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By Ogden Tweto

The Leadville district, on the west flank of the Mosquito Range in central Colorado, has produced silver, zinc, lead, gold, and minor metals valued at $512,000,000. The ore deposits are in a sequence of dolomites and quartzites, Cambrian through Mississippian in age and about 500 feet thick, which is extensively intruded by porphyry sills, dikes, and plugs of Tertiary age. The sedimentary rocks and sills dip about 15°E and are broken by many faults, which are predominantly of nearnorth trend and downthrown to the west. The ore deposits are principally blanket or manto replacement deposits, but in the eastern part of the district many veins occur also. The replacement deposits are largely confined to three dolomite units in the stratigraphic sequence. Of these, the uppermost or Leadville Dolomite is the most productive. Most ore bodies are on the underside of porphyry sills and, particularly, beneath sills that occupy unconformities. Many replacement bodies have vein roots or branch from veins. The veins occupy faults and are productive mainly in the section of quartzites and dolomites and included sills. The primary ores consist principally of pyrite, marmatitic sphalerite, and galena but locally contain chalcopyrite, silver minerals, bismuth minerals, and gold. Principal gangue minerals are manganosiderite and jasperoid. The ore deposits have a crude zonal pattern centered around an intrusive center at Breece Hill, which evidently influenced ore deposition thermally. The ore deposits were oxidized to depths of several hundred feet in Miocene time. Bonanza ores mined in the early days were characterized by cerussite, cerargyrite, and embolite. Later, zinc carbonate ores were identified and mined on a large scale. The Leadville district is a complexly faulted and intruded area at the intersection of major fault systems trending N20°W and N15°E in the Mosquito Range. The intensely fractured area evidently localized igneous intrusion and subsequent mineralization. Ore solutions rose on many of the faults in the area, presumably from the same source as the porphyry magmas. Movement on these faults continued into the Pleistocene, displacing ore bodies, oxidation zones, Pliocene sediments, and glacial deposits.

Jan 1, 1968

By J. M. Boutwell

I. Introduction. THE object of this paper is to present a concise statement on the genesis of the copper- and lead-deposits of the Bingham Mining District, Utah. It is essentially a condensation of a chapter in a detailed report on this district, together with so much on geologic features, and on the character and occurrence of the ores as bears on the problems of ore-deposition. The studies upon which the paper is based were undertaken in 1900 under the direction of S. F. Emmons, Geologist-in-Charge of the Section of Metalliferous Deposits, U. S. Geological Survey; and a little additional data was secured in subsequent years. The evidence then obtained as to the genesis of the replacement copper-ores has led, to conclusions which differ somewhat from explanations hitherto current. Accordingly, it seems desirable briefly to present the facts together with the resulting conclusions in a separate paper.

Nov 1, 1905

R. 8. MACPHERRAN, Milwaukee, Wis. (communication to the Secretary): The importance of carbon in pig-iron, as well as the desirability of buying, for some purposes, irons which are high in carbon, has always been recognized. Mr. Summers, I think, has given undue weight to the carbon-determinations. The combined carbon often decreases materially as the center of the pig is approached, with a corresponding increase in the graphite. Even the determination of total carbon, to be of service, must he supplemented by that of other elements. By it alone, the softness of a foundry-iron cannot be determined. Car-wheels and No. 5 iron, for instance, frequently contain 3.75 per cent. of carbon. This is the percentage specified by Mr. Summers for his No. 1 iron, " with the silicon about anywhere the furnace-man wants it." It is true that, other things being equal, the higher the carbon the softer the iron for foundry-use. But to introduce any given percentages of graphitic and total carbon into a pig-iron specification would but make the specification more complicated, without increasing its value in a commensurate degree. Mr. Summers does not believe in the governing of mixtures by the silicon, and, in support of his views, gives several tables. It seems to me that both his conclusions and his tables are somewhat unsatisfactory. He comments on the irregularity in carbon, but fails to note the significance of the irregularity in silicon..The variation of 0.7 per cent. in silicon, for example, is too great to be accounted for by difference in blast. It might better be attributed to bad grading at the furnace, unsystematic sampling, or irregular charging. Deductions drawn under such conditions are of little value. In ordinary work the castings from the same mixture should

