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By Alfred E. Hunt

By the death of Joseph Dame Weeks, past-President of this Institute, which occurred December 26, 1896, the world has lost an earnest and unwearied philanthropist; the Christian church, a zealous, active and consistent representative; the United States and the State of Penusylvania, a patriotic, pub-

Jan 1, 1898

By H. Morgolin, M. A. Greenfield, P. A. Farrar

In attempts to correlate mechanical properties with microstructure, it is desirable to determine the effect of ß grain size. Determination of 6 grain size is not a problem where a has precipitated at ß grain boundaries. However, in alloys which have been processed to produce an equiaxed a +ß structure the ß grain size is difficult to determine because ß grain boundaries do not etch. The ß grain size can sometimes be laboriously determined by searching for grains which have some a! outlining the 6 grains. This difficulty of ß grain size determination in equiaxed a + ß alloys can be overcome by heating below the ß transus temperature for a short time and water quenching. Fig. 1 shows the starting equiaxed a + ß structure of the Ti-5.25A1-5.5V-0.9Fe-0.5Cu alloy used in this investigation, and Fig. 2 shows the microstructure of the same sample water-quenched after heating 1 min at 1675"F, which is 25°F below the 0 transus. The heavily etched microstructure consists of some equiaxed a! in a structure showing considerable amounts of transformed ß. The ß grain

Jan 1, 1969

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

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

Jan 10, 1963

INSTITUTE OF METALS DIVISION Ferrous and Nonferrous Physical Metallurgy (By-laws in Transactions, Vol 156, 1944) Established as a Division April 26, 1918 Walter A Dean, Chairman R. M. Brick, Past-Chairman Morris Cohen, Senior Vice-Chairman J H Scaff, Vice-Chairman Ernest Kirkendall, Secretary-Treasurer

Jan 1, 1952

By J. M. Uys, T. B. King

WalSH, Chipman, King, and rant' have measured the water content (as hydrogen) of actual steel-making slags. An average water content of 290 ppm was found for basic open-hearth tapping slags and 114 ppm for acid open-hearth slags. Upon equilibration of these slags at 1550°C with a 25 pct H20-75 pct Nz atmosphere, the water content increased to about 410 and 300 ppm for the basic and acid slags, respectively. Walsh et al. concluded that an acid slag was thus relatively far removed from equilibrium, and that basic slags showed a closer approach to equilibrium, with the water vapor in the furnace atmosphere. Herasymenko2 contended that these conclusions were unjustified, as the oxygen pressure used in the equilibration experiments, ;bout 5 x X atm, was quite different from that found in the furnace. Consequently, during the experiments the slag composition would have changed due to oxidation of ferrous iron. As an extension of Walsh's work and to attempt to clarify this matter, the solubility of water in a basic open-hearth slag was measured as a function of oxygen pressure. Similar measurements were also made on synthetic silicates in the "Fe0"-Fe203-SiO, system. The experimental technique has been described previously by Walsh et a1.l and Uys and King.3 Samples of the basic open-hearth finishing slag, contained in 10-cc platinum crucibles, were equilibrated at 1550°C with atmospheres of different oxygen pressure but constant water-vapor pressure, Ph~o = 0.192 atm. Calculations, as well as measurements, indicate that this figure approximates the water pressure of the combustion gases in a steam-atomized, oil-fired open hearth. Oxygen pressures in the open hearth can vary from 10"2 atm in the combustion gases to between l0-' and 10" atm in the steel bath. The former figure depends on the combustion practice and the latter on the carbon content and temperature of the bath. The oxygen pressure of the slag should lie somewhere between these extremes and is expected to be closer to that of the steel bath than that of the combustion gases. Oxygen pressures were therefore varied between 10" and 6 x l0 atm. At the lowest pressure the slag "puffed up" when quenched (indicating possible loss of water) so experiments were not conducted at lower oxygen pressures. The results are shown in Fig. 1, which includes the water content of the slag "as sampled". The results show that the water content of the slag increased appreciably on equilibration with water vapor at 0.192 atm pressure and that the water solubility apparently decreases with increased oxygen pressure. The solubilities found are comparable to those of the Li20-Ca0-Si02 system.3 Work with synthetic slags in the "Fe0"-Fe203-SiOz system was performed at 1500" C, with Ph20 = 0.192 atrn and for oxygen pressures varying between 10"2 and 10-lo atm. Samples for chemical analysis were prepared as described by Larson.4 The results are shown in Fig. 2. Some low-silica melts tested at low oxygen pressures "puffed up" when quenched and analyzed less than 100 ppm water; these results are not included in Fig. 2. The melts containing 40 mol pct silica also showed a tendency to "puff up" during the quench, when they were tested at the lowest oxygen pressure. These results indicate that, at constant silica content, the solubility of water decreases somewhat with increased oxygen pressure. The effect is, however, small considering the wide range of oxygen pressures studied. Also, at constant oxygen pressure (above about lom5 atm) the solubility increases

