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By Ruiqing Li

It is possible to purify some liquid metals by exploiting the difference between the vapour pressure of the bulk metal and the minor constituents or impurities. The rates of purification can be improved by carrying out the process under reduced pressure, that is, so called, vacuum. Some commercial examples of vacuum refining are the purification of molten tin to eliminate trace amounts of lead and the refining of cobalt, also to remove lead. The objective of this paper is to review the basic theory behind vacuum refining technology in order to show how the feasibility of vacuum refining can be determined simply for a particular system by evaluating Olette's Volatility Refining Criteriont.

Jan 1, 1991

By S. H. Ash

NO MORE important question has come before the coal-mining industry in many places, especially in the anthracite region of Pennsylvania, than prevention of stream pollution by mine drainage. Available information on acid mine drainage in the anthracite region of Pennsylvania indicates that a pollution problem must be solved in any program of anthracite mine drainage. The major problem concerns satisfactory disposal of the daily average mine-water discharge of 327,000 gallons per minute (g. p. m.), or 472 million gallons per day (g. p. d.), containing a free-acid load of 431 tons or a total acid load of 934 tons a clay as H2S04. This report indicates the scope of the problem and gives some suggestions concerning its solution.

Jan 1, 1951

By H. R. Hanley

IT is a well-known fact that the solubility of zinc compounds decreases when these compounds are roasted in contact with iron compounds, but descriptions of tests to quantitatively express the fact have not appeared in the literature. Possibly such an expression cannot be uniformly and exactly duplicated by different operators because of the variation in the personal equation. In a general way, however, the reactions between zinc compounds and iron compounds under roasting conditions will show a certain trend with changing conditions and the approximate quantitative expression of this trend appears reasonably well established by experimental work conducted for this purpose. Ferrites and Marmatites The name "ferrite" has been given to the compound of zinc and iron which has the formula Zn0.Fe203. Among the questions pertinent to this subject are those involving inherent or natural ferrite, and also the synthetic or artificial variety. The inherent or natural product is formed when the mineral containing iron and zinc sulfides isomorphously crystallized is subjected to oxidation at roasting temperature. These isomorphously crystallized minerals are known, mineralogically, as marmatites, and contain ZnS and FeS in ratios of 2 to 1 up to 5 to 1 respectively. The zinc and iron sulfides form a definite mineral. They are firmly attached to each other and form common contact planes through which diffusion of the entities occurs during the roasting process. This diffusion of the molecularly intimate entities produces, during roasting, the compound referred to as ferrite, in proportion to the amount of iron originally present in the marmatite. For example, a marmatite from British Columbia containing 9.739 per cent. Fe and 56.87 per cent. Zn corresponds with the mineral having the formula 5ZnS.FeS. The ferrite produced in roasting, which has the formula ZnO.Fe203, contains 27.07 per cent. Zn and 46.40

Jan 1, 1929

By F. F. Lines

It is not the intention of the writer to enter into a discussion of the relative merits of the duplex process as compared with the straight scrap and pig iron process, working under the same conditions, but rather to present in a general way several modifications of the former process, and then describe the method adopted by the Maryland Steel Co., as best suited to local conditions, and also to meet the metallurgical problem presented in the removal from the iron of an unusual constituent— chromium. The principal factors to be considered in. deciding whether or not duplexing should be employed are: (1) Chemical constituents of pig iron. (2) Variety and quantity of steel to be produced. (3) Relative cost of pig iron and scrap. (4) Regularity of operation. (5) Capital to be invested. (6) An existing Bessemer plant. Having decided to adopt the duplex process, several combinations may be used, viz.: (1) Acid-lined converter with basic open hearth. (2) Acid-lined converter with electric furnace. (3) Basic-lined converter with basic open hearth. (4) Basic-lined converter with electric furnace. (5) Basic open hearth with electric furnace. The combination of an acid-lined converter with a basic open-hearth furnace is the one most commonly employed, and as it is the one best adapted to the conditions encountered at the plant of the Maryland Steel Co., we will briefly outline the advantages and disadvantages of the different methods of working. There are two general methods of blowing, as follows: (1) The charge is desiliconized and partly decarbonized in the converter. On account of the difficulty in regulating the percentage of car-