Jan 1, 1899

By WILKES BARRE

AS PREVIOUSLY announced, the semi-centennial meeting of the Institute is to be held at Wilkes-Barre, Pa., on Sept. 12, 13, 14, and 15. An interesting program of technical sessions and excursions is now being prepared by the Local Committee. At the time of going to press the program had not been completed in sufficient detail to permit its being pub¬lished in this number. The detailed program will be published in the September MINING AND METALLURGY, which will be printed in time to be distributed before the Wilkes-Barre Meeting. It may be said in advance, however, that the Com¬mittee has progressed so far in its work that we are assured of one of the -most notable meetings the Insti¬tute has held and that members will miss a rare .treat if they do not attend. The many trips and excursions, as well as the banquet, will be -given to the members as a compliment from the members of the Local Com¬mittee. . . The paper by Howard Eavenson on the Lynch Plant of -the United States Coal and Coke Co. will be illustrated by lantern slides and moving pictures. One of the most appropriate discussions will be that opened by Prof. J. F. Kemp on the Stratigraphy of the Anthracite Region; this also will be amply illustrated.

Jan 1, 1921

By Charles A. Kliche

INTRODUCTION The Northern Great Plains Coal Province which occupies approximately 36.6 ha contains about one-half of the nation's total coal resources. About one million ha are underlain by coal that is considered to be mineable from the surface. The topography of the province is predominately plains, rolling hills, and some badland areas characterized by breaks or sharply eroded hills. Elevations range from about 1500 m above sea level on the west to about 600 m above sea level on the eastern boundary. The average slope of the ground is approximately 2 m per km. Streams in the province drain generally easterly and southeasterly (1). In the United States, the Northern Great Plains Province lies within the states of North Dakota, South Dakota, Montana, Wyoming, Nebraska, and Colorado. The coal within the province is located almost entirely in the states of North Dakota, Montana, and Wyoming. Although it is relatively low rank, the coal within the province encompasses a large portion of the total remaining U. S. reserves. The U. S. Geological Survey estimates the total remaining coal resources of the United States to be 2.6 trillion mt within 1000 m of the surface, and 2.9 trillion tons within 1830 m of the surface. Of this total, only about 177 billion mt are classified as reserves meaning that they are (1) known in location, quantity and quality from geologic evidence supported by engineering measurements, and (2) economically recoverable based on currently available technologies and current market value (2).

Jan 1, 1983

By H. N. Thomson

(Butte Meeting, August, 1913.) GENERAL. THE Tooele plant. off the International Smelting & Refining Co. is situated at the mouth of Pine canyon, Tooele county, Utah. It is connected with the main line of the San Pedro, Los Angeles & Salt Lake railroad by the Tooele Valley. railway, and is about 7 miles from Tooele Junction. Fig,. 1 is a general view of the plant. The copper plant has been in operation since July, 1910, and the first blast furnace it the lead plant was blown in on Feb. 29, 1912. The location of the plant was selected on sloping ground with the idea of using gravity to the fullest extent and thus keeping labor at a minimum. Practically the entire plant is constructed of steel, reinforced concrete, and. brick.

Jan 7, 1913

By K. A. Pauly

(Wilkes-Barre Meeting, June, 1911.) COMPRESSED air has been and is still very extensively used in connection with mining-operations, but its application in the past has been almost entirely confined to supplying power to underground machinery. Its introduction was due to the difficulty of taking care of the steam which is exhausted underground, rather than to any advantage in efficiency to be gained by its use. The ease with which electric power may be carried to the remotest parts of the mine and the high efficiency of the electric motor have long been appreciated by mine-operators, and electric power is now extensively used underground in the more recent developments, while many of the compressed-air engines in the older workings are being rapidly replaced by electric motors. Recently, however, it has been suggested to use compressed air for driving the large shaft-hoists, the air for the engines being supplied by electrically-driven compressors, and an installation of this character is being erected at Butte; Mont. It is the object of this paper to compare the compressed-air system of hoisting with the various electrical systems, from the stand-points of first-cost and cost of operation. However, before entering into a discussion of the various systems, it will be well to consider briefly the conditions affecting the choice of a system of hoisting in which electricity is the ultimate source of power. The power required by a mine-hoist is extremely intermittent and fluctuates between very wide limits, the all-day average consumption of power not exceeding from 5 to 15 per cent. of the maximum demand during hoisting. The cost of supplying power for such a fluctuating load is necessarily higher than that for supplying an equal amount of