Jan 1, 1963

Executive A R LEDOUX, Chairman ARTHUR S DWIGHT CHARLES F RAND E P MATHEWSON J V W REYNDERS Membership E DEGOLYER, Chairman W Y WESTERVELT, Vice-chairman WILLIAM H BASSETT H G MOULTON C MINOT WELD Finance WALTER H ALDRIDGE, Chairman GEORGE D BARRON GALEN H CLEVENGER Library GEORGE C STONE,' Chairman JOHN H JANEWAY ALEXANDER C HUMPHREYS, ROBERT LINTON FREDERICK F SHARPLESS

Jan 1, 1923

By M. Cross

INTRODUCTION The results of the Japanese dissective investigations have [l-4] transformed our understanding of how the blast furnace operates. These studies revealed an internal structure of the furnace burden with five main zones, as illustrated in Figure 1. In the granular zone the charged material retains its structure whereas in the cohesive zone the iron ore particles are at advanced stages of reduction and form a semi-molten mass with a relatively high flow resistance. In the active coke zone molten iron and slag flow through a matrix of loosely packed coke. The raceway is a relatively small void space generated by displacement of coke due to the hot blast momentum, whilst the hearth is packed with coke, slag and molten iron. [ ] It is now well appreciated that furnace control is largely achieved and maintained by using the burden charge distribution to determine the gas glow distribution within the furnace and, hence, the shape and extent of the cohesive zone. In fact, Wakayama et a1 [5] of Nippon Steel Corporation state that optimum furnace operation is synonomous with the formation of a desirable cohesive zone shape, which in turn is almost solely determined by the burden charge distribution and its mechanical properties [6]. Much of the development work on operating furnaces since the dissective investigations has been oriented towards the identification of external furnace measures which reliably predict the shape of the cohesive zone. Currently the most popular measures are top gas temperature, velocity and CO/CO, ratio profiles [5]. More recently pressure distributions as evaluated from a series of wall measurements down the height of the furnace are also being utilised [7] to identify the position and shape of the cohesive zone. A great deal of emphasis has been placed upon achieving a consistent quality in the burden charge materials, establishing a suitable set of operating conditions and only making changes when forced to, ie., the operation for some reason moves outside a desired operating range or the production requirements change. Operational control schemes based upon this philosophy (eg., Kawasaki's GO-STOP system [8]) have been remarkably successful at achieving both high production rates and relatively low fuel costs. Mathematical models have long been used as tools to assist in the analysis of the blast furnace process. Although, the models have been useful in post-operative analysis and for identifying trends, etc., they have not proved reliable for detailed design criteria or as the basis for effective control schemes. Such mathematical models have moved from simple statistical correlation, through overall and stagewise heat-and-mass balance calcu-

Jan 1, 1984

By A. T. Yu

On March 18, 1964, the 52,000 dwt ore carrier M/S Houn Maru called at the port of Coquimbo, Chile, on its maiden voyage to take iron ore to Japan. This marked the first time a vessel of this size ever arrived at Coquimbo, and the event promises to drastically accelerate henceforth iron ore exports from Coquimbo province. This was made possible by the use of a versatile shiploading system recently installed by Cia. Minera Santa Fe. Coquimbo has no mechanized loading facilities other than six conventional 5-ton cargo cranes. Limited space on shore further complicates the stocking problems. To make the best of what is available, a meticulously organized semi-hand-loading system has been developed through the years.

