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By AIME

BORN in 1899, in Bridgeport, Conn., E. A. Anderson grew up in a center of the nonferrous metal industry. Perhaps that had something to do with his selection of mining as a career while an undergraduate in Yale. After securing his Ph.B. in mining he worked for a year at Handy & Harman. By this time physical metallurgy had supplanted his interest in mining and he entered the Yale graduate school where he secured his M.S. degree in metallography under C. H. Mathewson. After completing his graduate work he entered the employ of The New Jersey Zinc Co. in their research division where he has remained ever since. The transition from graduate study to industry involved no disruption of technical interests. Academic research relating to the zinc-aluminum alloys, then coming into use for die-casting, was followed by extensive and productive industrial research in the perfection and commercialization of these alloys. Research on rolled zinc and rolled zinc alloys, corrosion and stress corrosion, dry cells, electroplating on zinc, and electrodeposition of zinc followed in overlapping succession as time passed.

Jan 1, 1947

By Edward Halse

THE occasional occurrence in metalliferous veins of rounded fragments of rock, matrix or ore, lying loose, embedded in clay, or enclosed in some kind of cement, may be attributed to four causes:¬ I. They have been washed in from the surface, or from an upper portion of the vein. II. They are of concretionary origin. III. They have been produced by movements in the country-rock or in the walls of the vein. IV. They have been found in situ, by the upward, downward or lateral flow of water in the vein itself. In this paper the word " conglomerate " is confined to a rock composed of rounded fragments or pebbles cemented together, as distinguished from a " breccia," in which the rock-fragments are angular. I. BOULDERS AND PEBBLES WHICH HAVE BEEN WASHED IN FROM THE SURFACE, OR FROM AN UPPER PORTION OF THE VEIN. In this type it is presupposed that the vein at onetime com¬municated by a fissure or open space with the surface, or with the upper portion from whence the fragments have been washed. One well-authenticated occurrence was described long ago by Fournet. Owing, no doubt, to later dislocations in the lode, pebbles from an old alluvium and sands containing titaniferous iron, as well as fragments of wood, were found in a vein at Huelgoët, in France. "Toutes les parties tendres du filon de Pranal ou ces pédnomènes sont les plus prononcés ont été excavés jusqu'a d'assez grandee profondeurs par l'impétuosité des torrents, qui ont deposé la matière alluviale."1

Jul 1, 1905

By John J. Egan, A. B. Kinzel, Walter Crafts

The demands of the petroleum and chemical industries for steels to be used in pressure vessels and similar structures at artificially low temperatures are continually increasing, and the writing of proper specifications with suitable tests becomes increasingly important. Likewise, the selection of suitable steels for such applications is of increasing concern to the metallurgist. It is generally recognized that highly alloyed steels of the austenitic stainless type retain their properties even at very low temperatures and represent the best technological solution of the low-temperature steel problem. However, in many instances less expensive carbon or low-alloy steels suitable for service within limited temperature ranges are available. The problem thus becomes one of defining the various factors involved in the production and fabrication of these less expensive steels and determining the temperature ranges in which their properties justify engineering application. Most of the applications involve welded structures, and the heat effect of welding as well as the nature of the weld metal are matters of prime concern. The first problem that the metallurgist faces is the determination of the type of test to be used as a criterion of the performance of the steel in low-temperature service. It has been generally recognized that the static properties of steel as determined in the ordinary tensile test undergo a gradual and relatively slight change as the temperature of test is lowered in the range of current interest; i.e., from room temperature to minus 120' C. It is further generally recognized that the behavior of steel under impact involving notch sensitivity is definitely affected at the lower temperatures. While the major subject of this paper is the effect of grain-refining deoxidizers, of low-alloy additions and of welding on the low-temperature notched-bar impact properties, an inquiry into the general behavior of steel under low-temperature impact testing is included. This is a pertinent portion of the investigation and the results thereof are