Jan 1, 1916

By C. C. Hwang

The Bureau of Mines formulated a method for calculating the concentration of entrained dust from a dust deposit by a turbulent gas stream. In particular, a diffusion equation is used to calculate dust concentrations in a channel following an explosion. Dust leaving the channel walls was treated as originating from stationary or moving, and single or multiple material sources. Formulas and sample computations for various types of dust sources in circular and rectangular channels are given, based on experimental entrainment rates. The analysis predicts the dust concentration as a function of time and channel space. The results appear to agree with the physical characteristics of explosion-driven dust dispersion in a O.6-m-diameter, 50-m-long explosion tunnel. The analysis is also applied to simultaneous and consecutive dispersion of coal and rock dust from simulated coal mine surfaces (walls, floor, roof, and ribs).

Jan 1, 1974

By L. D. Lamont, W. C. Muehlhof

Throughout the anthracite industry's history, the problem of handling and disposing of refuse material has been one of major importance. In the early days of the industry's activities, only the large sizes of anthracite were satisfactory for market requirements and the smaller sizes were deposited as refuse. As time went by, more efficient coal-burning equipment was developed and a market demand was created for the finer sizes of coal. This demand made it possible to recover marketable coal from banks deposited as refuse in the earlier days of mining. The same condition holds good today and we can see a definite trend toward the objective of utilizing the No. 4 and No. 5 buckwheat sizes. Under present conditions, we know that a limited market exists for No. 4 and 5 buckwheat; we know that the finer sizes of anthracite can be burned as pulverized fuel; we know that these fine sizes can be processed and sold as briquettes, and we also know that the heat content of these fine sizes of coal is comparable with that of the sizes now merchandized. Therefore, it should be the objective of the industry to conserve these fine sizes of coal in such manner that if and when processing facilities are developed, and market demands exist, the material can be salvaged and made available to meet these demands. From the standpoint of economical future reclamation, the ideal method of disposing of refuse containing the finer sizes of coal is to deposit it in banks separate and apart from other breaker refuse. By this procedure, the minimum amount of material will be processed in future salvage operations to recover the No. 4 and No. 5 buckwheat sizes. Many collieries in the anthracite region are operated under leases that have a specific term. These lease agreements provide that, upon expiration of the lease by term, exhaustion or otherwise, the ownership of the refuse material reverts to the lessor. Therefore, a question was raised in the minds of these operators: Why should I assume the expense of such procedure when I have no assurance that I will benefit by the future processing and sale of these fine sizes? Under present conditions, the answer to this question is not one of choice but of necessity, as restrictions imposed by legislation make it mandatory on operators of preparation plants to take necessary steps to properly treat silt-laden waters before permitting them to enter the streams. By reason of these restrictions, the disposal of fine sizes becomes a secondary rather than a primary operating consideration, and the procedure for disposing of this refuse becomes a matter of choice governed principally by topographical and geographical conditions. Methods of Handling Refuse There are three principal methods of handling and disposing of fine-size refuse; namely:

Jan 1, 1947

By W. C. Muehlhof, L. D. Lamont

Throughout the anthracite industry's history, the problem of handling and disposing of refuse material has been one of major importance. In the early days of the industry's activities, only the large sizes of anthracite were satisfactory for market requirements and the smaller sizes were deposited as refuse. As time went by, more efficient coal-burning equipment was developed and a market demand was created for the finer sizes of coal. This demand made it possible to recover marketable coal from banks deposited as refuse in the earlier days of mining. The same condition holds good today and we can see a definite trend toward the objective of utilizing the No. 4 and No. 5 buckwheat sizes. Under present conditions, we know that a limited market exists for No. 4 and 5 buckwheat; we know that the finer sizes of anthracite can be burned as pulverized fuel; we know that these fine sizes can be processed and sold as briquettes, and we also know that the heat content of these fine sizes of coal is comparable with that of the sizes now merchandized. Therefore, it should be the objective of the industry to conserve these fine sizes of coal in such manner that if and when processing facilities are developed, and market demands exist, the material can be salvaged and made available to meet these demands. From the standpoint of economical future reclamation, the ideal method of disposing of refuse containing the finer sizes of coal is to deposit it in banks separate and apart from other breaker refuse. By this procedure, the minimum amount of material will be processed in future salvage operations to recover the No. 4 and No. 5 buckwheat sizes. Many collieries in the anthracite region are operated under leases that have a specific term. These lease agreements provide that, upon expiration of the lease by term, exhaustion or otherwise, the ownership of the refuse material reverts to the lessor. Therefore, a question was raised in the minds of these operators: Why should I assume the expense of such procedure when I have no assurance that I will benefit by the future processing and sale of these fine sizes? Under present conditions, the answer to this question is not one of choice but of necessity, as restrictions imposed by legislation make it mandatory on operators of preparation plants to take necessary steps to properly treat silt-laden waters before permitting them to enter the streams. By reason of these restrictions, the disposal of fine sizes becomes a secondary rather than a primary operating consideration, and the procedure for disposing of this refuse becomes a matter of choice governed principally by topographical and geographical conditions. Methods of Handling Refuse There are three principal methods of handling and disposing of fine-size refuse; namely:

Jan 1, 1947

By S Grant, S Emeric, P Baker, E Jones, D Clark

As we strive for a sustainable and resilient future, repurposing assets has become a top priority. In Australia alone, we have a significant number of mineral projects in the pipeline, extensive existing operations, and over 50 000 legacy sites. Collectively, this presents a unique opportunity to be a world leader in mine rehabilitation. Complex stakeholder landscapes, inflexible policies, aged regulatory frameworks, technical uncertainties and increasing liabilities are all barriers hindering effective transition of legacy assets. The impetus for change is further catalysed by shifting consumer preferences, workforces in flux and regional Australians questioning what the transition means for their local community. We need innovative approaches to take a leading role in the industry and support global efforts more broadly. Co-designing an ambitious, shared vision spanning projects, operations and legacy assets with all key parties is a fundamental step to unlock and realise maximum societal, environmental, economic and reputational value. Serious play and gamification can further enhance this visioning process.

Aug 2, 2023

By Hewitt Wilson

Until recent years the term "whiting" was applied exclusively to the water-ground chalks of certain north European countries. In many industries these are still considered superior to the whiting made from domestic limestone and marble. However, the latter material has replaced much of the European whiting in the American market, largely due to improvements in grinding and classification by American manufacturers.4 To encourage the domestic industry, the Bureau of Mines in 1931 undertook a study of the preparation of whiting from American raw materials and a comparison of the finished products with European whitings.

Jan 1, 1937

By R. D. Eash

The purpose of this research contract was to develop and test a Saran latex modified portland cement concrete lagging to be used as a replacement for wood lagging. The scope of work performed was divided into four phases: Phase I - Engineering Criteria; Phase-! I1 - Design Study; Phase III - Fabrication of Lagging; and Phase IV - Prototype Demonstration Project. Each phase of work was completed and is described in detail in this report. The prototype latex modified concrete lagging developed in this program weighed 52 pounds. When tested in flexure, it supported center point loading of 4500 pounds and under 1/4 point loading it supported loadings of 7000 pounds. Deflections at maximum loading ranged from 1/2 to 1 inch. Maximum deflections exceed 2 inches. The lagging does not exhibit catastrophic failure. Two hundred and twenty of the LMC lagging were produced and shipped to the Bunker Hill Company in Kellogg, Idaho for installation in their mine at the 17 level. The lagging are performing satisfactory after 22 months exposure in the mine.

Jan 1, 1980

By W. C. Holliman

This report is one of a series of reports on the characteristics of commercial aviation gasolines, It presents compilations of inspection test data on their products furnished by 16 manufacturers of commercial grades of aviation and special date obtained in Bureau of Mines laboratories on 66 samples of these gasolines, Data are presented for 19 samples of grade SO, 17 of grade 91/98, 22 of grade 100/130, and 8 of grade 115/145 aviation fuels. These gasolines are designated July 1948 production, although some of the samples may have been produced a month earlier or later.