Jan 5, 1964

By J. H. Schulman, M. H. Buckenham

R. W. Christy (Manager of Sales, Sanitary Engineering Equipment, Link-Belt Co.) and C.D. Rubert (Barrett, Haentjens & Co.) — Messrs. King and Schepman have presented an excellent paper which outlines the general practice in the design of thickener mechanisms. Lifting devices, controls, special applications and underflow pumping arrangements have been reviewed in detail. Pumping arrangements were illustrated which eliminate the need for an expensive tunnel beneath the thickener floor. Most of those illustrated have the common feature of a relatively long underflow suction line extending from the hopper floor to the pump located on the bridge at the periphery of the tank. The authors limit these arrangements to comparatively dilute or thin slurrys. It is implied that dense and coarse concentrates, which are difficult to pump, cannot be handled unless a tunnel is constructed. Fig. 1 shows an underflow pump arrangement which negates the need for a tunnel but which permits the operator to convey a heavy dense slurry. The pump is mounted directly on the fixed hoist platform and the impeller is located at the base of the steel center column. Priming water is not needed. The column

Jan 1, 1963

By George C. Coupland

Ecstall Mining Limited, a wholly owned subsidiary of Texas Gulf Sulphur Company, is the owner and operator of the Kidd Creek Mine including the concentrator complex located near Timmins, Ontario. Canada, approximately 450 miles north of Toronto. The mine, concentrator and Timmins form a triangular arrangement with a 17-mile rail link connecting the mine and concentrator and both of these facilities 18 and 14 miles respectively by road from Timmins. A core drilling program in the spring of 1964 established the presence of a large massive sulphide orebody which was to become the Kidd Creek Mine. Texas Gulf Sulphur had been conducting an intensive search for base metal in various parts of Northern Ontario and Quebec since 1957. Of several thousand anomalies detected in airborne electromagnetic surveys, several hundred warranted ground inspection, but only one of more than sixty drilled became a commercial orebody, the Kidd Creek Mine. The geophysical exploration work has been well covered in a paper written and presented by Van Donohoo, presently a Vice-President of T.G.S., at the American Mining Congress in San Francisco in October 1969. GEOLOGY The orebody lies within a series of overturned rhyolitic flows and pyroelastics with a major peridotite intrusive to the east. The hangingwall and footwall are composed chiefly of intermediate volcanics, andesite and dacite. The southern end of the orebody appears to terminate abruptly against greywacke while the north end is bifurcated and the structure obscured.

Jan 1, 1970

By M. R. J. Wyllie, Michael A. Torcaso

With the continued deep drilling of today, increasing numbers of high pressure and high temperature gas-condensate reservoirs are being discovered. Correspondingly, the ranges of properties of gas-condensate reservoir fluids are also being increased. The literature1*'." contains several excellent reviews of the property ranges in presently known condensate reservoirs. When one examines these property ranges, it becomes apparent that the need for reliable data is great if the engineer is to evaluate properly or appraise a gas-condensate reservoir. It is the purpose of this paper to present phase-behavior data that will point out some of the important variables that influence recovery from gas-condensate reservoirs produced by pressure depletion. All these variables may be resolved into two major categories: the hydroc:arbon composition of the reservoir fluid and the physical properties of the reservoir. But the variables which we will consider are those which are usually determined from well tests shortly after discovery and are, consequently, readily available to the engineer. They are as follows: (1) the producing separator gas-stock-tank liquid ratio, (2) stock-tank liquid gravity, and (3) reservoir temperature. Laboratory depletion studies have been performed on several reservoir fluids to illustrate the effect of changes in the cronsidered variables upon ultimate recoveries. The deviation factors, Z, of a series of reservoir fluids were determined experimentally to illustrate their order of magnitude and their effect upon the calculation of in-place reserves existing at high pressurcs and temperatures. The procedures followed in conjunction with the performance of these studies and their associated calculations are illustrated in Fig. 1. For the purpose of this paper, the depletion recoveries are expressed only in terms of pcr cent of initial stock-tank liquid, with the abandonment pressure assumed to be 500 psig. VARIATION OF RECOVERY WITH INITIAL PRODUCING SEPARATOR GAS-STOCK-TANK LIQUID RATIO The producing separator gas-stock-tank liquid ratio has long been one of the principal criteria in assumptions and generalized correlations' used for the estimation of ultimate recovery from gas-condensate reservoirs. Fig. 2 presents a plot of the cumulative recovery of stock-tank liquid at abandonment as a function of the initial producing separator gas-stock-tank liquid ratio. The graphical illustration represents the results of 44 laboratory depletion studies performed on actual gas-condensate fluids. These data are presented not only to illustrate the general trend of ultimate recovery increase with initial producing ratio increase but to emphasize the considerable variation in possible recovery at any given producing ratio. Table 1 presents the properties of two actual reservoir fluids chosen to illustrate the approximate extremities of producing ratios for gas-condensate systems. The fluids designated as A and B exhibited initial producing ratios of 3,400 and 114,000 scf/bbl, respectively. Fig. 3 presents a graphical comparison of the cumulative stock-tank liquid recoveries, calculated from the well-stream compositions and produced volumes for each fluid during depletion. It is to be noted that Fluid A exhibited a recovery of only 16.5 per cent when produced to an assumed abandonment pressure of 500 psig while the corresponding recovery for Fluid B was calculated to be 62.2 per cent. This difference in recovery, which exemplifies the general trend of recovery increase with initial producing ratio increase, is readily explained by consid-