Dec 1, 1911

Organization Place Date 1917 American Institute of Architects Philadelphia,.,; Pa. Dec. 26-29 American Society of Mechanical Engineers New York City. Dec. 26-29 American Mining Congress State Chapter Phoenix, Ariz. Dec. 26-29

Jan 11, 1917

By AIME AIME

NEW place was assigned to the women for their headquarters at the annual meeting of the Auxiliary but they, as usual, occupied a large place in the activities of the annual meeting. The alcove on the Thirty-ninth Street side of the building was a busy place on Monday morning, as the members of the various sections from New York to California greeted each other. The registration was conducted under the supervision of Mrs. Wolfes, Miss Georgene Davis and Mrs. Jennings, while Mrs. Hursh, Mrs. Hyde, Mrs. Charlton Reynders, and others dispensed tickets to the various functions that had been provided for entertainment. There seemed to be the usual number registered, but when only one member of the District of Columbia Section made herself known everyone wondered why the large delegation of last year had so dwindled. The explanation appeared next day, when a number of others from that Section arrived, telling of a delightful reception on the night before, at the White House. Mrs. Hoover had honored the "Canaries"¬(the organization of Lone Girl Scout' workers) the officers of the Section, and their husbands, who for once became only "so and so's husband." Luncheon was served on the fifth floor on Monday, the hostesses for that day being Mesdames C. F. Ayer, Willis Burns, G. W. Farny, H. G. Moulton, and T. T. Read. A number of sight-seeing trips had been arranged for the afternoon. The most popular proved to be an expedition to the new Riverside Church; where Dr. Fosdick is pastor. Guides were there to conduct

Jan 1, 1931

By Gerald C. Dohm

INTRODUCTION After a mining company has discovered a mineral deposit, the problem is then how to mine and process that deposit the best way. The principal problem facing managers or engineers who must decide on mine plant size, equipment selection, and long-range scheduling is how one can optimize a property not only in terms of efficiency but also as to project duration. Mine opti¬mization is dependent upon the interaction of con¬tributing parameters which leads to maximizing the net present value (NPV) Realistic mine planning is the key, to the analysis. The process is to be used when evaluating undeveloped properties or when a complete revamping of existing facilities is scheduled The proc¬ess is not intended for detailed mine design but rather for property evaluation and feasibility studies. The derivation of the various input parameters will only be discussed to the point where a meaningful correlation can be made with the overall analysis. The interrelationship of the parameters will be the central point because most company guidelines and financial analysts have their own standards when deriving the various inputs. Assume that the data is totally acceptable and pro¬vides at least the following categories of information and guidelines- (1) mineral and waste inventory; (2) geologic, hydrologic, and geotechnical criteria; (3) topographic layout including property boundaries; (4) metallurgical flowsheet, recovery and design criteria; (5) access, water, power, and environmental base-line study; and (6) financial constraints (minimum rate of return, payback period, etc).

Jan 1, 1979

By A. Raja, C. C. Harris

Apparatus for maintaining constant — but adjustable — pulp level and rate of froth removal are described. The results of preliminary experiments into the effect of scraping speed on the rate of solid and liquid recovery with a semi-batch system are presented. Glass spheres restricted to a narrow size range is the solid under investigation. Graphical methods for estimating the mass of recoverable material and the zero error are given. The semi-batch procedure1 is extensively used in laboratory flotation testing, though the method is subject to variability of moderate severity. Raffinot2 concluded from a statistical study of the difference between replicate tests, that the ptincipal source of errot was the test itself and not sampling or chemical analysis. These differences can be ascribed principally to changes in pulp volume and reagent concentration, and uncontrolled rate and depth of scraping. Semi-batch testing has been criticized1 on these grounds as a means of investigating flotation kinetics. This paper discusses and describes modifications to laboratory flotation equipment which reduce the number of manual operations and lead to improved control. Kinetic studies were the primary reason for developing the apparatus described. It should, however be a useful aid in normal flotation testing. Some preliminary results of experiments are presented.