Jan 1, 1937

By Frank C. Smith

The following article covers the history of a metallurgical campaign, commenced in March, 1905, at the mines of the Socorro Bold Co., in the so-called desert region of Yuma county, Arizona. The results obtained were simply a function of necessity, as will be seen from the description of the local economic conditions and the character of the ores treated. The mines and mill of the Socorro Gold Co. are located near the small village of Harrisburg, about 60 miles from Congress Junction, Ariz., which, at the time this work was undertaken, was the nearest railroad station, and from which all supplies were brought by wagon through the desert, at a cost varying from $10 to $15 per ton in addition to the railroad freights. Wood, the only available fuel, cost $7 per cord. Water for all purposes was pumped to the plant from a well in the valley about 4 miles away. Under the Arizona law, a working-shift is 8 hr. Wages were $6 per day for foremen and mill-men, $4 per day for blacksmiths and engineers, $3.50 per day for miners, and $3 per day for shovelers and trammers. The ore consisted of quartz, in which, above the 250-ft. level, the iron-minerale were largely oxidized and some free gold was visible; below that level few traces of oxidation occurred, and pyrite constituted the principal mineralizer in the quartz, together with occasional pockets of galena and a few eccentric specks of covellite. The 20-stamp mill was equipped with plates for amalgamation, and three Standard tables for concentration. The tails from the tables mere elevated by a centrifugal pump to a launder, by which they were conveyed to a 60-ton cyanide-mill for further treatment. The cyanide-mill was erected at so great a distance from the stamp-mill that a separate crew of workers and a separate power-plant were necessary. No arrangement had been made for the treatment of the concen-

Jan 1, 1907

By William I. Watson

Problems encountered in beneficiating mineral raw materials become increasingly difficult as there is a shift to lower grade and more complex raw materials, and because of the economic need to strive for ever higher recoveries, higher grade products, and lower processing costs. Methods of attacking the many problems should include not only the familiar chemical and physical tests and equipment, but such techniques as X-ray analysis, infra-red analysis, differential thermal analysis, and the use of electron and X-ray microscopes. Many people in the mineral-treating field are unfamiliar with these newer methods and techniques. The differential thermal analysis method, in particular, does not seem to be very well known, even though it offers interesting possibilities in the study of many ore treatment problems.