Jan 1, 1948

By P. de Vitry, Oliver Bowles

THE conventional wire saw, introduced in the slate district of Pennsylvania by the Bureau of Mines in 1927, and used thereafter with remarkable success, consists of a three-strand steel cable having a diameter of 3/16 or 1/4 in. The equipment, methods used, and accomplishments have been described in previous reports.1-7 Similar wire saws have been used extensively in Europe, in quarries and in shaping blocks and slabs. During the period 1932-1937, competition in European marble quarries was keen, prices were declining, and orders were not abundant. When orders were received, there was generally an urgent call for speedy delivery. Because of the diversification of demands, it was impossible to maintain in stock marbles of the color, size, and thickness called for, therefore the material generally had to be fabricated after the order was received. The wire saw enabled stone mills to fill such orders promptly. With skillful handling, 7/8-in. slabs could be cut accurately and rapidly with this equipment. It was found, however, that, as the three-strand wire became worn, the cutting speed dropped rapidly and the cut became less accurate. To overcome these difficulties the junior author of this paper, after much experimentation, developed a new type of wire consisting of a single ribbon-shaped strand, twisted as shown in Fig. 1. To ensure straight sawing, the twist of the ribbon is reversed from right to left and vice versa every 25 ft. The reversal of the [ ] twist is shown in Fig. 2. This is not a new feature; it has been used to advantage with the three-strand wire both in Europe and America for several years. However, some difficulties arise in splicing the three-strand reverse-twist wire, and the claim is made that cutting is less accurate as the wire becomes worn. To make an endless belt, the ends of the single-strand wire are brazed together with

Jan 1, 1941

By W. E. Cassan, W. L. Eaton, James Westfield, W. M. Romisher, Karl Hughes, S. H. Ash

"INTRODUCTION Funds were made available to the Bureau of Mines, United States Department of the Interior, for anthracite investigations during the fiscal year ended June 30, 1945. One of the approved projects was to conduct inquiries and scientific and technologic investigations having a bearing on the anthradite mine-flood problem. The investigative work done from July 1,1944, to June 30, 1946, is described in previous reports (5, 8, 10, 24, 28). 6/Purpose of Report The purpose of this report is to describe the investigative work conucted by the Anthracite Food-Prevention Section, Safety Branch, Bureau of Mines, during the period July 1, 1946, to June 30, 1947,Scope of WorkInvestigative work during the fiscal year ended June 30, 1947, was conducted under the direction of D. Harrington, chief, Health and Safety Division, and S. H. Ash, chief, Safety Branch, Bureau of Mines, Washington, D. C.The broad objective of the investigative work was to obtain factual day on: 1. Anthracite reserves of Pennsylvania.2. Underground water pools.3. Barrier pillars.4. The ""buried valley"" of the Susquehanna River.5. Infiltration of surface water into underground mine workings.The above-mentioned investigations are being continued during the fiscal year July 1, 1947, to Juno 30, 1948.In addition to the investigative work covered in this report, Ash end Eaton presented a paper on barrier pillars, which proposes a method for designing barrier pillars and has been Published by the American Institute of Mining and Metallurgical Engineers (5);"

Apr 1, 1948

By R. V. Ramani, R. Stefanko, G. W. Luxbacher

Comprehensive ventilation surveys are made to review the adequacy of the mine system with regard to both statutory requirements and/or company policy, to evaluate improvements to the current ventilation system and to plan for £stun expansion. If computer simulation is to be used for these purposes, accurate quantity and pressure measurements become an absolute necessity since the validity of the computer generated output is heavily dependent on the accuracy of the input data. Consequently ventilation surveys that are run to generate input data for computer simu¬lation must use the best data collection procedures to guarantee as accurate results as are possible. These requirements have led to modifications in procedures that are used for routine ventilation surveying. McElroy and Kingery (1957) have recommended that pressures be measured independent of quantities since minor changes in mine conditions have a greater effect on absolute pressure measurements than on quantity measure¬ments. They estimate that, for large mines, a pressure survey may take only 1 to 3 days while the corresponding quantity survey would require 1 to 3 weeks. Although this procedure would undoubtedly lead to more ac¬curate pressure measurements, its use for the development of computer input data is not recommended for the following reasons. Atkinson's equation, H = RQ2, is used in computer oriented analysis to develop the airway resistance, R, based on quantity and pressure loss measure¬ments. It can easily be seen that since R a 1/Q2 and R a H, the effect of errors in quantity measurement is, in fact, more significant than those in pressure measurement. If the quantity and pressure measure¬ments are made at different times another problem results. Minor changes in quantity that may occur in the time between the pressure and quantity

Jan 1, 1977

By John E. Conley

Of the three chemical elements most vitally essential for plant growth the United States, before World War I, had developed ample domestic supplies of but one-phosphorus. During and shortly after the war period, the fixation of nitrogen was greatly expanded in this country, as in many others, insuring a supply adequate for agriculture as well as for munitions. However, in spite of a search for sources of the third element, potassium, which began years before the war, attained almost frantic intensity between 1914 and 1919, and continued for 10 years thereafter, it was not until 1921 that the American Trona Corporation put its Searles Lake operations into continuous production. This company in 1926 became The American Potash & Chemical Co. but has never supplied much more than 15 percent of the potash consumed in the American market. Likewise, though discovered in 1921 in drill cuttings from oil wells, it was not until 1926 that domestic deposits of potassium salts adequate to render the United States independent of foreign sources of supply were proved to occur in the Permian Basin of Texas and New Mexico.

