefore, to be resorted to. The finite element method as applied to plane stress analysis was introduced by Clough.1 It has developed into a powerful tool for the analysis of various field problems in structural and continuum mechanics. The method is well documented in the literature2-6 and, therefore, its historical development will not be discussed here. Wilson's analysis of the plane stress/strain problem has found extensive use in the area of soil and rock mechanics including stresses around underground openings; stresses and displacements in dams, foundations, etc.7-11 In his analysis of the axisymmetric solid,3 Wilson proposed a procedure to allow for certain cases of nonlinear material properties. In this chapter, the develop-

Jan 1, 1972

Thomas H. Beddall, so we are informed by Major J. B. Carlock, has been promoted and is now Adjutant of the 1st Battalion, 1st Gas Regi¬ ment. He was awarded, last summer, the Croix de Guerre. R. A. Bull. See letter in Proceedings of Milwaukee Meeting. Captain Stanley C. Bullock's record since entering the service is given as follows in a letter recently received from Mrs. Bullock: Resigned position of mine manager in Chile in November, 1915, to return to England to obtain commission in Royal Engineers. Joined Officers' Training Corps, Dec. 20, 1915. Commission gazetted, Jan. 27, 1916, 2d Lieut., R. E. Landed in France, Feb. 6, 1916. Posted to 179th Tunnelling Co., R. E. Took part in following battles: Somme, 1916; Ypres;1917; Arras, 1917; Somme, March and July, 1917; Messines, 1917. Gazetted: Acting Captain, July 11, 1916; Temp.-Lieutenant, Oct. 26, 1916; Captain, Sept. 29, 1918. Awarded Military Cross, Jan. 1, 1918, for conspicuous bravery and devotion to duty under a heavy enemy gas bombardment, when, by his example and perseverance in spite of every difficulty and obstacle, mining work was successfully completed which was vital for the success of the operations. The Cross was presented to Capt. Bullock by the King, on Sept. 25, 1918. First Lieut. J. J. Cadot, in a letter sent to Mr. H. `V. Hardinge from France, says he has been at the "Front." He also mentions that the Boche "is a good sprinter."

Jan 12, 1918

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members) The following is a partial list of members and guests who called at Institute headquarters during the period June 10, 1917, to July 10, 1917. Guy N. Bjorge, Boston, Mass. H. H. Lauer, Allentown, Pa. A. H. Burroughs, Jr., Britannia Beach, E. C. Lee, Pittsburgh, Pa. B. C., Canada. Montrose L. Lee, Port-au-Prince, Hayti. Karl Eilers, New York, N. Y. Eugene McAuliffe, Paducah, Ky. H. S. Emlaw, Grand Haven, Mich. R. H..McMillen, Pittsburgh, Pa. W. R. Hamilton, San Francisco, Cal. L. D. Moore, Providence, R. I. Fred N. Hays, Sharon, Pa. Fred J. Pope, New Rochelle, N. Y. E. Hibbert, Nickelton, Ont., Canada. George S. Rice, Washington, D. C. Charles Janin, San Francisco, Cal. W. G. Swart, Duluth, Minn. Milton A. Allen has resigned his position with the Federal Lead Co. and accepted a position with the Arizona State Bureau of Mines, Tucson, Ariz. L. W. Bahney has resigned as Professor at Yale University and accepted a position as metallurgical engineer with the Scovill Manufacturing Co., Waterbury, Conn.