Jan 7, 1959

By Eugene A. Mizikar

A mathetnatical model of heal transfer in continuously cast steel slabs is described. The model, consisting of a unidimensional transient conduction equation and boundary condition equations, has been pvogrammed for computer solution. Temperatuve and solidification profiles calculated for a 6-in. slab, being cast under several conditions of secondary cooling, are presented and compared. Calculated solidification profiles are in agreement with reported expevinle~ztal values. For the mold zone, the predicted slab shell thickness can be described by: Resuilts of the study indicate that multibank spray cooling followed by radiant cooling should be employed when solidifying thick slabs with minimum surface temperature of 1600°F. Under these conditions, a 6-in. slab can be expected to solidify in about 8.3 min. Computer results also indicate that radiant cooling can replace spray cooling during solidification of the final 30 pct of slab with little increase in overall solidification time. CONTINUOUS casting has come to the forefront of the steel industry in recent years because of economic advantages resulting from increased yields and elimination of several processing steps. Considerable work, however, remains to be done regarding modifications to the process and operating procedures. Both a lack of operating plants in this country and the experimental difficulties associated with direct measurements on moving castings have made determination of solidification rates and temperature distributions difficult. An alternate approach is to mathematically simulate heat transfer in a continuously cast section, and then calculate the temperature distributions as a function of the controllable variables of the process. Simulation of heat transfer during solidification requires that a nonlinear mathematical problem be solved. As pointed out by Ruddle,' there are two mathematical approaches to the problem- the analytical approach and the numerical approach. While the analytical approach is certainly the more elegant of the two, it does require a number of inexact assumptions because of the complexity of the problem. For example, noteworthy analytical treatments of heat transfer in continuous casting have been developed by Savage Hills,3 and pehlke4 only by making one or more simplifying assumptions such as invariant thermophysical properties, constant heat-transfer coefficients in the mold, and linear temperature profiles in the shell. Simplifying assumptions such as these can introduce considerable uncertainty in the validity of results calculated with analytical solutions. Numerical solutions, which are considerably more versatile, appear to be better suited for solving solidification problems. Complex variations in the boundary conditions and variable thermophysical properties can be handled readily with this technique. Whereas numerical computations can be long and tedious when done by hand, results can now be obtained quite rapidly with the use of either the digital or analog computer. Several numerical models of heat transfer in continuous casting have been published. In 1963, Adenis, Coats, and Ragones published a numerical model used to calculate temperature distributions in direct-chill-cast magnesium billets. More recently, Donaldson and Hess 6 presented results obtained with a numerical computer model of heat transfer in continuously cast steel billets. In the present study, a model of unidimensional heat transfer in continuously cast slabs is presented. The method of solution on a digital computer is also included. Calculated temperature distributions and solidification profiles for various schemes of secondary cooling along with attempts to verify the model are also discussed. MATHEMATICAL MODEL The schematic representation of the slab continuous casting process in Fig. 1 illustrates that the slab passes through three distinct zones of cooling. Accordingly, the mathematical model consists of three parts: 1) solidification in the mold; 2) solidification in the spray cooling zone ; 3) solidification in the radiant cooling zone. Heat-Transfer Equations. The model was developed bymaking a heat balance on a horizontal slice of slab over the time period required for the slice to proceed from the liquid metal meniscus in the mold to the cutoff station. As shown in Fig. 2, the imaginary slice extends from the center line to the surface of the slab. As the slice moves downward, heat is conducted from the center line to the surface of the slab at a rate governed by the surface boundary condition and thermophysical properties of the metal in the slice. The following partial differential equation describes the conduction of heat in a medium moving at velocity U in direction Z:

Jan 1, 1968

By J. C. Bowling

Factors governing the choice of building types, materials, and the details of construction for mineral processing plants in remote locations with cold climates are discussed. Alternative types of building insulation in common use are described and a comparison is made of their suitability under various conditions.

Jan 1, 1973

By W. H. Blauvelt

The only way in which the difficult problems of classification of coal for the manufacture of by-product coke can be solved is to analyze them by the use of scientific data. It is very easy to adopt classifications for coal for the manufacture of by-product coke along certain lines; we can easily say that for a certain class of metallurgical operation coke made from bituminous coal must not contain more than so much sulfur or more than so much ash and should yield certain returns in the by-products, tar, ammonia, benzol, gas, etc. Those points we are fairly clear on and I think it is hardly worth while to discuss them because I presume that they are familiar to most of us who have any occasion either to make coke or to use it. But there is a field in the manufacture of coke which we know very little about. For example, we are operating a plant on a certain mixture of coal. Suddenly our blast-furnace man or the user of the coke tells us the coke is not as good as it was before. The coke is analyzed and the coal is analyzed. Everything seems to be about the same as it was— the ash is the same, there is no more sulfur, and so on—but the coke, for the use to which it is put, particularly in the blast furnace, is wrong. What happens? The management decide to try a slightly different coal mixture. They do not necessarily raise the total hydrocarbons, the volatile matter in the mixture, nor change the sulfur or the ash, but they do make a change which improves the value of the coke for metallurgical use. The reason for this difficulty, as I see it, is the " combustibility " of the coke—I hesitate to use the word, but it is the best one I have available. Combustibility of Coke We know now that the combustibility of coke is a very vital point in many metallurgical processes and I think one of the most notable instances of the proof of this is the experience of the Carnegie Steel Co. in the production of coke at its Clairton plant. The history of that

Jan 1, 1930

By David Russell, Courtland Lee

FOREWOHD-Americans have been able to create wealth from the nation's natural resources to an extent unprecedented in recorded history, thanks largely to the existence of a free market and of a rational body of laws. The General Mining Law of 1872, for instance, by establishing the rules of the game, was quite effective in channeling the ability of Americans to discover and develop mineral deposits. Another example was the Mineral Leasing Act of 1920 which made available the more easily discovered mineral deposits by spelling out the conditions and rules under which miners could obtain leases on federal lands.