By Sherwin F. Kelly

Twenty five years of exploration has shown that the "geophysical dollar" is worth $1780 in the Orange Free State, $1488 on the Witwatersrand, $85 in Sweden, $28,000 in the Transvaal and $3500 or more in the U.S.

Jan 6, 1951

By L. W. Bahney

MANY methods for the determination of gold or silver, or both, in cyanide solutions have been published, which with care in manipulation, and modification in some cases, will give results that are satisfactory. It is possible to classify or group these methods as follows: 1. Evaporating the solution in a porcelain or agate-ware dish containing litharge,1 or in a "boat" made of lead foil. 2. Forming a lead sponge containing the precious metals by means of zinc shavings,2 zinc dust,3 or a piece of aluminum.4 3. Decomposing the cyanide solution with an acid and precipitating the precious metals by the use of one or a combination of some of the following: Copper sulphate,5 sodium sulphite,6 hydrogen sulphide,7 cement copper.8 4. Precipitating the silver by zinc dust held in a Hooch crucible and determination with a standard solution of sulphocyanate.9 5. Electrolysis.10 6. Colorimetry.11

Jan 2, 1915

By T. Sekimoto, T. Kokubo, M. Yamamoto, K. Masuda, T. Moro, H. Sakamoto

The choking-free cyclone was developed primarily to remove solid particles suspended in a slurry containing fibrous materials, such as municipal solid waste. This cyclone is characterized by a screw conveyor at the underflow side of the cyclone. The screw conveyor has a hollow rotational shaft for air supply and is driven by a variable speed motor for discharge control. Even if the underflow discharge is highly concentrated, this type of cyclone can be stably operated without nozzle choking. High classification efficiency similar to that of a conventional cyclone can be obtained as a result of air introduction through the hollow rotational shaft. The recovery of organic matter and the removal efficiency of inorganic matter were actually improved by the application of this cyclone to municipal solid waste. After applying this cyclone to the desliming of fine sand, sand product of low water content was recovered.

Jan 1, 1980

By AIME AIME

THE following Officers, Directors, and guests were present: Herbert Hoover, A. R. Ledoux, Henry S. Drinker, Edwin Ludlow, Samuel A. Taylor, Charles F: Rand, William M. Corse, Arthur S.. Dwight, Glen H. Clevenger, L. W. Francis, F. G. Cottrell, Bradley Stoughton, Percy E. Barbour, E. P. Mathewson, Dorsey A. Lyon, Archibald Douglas, A. D. Flinn, RobertLinton, James F. Kemp, William Y. Westervelt, J. W. Richards, W. L. Saunders, George Otis Smith, Thomas T. Read, J..C. Murray, Ralph Arnold. A Committee on Mine Equipment was appointed composed as follows: Graham Bright, chairman, William Kelly, Howard N. Eavenson, R. E. Hobart, and S. P. Rumsey. B. D. Saklatwalla was added to the Committee on Miscellaneous Metals and W. Spencer Hutchinson was added to the Committee on Mining Geology. A revised budget for 1921 was approved. A petition duly signed to amend Section 1., of Article III of the Constitution, increasing the initiation fees from ten dollars to twenty dollars, was approved by the Board.

Jan 1, 1920

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

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

Jan 1, 1970

By William E. Ford, Edward Salisbury Dana

Secondary Twinning. - When there is reason to believe that the twinning has been produced subsequently to the original formation of the crystal, or crystalline mass, as, for example, by pressure, it is said to be secondary. Thus the calcite grains of a crystalline limestone often show such secondary twinning lamella?. The same are occasionally observed (Ilc, 001) in pyroxene crystals. Further, the polysynthetic twinning of the triclinic feldspars is often secondary in origin. This subject is further discussed on a later page, where it is also explained that in certain cases twinning may be produced artificially in a crystal individual - e.g., in calcite (see Art. 282).