Jan 1, 1944

By L. Heber Cole

Introductory During the past few years, salt (sodium chloride) strata have been encountered in western Canada in a number of wells, while prospecting for oil and gas. The ever increasing number of such wells points to the presence of a vast salt basin, the boundaries of which are at present unknown. This basin extends in a northwesterly direction from a point near the United States boundary south of Regina, crosses the Saskatchewan- Alberta boundary northwest of Unity, Sask., and continues with more northerly trend to Waterways and beyond. The beds, as encountered, appear to have a general dip to the southwest of between 10 to 20 feet to the mile and a pitch along the strike to the southeast. Thus one finds the salt strata at Waterways, Alta., at 600 feet below the surface (121 feet above sea level) whereas at Radville, Sask. south of Regina, the top of the salt is at a depth of 6,643 feet below the surface (4,430 feet below sea level). Whether this is a continuous salt basin or a series of separate basins is not yet known. We do know however, that in some of the well~ more than one salt horizon occurs while in others which normally should have encountered corresponding beds, the salt strata are absent. This latter condition, however, may occur only in the southern part of Saskatchewan, where a barren area seems to come in from the southwest. In the northwestern part of the basin, on the other hand, the occurrence of the salt strata seems to be more regular and continuous, and depths at which salt should be encountered in a drill hole in this part of the basin may be predicted with a fair degree of accuracy.

Jan 1, 1948

By Clarence Hall, S. P. Howell, W. O. SNELLING

The explosives used in coal mines not only occasion accidents such as occur in the use of explosives elsewhere, but they frequently cause widespread disasters by igniting explosive mixtures of mine gas and air and of coal dust and air, or both. In addition, the firing of ex- plosives so shakes the walls and roofs of the mines as to cause falls, with their attendant casualities. Considering the large number of explosives and their wide range in composition and properties, it is obvious that certain of them should prove more suitable for use in coal mines than others. The problem is to determine which explosives are the most suitable for this purpose and the precise conditions under which they may be used with the greatest safety. Of course this problem could be worked out in actual mining, but experimental investigations when accompanying commercial opera- tions are hazardous and slow. To obtain the information sought, in the speediest and most economical manner, laboratory methods must be resorted to. The adoption of such methods began about 30 years ago with experiments in an iron gallery mounted on wheels, at Zwickau, Germany. This laboratory method of attacking the prob- lem has so commended itself that it has not only been repeated else- where in Germany but has at intervals been officially adopted, with many modifications and additions, by the Governments of Belgium, Austria, France, and Great Britain. Such was the status of coal-mine investigations in Europe when in 1904, an organization in the Geological Survey, which in 1907 be- came the technologic branch, was created to investigate the mineral- fuel resources of this country. At that time no division of the Na- tional Government had official cognizance of conditions existing in our mines, but through its system of collecting fuels for tests the technologic branch was forced to recognize that coal-mine accidents are a factor that must be reckoned with in determining the extent and availability of our mineral-fuel resources. This became so apparent, and it was so obviously a function of this branch to make a systematic research as to the cause and prevention of such acci- dents, that in July, 1907, experts were appointed especially to deal with this problem. As a result, not only was Bulletin 333, on Coal- Mine Accidents: Their Causes and Prevention, prepared and pub- lished, but through personal inspection of foreign testing stations, and a study of their reports and the critiques of their methods and operations, definite plans for the establishment of such a testing station in this country were formulated. In the latter part of 1907, four grave disasters occurred in close succession consequent on explosions in the Monongah mines in West Virginia, where 368 men were killed, the Darr mine in Pennsyl- vania, where 160 were killed, the Naomi mine in Pennsylvania, where 34 were killed, and the Yolande mine in Alabama, where 61 were killed. These frightful disasters so quickened the public con- science, and so plainly demonstrated that both humanitarian and economic needs demanded that steps be taken to prevent the re- currence of such accidents, that in 1908 Congress made a special appropriation for an investigation as to the "causes of mine ex- plosions." A similar appropriation was made in the following year. By act of May 16, 1910, the Bureau of Mines was created "to make diligent investigation of the methods of mining, especially in relation to the safety of miners, the use of explosives, the prevention of accidents," and other matters relating to mining. Therefore, these investigations are at present conducted in obedience to an organic act instead of being dependent solely upon special appropriations. The first appropriation became available July 1, 1908. Through the courtesy of the War Department a portion of the grounds and buildings of the arsenal at Pittsburgh was granted for the use of the technologic branch of the United States Geological Survey. Work was immediately begun in procuring and erecting the necessary instru- ments and appliances for carrying out the desired tests and inves- tigations and in adapting the existing buildings or in erecting new structures to contain the apparatus. The Pittsburgh testing station was officially opened and regular work was commenced on December 3, 1908, the apparatus and appliances having been tested, the force drilled in their use, and the equipment and methods inspected and passed upon by foreign experts.