Jan 5, 1977

By C. Chamberlain

The Telfer Project, Australia's newest, largest, and most remote gold mine treats 480 kt of ore grading 9.33 g/t derived from open pit mining operations. Coarse gold is recovered by gravity concentration with jigs and further upgraded wing a continuous strake launder table, and by amalgamation. Remaining gold is recovered in a cyanide circuit and incorporates flat bottom air agitators, counter current decantation (CCD) and stellar filters for clarification and precipitate removal. Overall recovery into a bullion averages 98%. The mill incorporates a number of design features that allow for maximum efficiency and security wing a minimum number of operation personnel.

Jan 1, 1983

By Robert N. McIndoo, M. G. Woodle

10.5-1. Introduction. In the not-too-distant past, maintenance and the facilities for maintenance were considered a necessary evil to be given only secondary consideration in the development and planning of a surface mine operation. With the increasing sophistication of mining equipment and machinery, this concept has been replaced; and today's mine managers recognize that planning for adequate maintenance facilities is as important to a successful operation as a sound mining plan. This chapter will present the basic maintenance facilities and the fundamental considerations necessary to meet the varied requirements of surface mining. 10.5-2. Determination of Shop Facilities. The size, shape, and extent of maintenance facilities are contingent on the general mining plan, the location relative to outside facilities, and to the available capital. The type of construction employed is dependent on climatic conditions and preference. HAULAGE SYSTEMS. The type of haulage equipment used will dictate the kind of shops needed. Truck haulage requires entirely different facilities than rail haulage. Some mines will employ both systems, and can include hoists, skips, or conveyor belts in combination with locomotives or trucks. The requirements of each type will be discussed. MAINTENANCE ORGANIZATION. The pre-planning decision as to centralized maintenance vs. area maintenance, or a combination of both, will greatly affect the maintenance facilities required. A single pit with relatively short travel from shops to pit will probably have a centralized maintenance system. Where more than one mine is involved, or where there are diversified sections or functions in a mine (mine equipment, mill, conveyor, or