Jan 1, 1922

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

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

Jan 1, 1943

By B. N. Das, P. A. Beck

THE o phases have a complex tetragonal structure with Lo/ao = 0.52 and 30 atoms per unit cell.1 A large number of such phases are now known to occur in various binary systems of the transition elements and they exhibit the following typical features: 2,3 The composition of binary o phases is variable, ranging from approximately A4B to ABI. With only a few exceptions, in the o phases the A-ele-ment comes from the V- or Cr- group of the periodic table, while the B-elements are from the Mn-, Fe-, Co-, or Ni- group. In the first long period the corresponding o phases of the V- and Cr-series have approximately the same compositions. However, as the B-element changes from Mn to Fe to Co to Ni, the mean composition shifts monotonously toward higher A-contents.2-4 For example, if the mean compositions of the various o phases with vanadium are compared with each other, the composition shift mentioned above becomes plainly visible: V 30Mn0 80 Vo.45Feo..,, Vo .,Coo. 45 and Vo.5Nio.3. Similiar composition shifts, although not the same composition values, were observed in u phases formed by second and by third long-period transition elements.3'4 This behavior, very characteristic of o phases, is in rather sharp contrast to the usually quite well-behaved stoichi-ometry of the Laves phases. In the latter, the AB2 stoichiometry predominates, with A the large atom and B the small atom.= The p phase occurs in the four binary systems of Mo or W with Fe or Co. On the basis of their crystal structure determination, Arnfelt and westgren6 ascribed to the p phase in the Co-W system the ideal composition W,Co7. Since all four binary pphases have nearly the same composition, it would seem quite plausible that some definite stoichiometry such as A6B7, might be characteristic of this phase, as AB2 is of the Laves phases. On the other hand, it has been noted,7 that the phases occur at average electron concentrations near to those at which the various cr phases are found. Also, it has been pointed out by Shoemaker and associates8 that structurally the a phases and the p phases are somewhat related to each other; both of these structures may be described in terms of suitable stackings of quasi-hexagonal layers'of atoms. By studying a suitably chosen ter- nary phase diagram, one might expect to be able to find out which one of the two conditions, the analogy with the o phase or the constant ratio between the number of large atoms and the number of small atoms in effect governs the behavior of the p phase. Several isothermal sections of ternary systems containing o phases have been investigated. In all cases where two binary o phases occur, these were found to be connected b a more or less straight ternary o phase field.7' '10 Such elongated o phase fields were also found in ternary systems in which only one of the limiting binaries is known to contain o phase. In this manner a latent o forming tendency could be detected and the virtual composition of a "binary o phase", which does not actually occur as such was approximately determined by extrapolation. The behavior of the phases, including their composition shift, is analogous to that of the classical electron compounds, as described by Hume-Rothery.11 In order to decide whether the p phase is essentially a "size compound" like the Laves phases, where a fixed stoichiometric ratio is quite generally maintained between the "large atoms" and the "small atoms", or whether the p phase is typically an "electron compound" in the same sense as ois, it was decided to investigate an isothermal section of the Mo-Mn-Co system. The Mo-Co system12 and the Mo-Mn system13 each are known to have a binary o phase. It could be therefore expected that a ternary o phase field will connect these two binary cr-phase fields. The p phase is known to occur in the Mo-Co system. If the p phase should turn out to form an elongated phase field extending deep into the ternary system, the following considerations mighto apply. The atomic radius of manganese (1.314for C.N.12) is between the va,lues for Mo (1.40Afor C.N.12) and for Co (1.26Afor C.N.12). If it is assumed that p is a "size compound", and that Mn is substituting for the smaller Co atoms in the p-structure in the ternary system, the y-phase field might be expected to extend parallel to the Mn-Co binary line. If Mn is substituting for the large Mo atoms in the p-structure, the p-phase field may be expected to extend parallel to the Mn-Mo binary line. On the other hand, if the p-phase turns out to be an "electron compound" like o, the ternary p-phase field should extend parallel to the ternary o -phase field connecting (Mo,Mn)owith (Mo, Co) a

Jan 1, 1961

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

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

Jan 1, 1971