Jan 1, 1967

By L. L. Seigle

Free energies, heats, and entropies of mixing of solid Fe-Au alloys have been measured by the galvanic cell method between 800° and 900°C. A positive deviation from Raoult's law and a large excess entropy of mixing were observed, both attributable to lattice distortion caused by the disparity in component atom sizes. Since the terminal solid solutortiontions are not regular, thermodynamic properties computed from the location of the mis-cibility gap do not agree well with measured quantities. The electromotive force data suggest some changes in the existing Fe-Au phase diagram. ALTHOUGH a considerable amount of information has been accumulated about the thermodynamic properties of metal solid solutions which exhibit negative deviation from Raoult's law, particularly those in which ordering occurs, relatively few experimental measurements have been made on solutions with positive deviation. This is due to the infrequency of broad homogeneous regions suitable for experimental measurement in solutions of this type, since any marked positive deviations from ideality lead to restricted solubility and the formation of miscibility gaps. Thermodynamic data reported in the literature for such systems have usually been calculated from the location of the miscibility gap boundaries under the assumption that the entropies of mixing are ideal, i.e., the terminal solutions are regular.' One of the few binary systems with both positive deviation and a wide homogeneous range in the solid is the Ni-Au system. A recent investigation of solid Ni-Au alloys' revealed that the entropies of mixing were much larger than ideal and consequently thermal data computed from the phase boundaries assuming regular solutions were seriously in error. Theoretical considerations put forward by Zener indicated that high entropy values should generally be associated with systems possessing a miscibility gap in the solid, when this is due to differences in the size of component atoms. These facts suggest that the regular solution assumption is a poor approximation for many solid solutions with positive deviation and that reliable thermodynamic data generally cannot be obtained by conventional methods from the location of miscibility gap boundaries. The Fe-Au system, Fig. 1, resembles the Ni-Au system in certain respects. The presence of a miscibility gap in the solid indicates a large positive deviation from ideality, but there is nevertheless an extensive single phase region suitable for experimental measurement. The following investigation of solid Fe-Au alloys was carried out in order to obtain additional data on the thermodynamic properties of metal solid solutions with positive deviation from Raoult's law and to further compare thermodynamic data computed from miscibility gap boundaries with those measured experimentally. Experimental Method The thermodynamic properties were derived from measurements of the potential developed between pure solid iron and Fe-Au alloys in a high temperature galvanic cell. The experimental apparatus and technique were the same as those used for the Ni-Au alloys and described in a previous report.' Cell electrodes were 1/16 in. diam rods swaged from chill-cast ingots and annealed for one week at 850°C. The alloys were prepared by melting fine gold granules under argon with pure iron obtained from the National Research Co. The cell electrolyte was

Jan 1, 1957

By C. W. Davis, L. R. Messer

THE name fuller's earth, which was derived from its early use in "fulling" or removing grease from woolen goods, is a term that is generally considered to designate mineral matter, containing hydrous aluminum silicates of the clay group, which has a high capacity for removing colors from oils, whether of animal, vegetable, or mineral origin. Fuller's earths are usually dried and may be "tempered" by heating or may be treated with water or reagents to improve their efficiency. For our purpose the term "acid-treated earths" will include those products from the partial decomposition of mineral water by acid which are equal to or more efficient than an untreated fuller's earth from Quincy, Fla., when used in bleaching mineral oil by the "contact" process. In general, the contact process for treating oils consists of heating and agitating a mixture of oil and finely divided adsorbent, the latter being subsequently removed by filtration. The term "adsorbent" is used because, although there has been a great deal of controversy over the mechanism of removal of impurities from oils by mineral matter, there is no doubt that adsorption, which involves the surface of the solid, plays a major part.' The properties that make fuller's earth useful in the treatment of petroleum products by "percolation1' and in the purification of edible oils by the contact process have long been studied, but the comparatively recent adaptation of the contact process to the bleaching of petroleum products has made desirable the further investigation of fuller's earth and other adsorbent earths.

Jan 1, 1929

By HUGH E. McKinstry

OPENING the sessions of the Mining Geology Committee, the program on postwar mineral controls drew a larger attendance than any other session of the entire meeting. In view of its general interest, the papers of this session, or a substantial portion of them, are printed elsewhere in this issue. Whether control of mineral resources can help to promote peace, how controls could be applied and to whom, are questions so far-reaching that naturally no pat answer was agreed upon. In fact the discussion took on something of the flavor of a debate between those who favor strict control and those who felt that attempting to ration nations in peacetime would defeat its own ends. Discussion from the floor emphasized the difficulties in administering any international control and the $64 question, that no one cared to answer, asked by a courageous young lady who was induced to mount the rostrum for the purpose, was whether the United Nations should exchange mineral controllers to police each other.