Jan 1, 1968

By Katherine Mather

This paper is an attempt to put together petrographic, physical, and chemical data about the large and varied group of rocks generally called limestones. Results of the properties of these rocks on their performance as concrete aggregates are discussed. CRUSHED stone classified as limestone comprises about 70 pct of the crushed concrete aggregate and roadstone produced in this country, and the product has amounted in the recent past to about 97 million tons per year, valued at more than $123,-000,000.' Therefore an evaluation of the properties of rocks classified in these statistics as limestones and an ability to predict their behavior as aggregate in portland cement concrete are matters of considerable economic consequence to producers and consumers of aggregate. This paper is an attempt to put together petrographic, physical, and chemical data about the large and varied group of rocks generally called limestones. It also points out certain results of the properties of these rocks on their performance as concrete aggregates. The problems encountered in efforts to explain the behavior of limestones, dolomites, and related rocks as concrete aggregate lie on the frontiers between the ignorance of the geologists and the ignorance of the engineers. The mineral composition and textures of the rocks have not been adequately explored and described, and the effects of mineral composition and texture on the performance of aggregates have been worked out in only a few cases. There are instances of unsatisfactory performance and some generalizations of those experiences. There are many more examples of satisfactory performance than of unsatisfactory, but there is practically no published information as to why a particular aggregate was satisfactory in a specific use. There are all too few investigations of undeteriorated concrete; more is known about the pathology of concrete than about its normal structure and aspect. As part of the investigation of aggregates, the classification of rocks is not an end in itself, but is a step toward recognition of properties expected to influence the behavior of aggregates in their intended use. Rock of any type may perform well or poorly as concrete aggregate, depending on the physical condition of the rock, its physical and chemical properties as compared to those of the matrix in which it is placed, and the circumstances under which the concrete is exposed. Some classification and descrip- tion of the limestones is necessary to distinguish subgroups whose members will probably behave in similar ways and to evaluate the group as a whole. The group name, limestone, includes and tends to conceal the identity of rocks that have a very great range in chemical and mineralogical composition, structure and texture, conditions of deposition, subsequent history, and suitability for use as concrete aggregate. All the rocks classified as limestones include one or both of the most abundant rock-form-ing carbonate minerals, calcite and dolomite, as major constituents. Carbonate rocks is a more descriptive and more accurate group name than limestone, which has generally been used to include dol-omitic or magnesian limestones and dolomites as well as calcitic limestones. Classification and Description of the Carbonate Rocks The question of names to be applied to the carbonate rocks may appear academic, but it is of practical importance as long as there are specifications for aggregate that result in acceptance or rejection of rocks by name and as long as failure to make distinctions among the carbonate rocks leads to misunderstandings of their properties and of what may be expected of them in performance. Materials included in production statistics as limestone and tested for concrete aggregate as limestone range in fact from calcareous shale and calcareous or dolomitic sandstone and argillaceous limestone and dolomite to calcitic limestone and pure dolomite and to rocks close to calcitic and dolomitic marble. To take a simple example: consider two manufactured coarse aggregates, both dense and unweathered, one composed principally of crystalline calcite and the other of crystalline dolomite, but both known as limestone. If each is used as coarse aggregate in a standardized concrete mixture with the same fine aggregate used in both cases, made into concrete specimens, and tested in accelerated freezing-and-thaw-ing, the test results will probably be quite different, because of the differences in internal bond and thermal properties between the two aggregates. As long as both aggregates are called limestone, the test results cannot be explained, or used except in a very limited way; if the aggregates are distinguished as limestone and dolomite and the consequent differences in texture and thermal properties are recognized, the results are reasonable. Classification of the carbonate rocks used as aggregate should be based on structure and on composi-

Jan 1, 1954

By Frederick M. Becket

SHORTLY after the Armistice there appeared a few references to numerous attempts that had been made to produce steel without the aid of manganese, or at least with manganese in abnormally low percentage. Some years later, during two consecutive days of train travel, I had excellent opportunity to read Sir Robert Hadfield's book, entitled "Metallurgy-Its Influence on Modern Progress," and also his paper, "The Metal Manganese and Its Properties : Also the Production of Ferro-Manganese and Its History," presented at the spring meeting of the Iron and Steel Institute, 1927. Both the book and the paper are most interesting historically to makers of alloy steels and

Jan 1, 1931

By Kenneth Seaver

(San Francisco Meeting, September, 1915) INTRODUCTION IT is rather gratifying that in the field of the manufacture 'of refractories, in which, as a whole, foreign practice has surpassed us, the United States stands pre-eminent in the making of silica brick. In some instances European manufacturers have refused point-blank to credit the possibility of making to such specifications as are common with us, until the actual 'completed shapes were shipped for inspection. But both the manufacturer and consumer in foreign lands are now frankly learning from us, and benefiting by our advanced practice in this field, as is evidenced by the orders placed here and the efforts put forth abroad to come up to the standard of American-made material. In no metallurgical operation has the employment of silica brick spread with. such leaps and bounds as in the building of plants for the carbonization of coal, particularly in the byproduct coke oven. Today, in practically all types of oven, the structure above the floor level (except the facings) is of silica, while in the recuperative and in some regenerative types, its use is extended to that portion of the oven below the floor as well. By reason of the fact that there are a number of classes of refractories of higher silica content than the usual so-called fire-clay brick, there is sometimes a misunderstanding as to the class of material referred to as "silica" brick. We here refer only to a brick having a silica content of 94 per cent. or more and made usually from quartzite rock with a small percentage of lime as a binder. The term "silica" brick is sometimes rather loosely applied to brick front highly siliceous clays, or to a quartzite refractory of mingled fire-clay and quartz rock; but such products are not considered in this discussion.