Jan 8, 1917

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the period May 10 to June 10: Rene de Sallier, New York, N. Y. Karl Koelle, San Luis Potosi, Mexico. H. S. Chamberlain, Chattanooga, Tenn. W. A. Wilson, Salt Lake City, Utah. F. R. Pretyman, Oyster Bay, N. Y. P. E. Barbour, Candor, N. C. R. Eustice, South Australia. R. C. Blanchard, London, England. F. C. Darby, South Australia. S. K. Tong, Shanghai, China. Grant H. Tod, Livermore, Cal. W. T. Burns, Great Falls, Mont. J. Murray Clark, Toronto, Canada. F. W. Bacorn, Butte, Mont. J. H. Adams, Birmingham, Ala. H. B. Pulsifer, Chicago, 111. A. Faison Dixon, Encontrador, Venezuela. Dwight E. Woodbridge, Duluth, Minn. C. W. Merrill, San Francisco, Cal. Heinrich Ries, Ithaca, N. Y. Francis Church Lincoln, Boston, Mass. H. L. Slosson, San Francisco, Cal. Frank R. Corwin has severed his connection with the Arizona Copper Co., Clifton, Ariz., and is now shift superintendent at the smelting plant of the Copper Queen Consolidated Mining Co.. Douglas. Ariz.

Jan 7, 1914

By D. Atkinson, C. Bodsworth, I. M. Davidson

A geometric model of interstitial solid solutions, which has been used previously as a basis for the prediction of carbon activities in Fe-C austenite, is shown to serve also for the calculation of nitrogen activities in Fe-N austenite. The model has been developed to enable predictions to be made of the activities of an interstitial element in the presence of two host atom species. The activities calculated via the model are shown to be in satisfactory agreement with the measured values in the austenite phase for carbon in Fe-C-Co, Fe-C-Cr, Fe-C-Ni, Fe-C-~n, Fe-C-Si, and Fe-C-V alloys and for nitrogen in Fe-N-Ni alloys. The effect of the second substitu-tional solute on the logarithm of the activity of the interstitial element is expressed as the product of a constant mad the atomic concentration of that solute. The constants so derived we related to the thermo-dynamic interaction coefficients which describe the effect on the activity coefficient of carbon of an added solute element. In recent years the thermodynamic activities of carbon and nitrogen in the single-phase austenite field have been determined for iron binary alloys and for several iron-base ternary alloys. In order to extend the use of these measurements, it is desirable to be able to predict with reasonable accuracy the activities of the interstitials at compositions and temperatures other than those which have been measured experimentally. In all the systems studied to date, the interstitial elements do not conform to ideal behavior. Hence, the available data cannot be extrapolated or interpolated using the simple thermodynamic concepts of solutions. Several models have, therefore, been formulated for the purpose of predicting the activity of an interstitial element in the presence of one species of host atom. These models can be divided into the geometric1"5 and energetic6-' types. The former group is based on the assumption that at low concentrations the activity of the interstitial species is determined by a composition-dependent configurational entropy term and an excess free-energy term which is temperature-dependent but independent of composition. The purpose of this paper is to show that the treatment, based on a geometric model, can be extended to enable predictions to be made of interstitial activities in the presence of two substitutional host atom species. THE CONFIGURATIONAL ENTROPY OF MIXING ICaufman5 has shown that the configurational entropy, S,, for a binary solution comprising of a host atom species, A, and an interstitial species, I, can be expressed as: where NI is the atom fraction of the interstitial species, R is the gas constant, and (2 - 1) is the number of interstitial sites excluded from occupancy by the strain field around each added interstitial atom. The number of interstitial sites per host atom, p, is unityg for the fcc austenite solutions considered here. The configurational entropy of mixing for a ternary solution comprising two substitutional atom species, A and B, and one interstitial species, I, can be derived similarly. Let the number of atoms per mole of each of these species in the solution be represented by «a, ng, and nI. From geometric considerations, it is improbable that the addition of a few atom percent of a second host atom species will change the type of sites (i.e., octahedral) in which the interstitial atom can be accommodated in the austenite lattice. At higher concentrations (determined largely by the relative atomic radii of the atomic species present and any tendency to nonrandom occupancy of the host lattice sites) other types of interstitial sites may become energetically favorable. Restricting consideration to compositions below this limit, for 1 = 1 the number of suitable interstitial sites is given by (n + nB). However, if each interstitial atom excludes from occupancy (Z - 1) additional sites, the total number of sites available for occupation is reduced to (n + ng)/Z. The number of vacant interstitial sites is given by: The total number of recognizable permutations of the atoms must include the recognizable, different configurations of the A and B atoms on the host lattice. Assuming that these arrangements are purely random, and are not affected by the presence of the interstitial species, the total number of recognizable permutations in the ternary alloy is given by: The configurational entropy is obtained by expanding, using Stirling's approximation, and collecting like items, as:

Jan 1, 1969

By E. W. Davis

DURING late years, the proportion of beileficiated iron ore shipped from the Lake Superior District has increased very rapidly. By benefication is meant washing, screening, drying, sintering or any process by which the grade or structure of the crude ore is improved before shipment. In 1915, only 3,000,- 000 tons, or 9 per cent, of t6e total Minnesota shipment was beneficiated ore, compared with 13,500,000 tons, or 35 per cent, of the total Minnesota shipment in 1925. This increase is, of course, due to the fact that iron and steel can be made more cheaply after beneficiating these ores than they could have been had these ores not been so treated. Fundamentally, however, several causes contribute to the necessity for beneficiating iron ores, such as depletion of the reserves of high-grade ores, the iron ore leasing systems and taxation methods and, at the smelting plants, a better understanding of blast-furnace operations, increased operating costs and increased sulfur content of blast-furnace coke. As economic conditions change, it is by no means certain that the proportion of beneficiated ore shipped each year is going to continue to increase. Undoubtedly some of the beneficiation operations are not economically sound at the present time and what the future has in store for the iron ore industry is problematical. Generally speaking, the cost of fuel for blast-furnace operations will increase as time goes on and in order to continue to produce cheap iron and steel, some of the other costs must be lowered. Freight and labor rates probably can- not be reduced. The cost of producing iron ore cannot be reduced much below the present price. It therefore appears that the best opportunity for maintaining iron and steel prices at their present level in spite of in- creased costs of labor and raw materials is to use. less or cheaper raw materials. This, of course, contemplates an improvement in metallurgical processes all along the line and, as a matter of fact, we can confidently expect these improvements because scientific investigations will undoubtedly be even more productive in the future than they have been in the past.

Jan 1, 1926

By Clyde E. Williams

MODERN steelmaking has gradually evolved from an inefficient small-scale operation, utilizing tiny units, to a highly efficient one utilizing large units almost completely mechanized. The leading position of the United States in the steel industry is due to the possession of easily assembled high-grade raw materials and large-scale highly developed plants. Modern integrated steel operation is largely one of material handling. Mining and transportation of iron ore, coal, and fluxes, coking the coal in by-product ovens, smelting the ore with coke and limestone in blast furnaces, converting the resulting pig iron into steel in the Bessemer, or in the open hearth when supplemented with scrap, and fabricating the resulting steel ingots in the shapes of commerce all are done on a huge scale, mostly by machinery, most of the labor being employed either in operating the machine or keeping it in repair. At the same time the quality and uniformity of the product have been greatly increased by the development of scientific knowledge and operating skills. Thus, the steel industry in this country is highly developed both mechanically and technically.

Jan 1, 1942

By A. B. Kinzel

ALTHOUGH the iron-carbon diagram has undergone many changes in the last 20 years, the region below the eutectoid line and up to approxi-mately 1.7 per cent carbon has been little affected. This region is generally considered to consist of cementite and ferrite. Graphite has been noted occasionally in the hypereutectoid steel region, and the ready formation of graphite nodules in malleable cast iron is a phenomenon difficult to interpret in the light of cementite, supposedly stable at sub-eutectoid temperatures. In this case the graphite formation has been partly explained by the presence of silicon, and many have believed that silicon acts to change the stable state rather than to accelerate reactions so as to arrive at the stable state in a briefer period of time. Consider-ation of this phenomenon indicates that cementite is not the stable phase in the temperature composition zone referred to. In the course of examining a low-carbon steel tube taken from a petroleum cracking still, which had been in service for approximately three years at temperatures somewhat below the eutectoid temperature, observations were made that shed light on this entire subject. The tube in question analyzed:1 C, 0.15 per cent; Mn, 0.49; Si, 0.02; S, 0.023; P, 0.015. The microstructure of the tube after service is shown in Figs. 1 and 2. From these it is evident that cementite as such is absent, and that in its place nodular graphite has been formed. In order to check this observation further, samples taken from the tube were heated at 850° C. for varying periods of time. The small samples were put into a large hot furnace, and the total time is recorded. The structure of the