Jan 1, 1944

By F. Keller, E. H. Dix, L. A. Willey

The consideration of alloying elements for aluminum has led to a series of investigations of the equilibrium relations between aluminum and those alloying elements. Therefore, the aluminum end of the aluminum-antimony diagram has been studied. The general form of the aluminum-antimony equilibrium diagram has been worked out by Campbell and Mathewsi and by Tammann.2 Canlpbell and mathews described principally the beginning of solidification. They found the curve of beginning of solidification rising gradually from the melting point of pure alunlinum to a maximum at about 67 per cent. aluminum. After a slight lowering of the curve at a little greater antimony concentration the curve again rises to a maximum at 18.4 per cent. aluminum, which corresponds to the compound AISb. The curve then drops to the melting point of pure antimony. Tamrriarln explained the maximum occurring at about 67 per cent. aluminum as the result of the slow formation of the single compound AISb. The space lattice of the compound AISb, according to Owen and Preaton,³ is face-centered cubic, the antimony atoms being intermeshed with an identical aluminum lattice. Very little, if any, work has been done on aluminum alloys containing small amounts of antimony. The Present Investigation It has been the purpose of this investigation to determine the solid solubility of antimony in aluminum and also to investigate the eutectic temperature and concentration. The experimental work has been carried out in a manner similar to that described in a previous paper4 from this laboratory.

Jan 1, 1931

By Edward Griffith

The anthracite industry, which produces about 50 million net tons of coal annually, has been talked of as being able to last for another century; but if the water record of the past century continues into the expected century, this expectation of many years production still to come out of the remaining reserves will not be attained. The industry will be a submerged one in fact as well as in name. A recorded forecast of what has since occurred appears on page 34 of the Mine Inspectors' reports of 1897: It should also be noticed that bodies of water had accumulated in parts of abandoned mines before duplicate surveys of the same were required by law; and as a result we have today to contend with bodies of water, the exact location and position of which are not correctly known. Since that date, 47 years ago, the implications of the foregoing comment have grown enormously. This is shown in Fig. I and in the following table showing flooded and partially flooded areas that have come into existence since the early 1930's in the northern anthracite field: Number of Year Flooded Areas 1932...................... 2 1933...................... 3 1934..................... 3 1935...................... 5 1936...................... 7 1937...................... 9 1938.................... 11 1939...................... 11 1940...................... 11 1941...................... 14 1942...................... 14 1944...................... 26 Similar conditions exist in other fields in the anthracite region. In the period between 1923 and 1940, abandonment of collieries in the southern field resulted in the flooding of approximately 60 sq. miles (30 per cent) of the field. The ahandonment of collieries in this field has imposed additional expense for pumping on the collieries still operating. This condition will be aggravated by the extension of developments and cause suspension of operations if economic conditions do not justify the assumption of additional pumping costs. During the years, the region's rainfall has not altered, but the quantity going inside the mines through breakages in the surface, brought about by extraction of the coal, has increased materially, as indicated by the ratio of tons of water pumped to tons of coal produced underground for one of the large companies in the northern anthracite field: Year Ratio 1920................. 8.4:1 1925.................. 10.6:I I930.................. II.4:I 1935................. 26.2:1 1940.................. 32.7: I 1942.................. 30.3:I The data in Table I shows the total amount of water pumped and its ratio to underground production for one of the large companies in the southern anthracite field, and shows a rapidly growing serious situation. Rainfall quickly affects the workings in all the fields. In mine inspection district 7 of the southern field the rainfall in 1935 was 92,083,000,000 gal. The total water pumped was 36,274,000,000 gal. (39.4 per cent of the rainfall). The operating mines