Jan 1, 1912

By Joseph Grumer

About a century ago Bunsen and his associates invented the famous burner that bears his name and was to become the ancestor of today's gas appliances. Over the years, Bunsen's invention became the starting point of a highly developed, practical technology that culminated in the gas industry as we now know it. However, it did not occur to the early workers to investigate the scientific potentialities of the new device, and as a result the science of gas-burner performance did not keep pace with the growing industry. It was with the objective of closing the rapidly widening gap between science and technology that the present research was undertaken Its immediate purpose was to provide basic information on the combustion characteristics of .fuel gases, in particular as they affect flashback, blowoff, and yellow tipping. Information obtained in the present research and contained within this report consists of the following: (1) Fundamental flashback and blowoff characteristics have been determined, it is believed, for all fuel-gas mixtures in which the gas industry may be interested. These are critical boundary velocity gradients for flames in free air, on burners with ports at room temperature and pressure. Burner aeration is characterized by the parameter, fraction of stoichiometric. These basic limits are explained, values are presented, and calculation procedure is given for deriving corresponding values of port loading and percent primary air (chs. I and II).

Jan 1, 1956

By S. R. Mitchell, M. C. Fuerstenau, A. M. Gaudin

The two principal attributes of a thickener pulp are its settling rate and the ultimate pulp density of the thickened mud. Testing for evaluation of thickening attributes of a pulp has usually been done batch-wise by placing the pulp in a one-liter glass graduated cylinder and noting the position of the boundary between clear liquor and mud as a function of time. Refinements in testing have included repulping a thickened mud to various dilutions and evaluating the settling rate on these various repulped muds. This is considered to make possible an estimate of the settling rate as a function of pulp density and therefore to pinpoint the slowest settling pulp which ought to be critical from the standpoint of thickener plant design. Finally, tests are sometimes made with model-size continuous thickeners of arbitrary size. In batch tests it is generally accepted that the behavior of a pulp is described by a curve such as the one shown in Fig. 1, in which the position of the boundary between clear liquor and mud (the mudline) is plotted against time. It has also been assumed that the initial settling rate (the slope of the line segment AB) is descriptive of the pulp and independent of the size and shape of the container. Where the settling rate is slower and clearly a function of time (portion CD of the settling curve), it has been assumed that the data are not of much use because of the intrusion of compacting phenomena. The next important datum is the height, PE, which is a measure of the so-called ultimate pulp density. This quantity is assumed to be characteristic of the pulp and independent of the container.

Jan 6, 1959

By D. R. Tesarik

The factor of safety, the traditional measure of stability for earth embankments, is graphically presented in factor of safety charts in this Bureau of Mines report. Factor of safety contours are drawn for homogeneous earth embankments for two contrasting situations: (1) no phreatic surface and (2) a phreatic surface that assumes 10-pct freeboard. The factor of safety can be read directly from the charts if the physical properties of the soil and the geometry of the embankment are known. The curves provide a quick first approximation of the "most stable" and "least stable" condition of the embankment. The Simplified Bishop Method was used for the safety factor calculations, and a sequence of least squares curve fitting steps was used to present the factor of safety in final chart form.

Jan 1, 1981