Jan 1, 1934

By AIME AIME

0 N March 5, at Carnegie Hall, Cleveland, the Ohio Section held a joint meeting with the Cleveland Engineering Society, and the local sections of the American Chemical Society, American Society of Mechanical Engineers, and the American Society for Steel Treating. Prior to the meeting there was an informal dinner attended by 50 men. Then followed an address, "The Principles of Corrosion Protection," by Ulick R. Evans, the well-known British specialist in this problem. There were 266 present, presided over by Zay Jeffries, president of the American Society for Steel Treating and a member of the Cleveland Engineering Society. The address was well received and some discussion followed

Jan 1, 1929

PROF RICHARD ÅKERMAN Stockholm, Sweden DR. FRANK DAWSON ADAMS Montreal, Canada PROF RICHARD BECK Friberg, Germany ANDREW CARNEGIR New York, N.Y. DR. JAMES DOUGLAS New York, N.Y. PROF HATON DE LA GOUPILLIERE Paris, France SIR ROBERT A. HADFEILD London, England PROF HANS HOFFER Leoben, Austria JAMES FURMAN HOEFER Leoben, England PROF HENRI LOUIS LE CHATELIER Paris France

Jan 1, 1917

Idaho Bureau of Mines and Geology, University of Idaho, Moscow, Ida. John W. Finch, Director. A list of publications will be sent upon application. A series of Bulletins and Pamphlets have been issued by the Bureau to date since 1920 Of the Bulletins, six are out of print, and a charge is made for eight. Each of the Bulletins, in the main, treats of the geology and resources of a particular district in Idaho, as follows (only available Bulletins listed): Bulletin 1, South central Idaho (1920), 15 cents, 7, North central Idaho (1924), 50 cents, 8, Bonneville, Bingham and Caribou counties (1924), 50 cents, 9, Boise Basin (1924), 50 cents; 10, Boundary County (1926), 50 cents; 11, Region about Silver City (1926), 50 cents; 12, Clark Fork district (1930), 50 cents, 14, Eastern Cassia County (1931), 50 cents, Press Bulletin 15, Teton County (1927), Bulletin 16, Melon Valley near Buhl (1927); 17, Concerning land slips near Whitebird, Idaho (1928) The 37 Pamphlets are issued free of cost, and each treats, also, in the main of the geology and resources of a particular district in Idaho Nos 1, 2, 3, 4, 5, 7, 8, 10, 17, 18, 20, 22, 25, 26, 30 and 35 are out of print Of those available, attention may be called to Pamphlet 6, Reported platinum occurrences near Coeur d' Alene (1925), 11, Bruneau River Basin, 12, Power and Oneida

Jan 1, 1933

[PAGE PREFACE. A. B. PARSONS 3 OFFICERS AND DIRECTORS 7 STANDING AND SPECIAL COMMITTEES 8 PROCEEDINGS OF 1935 MEETINGS 10 NEW YORK, FEBRUARY 10 CHICAGO, OCTOBER 14 SAN FRANCISCO, OCTOBER 14 HOUSTON, OCTOBER 15 ST. LOUIS, OCTOBER 15 ABSTRACTS OF PAPERS PUBLISHED IN 1935 17 TECHNICAL PUBLICATIONS AND CONTRIBUTIONS, 1935 64 INDEX OF 1935 PUBLICATIONS 71]

Jan 1, 1936

What has happened to the basic coal industry during the past year? Has it been a better year for coal than 1961? What striking new developments have occurred in mining, preparation and utilization? Are there positive signs that production will go up? What has happened in the utility market, the metallurgical market and the export market? Is the controversial question of coal transportation nearer to a solution? What progress has research made for coal during the year? The answer to these and many other important questions are offered in the following review of the Coal Industry-1962.