Jan 1, 1947

By Edward Griffith

The anthracite industry, which produces about 50 million net tons of coal annually, has been talked of as being able to last for another century; but if the water record of the past century continues into the expected century, this expectation of many years production still to come out of the remaining reserves will not be attained. The industry will be a submerged one in fact as well as in name. A recorded forecast of what has since occurred appears on page 34 of the Mine Inspectors' reports of 1897: It should also be noticed that bodies of water had accumulated in parts of abandoned mines before duplicate surveys of the same were required by law; and as a result we have today to contend with bodies of water, the exact location and position of which are not correctly known. Since that date, 47 years ago, the implications of the foregoing comment have grown enormously. This is shown in Fig. I and in the following table showing flooded and partially flooded areas that have come into existence since the early 1930's in the northern anthracite field: Number of Year Flooded Areas 1932...................... 2 1933...................... 3 1934..................... 3 1935...................... 5 1936...................... 7 1937...................... 9 1938.................... 11 1939...................... 11 1940...................... 11 1941...................... 14 1942...................... 14 1944...................... 26 Similar conditions exist in other fields in the anthracite region. In the period between 1923 and 1940, abandonment of collieries in the southern field resulted in the flooding of approximately 60 sq. miles (30 per cent) of the field. The ahandonment of collieries in this field has imposed additional expense for pumping on the collieries still operating. This condition will be aggravated by the extension of developments and cause suspension of operations if economic conditions do not justify the assumption of additional pumping costs. During the years, the region's rainfall has not altered, but the quantity going inside the mines through breakages in the surface, brought about by extraction of the coal, has increased materially, as indicated by the ratio of tons of water pumped to tons of coal produced underground for one of the large companies in the northern anthracite field: Year Ratio 1920................. 8.4:1 1925.................. 10.6:I I930.................. II.4:I 1935................. 26.2:1 1940.................. 32.7: I 1942.................. 30.3:I The data in Table I shows the total amount of water pumped and its ratio to underground production for one of the large companies in the southern anthracite field, and shows a rapidly growing serious situation. Rainfall quickly affects the workings in all the fields. In mine inspection district 7 of the southern field the rainfall in 1935 was 92,083,000,000 gal. The total water pumped was 36,274,000,000 gal. (39.4 per cent of the rainfall). The operating mines

Jan 1, 1947

By J. F. Myers

AT the Regional meeting in Columbus, Ohio, in September 1949, the authors presented a progress report of the first year's operation with a Hardinge tricone mill in closed circuit with a Dorr hydroscillator. The present report covers our findings on this grinding circuit to January, 1950. In order to clarify our position, the authors wish to state that no invention or discovery is claimed. The Tennessee grinding circuit is simply an engineered arrangement of known equipment arranged to incorporate all of the recognized efficiency factors of comminution as they are known today. As we concluded our first report, it was not clear how effective the Tennessee mode of operation would be on harder ores. The only information we had at that time was that the Bond grindability test at 48-mesh gave 6.04 g of undersize per revolution. A later test on the same sample at 100-mesh reduced this to 2.04 g, which is definitely in the harder ore class, and which makes the reported 8.80 kw-hr per ton of -200-mesh produced a very creditable figure.

Jan 1, 1950

By Eugene Stephenson

CRITICAL analyses of the work expended in producing oil by the utilization of gas energy have appeared in the publications of Shaw,1 Pierce and Lewis,2 and Herold,3 authors who have ably discussed the factors which must be taken into consideration in comparing energy consumed per barrel in various wells which are flowed by means of gas-lift. However, two distinct phases of oil production are concerned with the ratio of gas energy consumed to oil produced. One of these phases is the gas-lift, which utilizes the differential gas pressures for the purpose of flowing oil, whether these pressures be natural reservoir pressures or be induced by artificial compression of gas or air. The other phase has to do with prorating oil production in pools which are operated either as units, or are subject to such restrictions as those imposed at Oklahoma City by the Corporation Commission, or, by similar controlling groups in other fields. An abundance of literature is available relative to the problems of flowing wells by gas-lift, but the first suggestion that the energy of the gas within the oil and gas pool might serve as a basis for proration, appeared in the timely article by McWilliams.4 Much of the. dissatisfaction with proration in certain fields is because some operators feel that besides the hazard to the wells which accompanies the test, the method of allocating production on the basis of the "potential" gage is inequitable and gives some operators a distinct advantage over others.5 The most severe penalty may be exacted from the most progressive operators or those who attempt to produce their oil with a minimum quantity of reservoir gas. If :no difficulties ever

Jan 1, 1931

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