Jan 2, 1963

By AIME AIME

THAT the copper industry is in serious straits is admitted. So are the lead and zinc industries, and both lead and zinc are tariff protected. Conditions in the Western lead, zinc and silver mining districts are desperate. These are illustrated by the present disastrously low prices of these metals compared with the levels of two and three years ago and by the comparative rates of metal production and the present activity of the western mining camps. The January production of copper was 32.2 per cent of the 1929 average rate, of steel was 32.3 per cent of the 1929 average, while January production of pig iron was only 27.6 per cent of the monthly average of 1929. The copper industry is only one of many industries that are suffering in this tragic depression. It has been exceedingly prosperous and will be prosperous again when business recovers. Its difficulties are not unique and it does not deserve the tariff equivalent of a dole. The burden of subsidizing through an effective tax or tariff the minority group of high-cost mines would be a heavy one on the consuming public of the United States. On the basis of 1929 consumption figures, an effective 5c. tariff would result in an increased copper bill to the country of over $109,000,000, of which the electric manufacturers would contribute $26,000,000, the telephone and telegraph companies $16,000,000, and the automobile manufacturers $14,000,000. And of this total bill, only $33,000,000 would go to those who are urging a tariff and the balance of $76,000,000 would be paid to those who do not admit either its necessity or usefulness under present conditions.

Jan 1, 1932

By R. F. Miller

DUE to wartime secrecy restrictions a large part of the technical information developed by government and industrial laboratories was withheld from distribution. Much of this information has now been released or "declassified" and reports of technical work carried out during the war in allied and enemy countries are also becoming available. Information on the latter subject has been augmented by the work of the Technical Industrial Intelligence Corps of the U. S. Army. Through the Joint Chiefs of Staff, rep¬resentatives of this Corps co-operated with the British Combined Intelligence Observations Subcommittee, and some of the observations were made by combined personnel of both groups. The U. S. Government has undertaken the indexing and abstracting of all of this information in the Bibliography of Scientific and Industrial Reports, a weekly bulletin which appeared first early in 1946. Other publications, such as the Bulletin of the British Iron and Steel Institute and The Metals Review of the American Society for Metals, provide abstracts of domestic and foreign magazine articles and papers presented to technical societies. However, they do not cover the industrial and government reports recently released by the Government nor the reports of the Army investigators hence the new bibliography is a welcome addition to our metallurgical library.

Jan 1, 1947

By James E. York

THE honor so fairly earned and so incompletely and tardily paid to Henry Cort, the inventor of the puddling-furnace and the, rolling-mill, has been fully set forth by Mr. Charles H. Morgan,1 and needs no further emphasis here. In view of the importance of the rolling-mill in the treatment of iron and steel, the paucity of information concerning it is surprising. With the exception of a hook, written about 35 years ago, by Peter Bitter von Tunner, an Honorary Member of this Institute, and of desultory articles on simple sections, which have appeared in technical journals, I know of no pub¬lication attempting to treat this subject, although volumes have been written on the scientific theory and technical manipulations involved in other branches of the iron- and steel-industry. This strange anomaly may be due to the fact that roll-turning cannot be called a scientific business. It does not ordinarily come within the range of an educated engineer; yet it cannot be performed by an ordinary mechanic. It demands some of the qualifications of an engineer, in designing, and those of a mechanic, in execution. The men who have followed this trade have controlled the training of their successors. In many cases the technical knowledge required bas been handed down from father to son, and there has been a motive of private interest to prevent its public dissemination. Moreover, the statement of the various principles involved in the process would require, besides manual experience, a degree of scientific knowledge which roll-turners do not usually possess; and, finally, any book on the subject, in order to possess real, practical value, would have to be so fully illustrated as to make it very costly to publish. Regarding my own experience, I may say that I served a six-

May 1, 1906

By J. F. Myers, F. M. Lewis

The paper reports the development of a large, slow speed ball mill closed circuited with a hydroscillator. This increased grinding efficiency 28 pct over conventional units.

Jan 1, 1950

By AIME AIME

General Local Committee.-John Fritz, Chairman; A. B. de Saulles, Vice-Chairman.; R. M. Bird, Treasurer; Henry S. Drinker, Secretary; Robert H. Sayre, E. P. Wilbur, Charles M. Dodson, Abraham S. Schropp, E. M. McIlvain Archibald Johnston, A. B. Fichter, C. G. Convers, W. A. Wilbur, Garrett B. Linderman, Frederick Conlin, George Pettiuos, Albert Brodhead, Garrett L. Hoppes, M.B. Cutter, H. J. Seaman, C. A. Matcham, B. F. Fackenthal, Jr., A. L. J. Queneau, Geo. R. Elder, Eldridge Wilbur, William H. Chandler, Mansfield Merriman, Joseph F. Klein, William S. Franklin, William Esty, Joseph AN'. Richards, Howard Eckfeldt, John D. Irving. Transportation Committee.-H. J. Seaman, C. A. Matcham, B. F. Fackenthal, Jr., A. B. Fichter, A. L. J. Queneau, Henry S. Drinker. Hotel Committee. -Garrett B. Linderman, Charles M. Dodson, W. A. Wilbur, Garrett L. Hoppes, Albert Brodhead. Steering Committee.-William S. Franklin, William Esty, John D. Irving, R. M. Bird, the members of the Tau Beta Pi Society of Lehigh University. Committee on Meetings - William S. Drinker, Joseph W. Richards, Howard Eckfeldt. Entertainmment Committee.-W. A. Wilbur, E. M. McIlvain, Archibald Johnston, A. B. de Saulles, G. G. Convers,.A. L. J. Queneau, Garrett B. Linderman, Frederick Conlin, George Pettinos, Garrett L. Hoppes, Henry S. Drinker, William S. Franklin, Eldridge Wilbur, Robert M. Bird, Secretary. The opening session was held at 8.30 p.m., Wednesday, February 21, 1906, in Gymnasium Hall of Lehigh University, which had been tastefully decorated with flags and bunting. Dr. Henry S. Drinker, President of Lehigh University, and Secretary of the General Local Committee, called the meeting to order, and welcomed the Institute to the Bethlehems, where its first meeting, after its organization in May, 1871, at Wilkes-Barre, was held in August, 1871.*

May 1, 1906

By B. T., Colley

AS always when metallurgical operations are conducted within or close to agricultural and stock-raising regions, the question of damage due to fume and smoke presented itself when the Cerro de Pasco Copper Corporation's new smelter commenced to operate in La Oroya in 1922, For more than twenty years the Corporation had operated its old plant close to Cerro de Pasco without encountering difficulties from smoke claims, owing to the fact that it was in an open plain where more or less constant air currents carried and dissipated the smoke over large areas, affording ample dilution. But Oroya is in a deep canyon formed by four contributing valleys up and down which the smoke travels for long distances in a more or less concentrated form. Though the altitude of Oroya is more than 12,000 ft., and the surrounding country rises to much greater elevations, nevertheless there exists there a large and important stock-raising industry and also a considerable development in agriculture, consisting of the cultivation of potatoes, barley, etc.

Jan 1, 1945

By Thomas A. Steven

Most mineralized areas in the central San Juan Mountains, Colorado, are associated with the youngest subsidence structures in a large volcanic cauldron complex that formed concurrently with eruption of the surrounding ash-flow field. Two local types have been recognized: (1) fissure-vein deposits along faults characterized by relatively late movement, and (2) hydrothermally altered and mineralized areas associated with postsubsidence Fisher Quartz Latite centers. The first type has provided most production in the past; the potential of the second type has yet to be adequately tested.

Jan 1, 1968