Jan 9, 1915

By AIME AIME

IN an address before the New York Section. A.I.M.E., Oct. 20, Alex L. ter Braake, speaking on the tin industry of the Netherlands East Indies, interjected a few remarks, at the chairman's request. on the mineral stock-piling project now before Congress in a bill sponsored by Senator Scrugham. The full text of Mr. ter Braake's paper was published in the Nov. 6 issue of the American Metal Market. Following mention of the buffer stock scheme as applied in the tin industry, Mr. ter Braake continued:

Jan 1, 1943

By John M. Loveioy

EVERY producer of crude oil knows what is meant by the Rule or Law of Capture. It means that the ultimate ownership of a migratory substance such as oil is not determined until that substance is reduced to physical possession. Unless, therefore, the producer moves quickly to capture his share from the common pool, he may lose to any neighbor who is drilling and producing more rapidly than he a portion of the oil originally underlying his property. And there is no recourse open to him if his property is so drained. Under this rule it is obvious that the owner of an oil property, if he is to protect his' ownership, must be governed in his development and production policies by the activities of his neighbor rather than by his own business requirements. He must drill as densely and as fast as the other operators in the field or lose part of the oil to which he should be entitled.

Jan 1, 1936

By W. R. Ingalls

THE present administration has made sincere and effective efforts to reduce the expense of the Federal Government, but it has reached a point beyond which it seems impossible, or anyway extraordi-narily difficult, to go. This is ascribable to the large part of the budget that is represented as war expense. There is no doubt that this spells high taxation for many years to come. Nevertheless, although a large part of the taxation will be attributable to the war, the paying out of the proceeds of that taxation by the government will not be war expense, except in minor part, as will be hereinafter made clear. It will be useful to explain the economic meaning of this situation, for it has bear-ings upon several open questions, such as a bonus to the ex-soldiers, the foreign debt accounts, etc. The expense of the war on the part of the American people was in the main paid concurrently with its prose-cution. This was necessary. Warfare is not conducted with money, but with materials and labor. Except for such previous production as was represented by stocks of goods, the requirements had to be supplied by coincident production. With the end of 1918 our war expense ceased, save for such production, e.g., of ships, that was allowed to run on unchecked, and the indemnities that had to be paid for cancelled contracts. When those matters have been settled we shall be done, barring one important thing. Of course, our war expense began to contract right after the armistice and shrunk rapidly with the demobilization of the troops in 1919. If we had not been able to obtain all needful material from our own sources and had been constrained to borrow it from foreign countries, incurring a foreign debt, we should have been in the quite different posi-tion of having to repay that material, or its equivalent, during subsequent years. The European countries had to come to us for such supplies. This outlines the fundamental difference between their present situations and ours. We were therefore compelled not only to furnish materials and man-power for our own warfare but also much for the Allies.

Jan 3, 1923

THE problem of picking the best students for an engineering college can no longer, be considered as simply one of determining the amount of general ability, but rather of finding special aptitudes for scientific work, according to Carl C. Brigham~ a Princeton University professor, who has been conducting researches on methods of selecting engineering undergraduates at Cooper Union, an evening school in New York City. When we first began this investigation seven years ago," says Dr. Brigham, "we thought the whole job would be done a soon as we had found a good method of measuring general intelligence. Today we feel that we are still about five years away from a solution, but on somewhat firmer footing than when we were looking for general ability.

Jan 1, 1928

By E. B. Swanson

There is only one way to transport natural gas and that is by pipe lines. In the past few years, these lines have been extended rapidly into areas which previously had been served mainly by solid and liquid fuels. In the subject given me, this extension is referred to as an invasion, which implies a rather forceful entry. Whether or not such an implication may be applied to recent natural-gas developments is unimportant. It is the fact of the extension, not its definition, which is important. For centuries, natural gas has been utilized for various purposes in many parts of the world. It was the foundation of fire worship at Baku. The Chinese used it for the evaporation of brine in salt manufacture. In our country, its history seemingly dates back 110 years to the vicinity of Fredonia, N. Y., where seepage gas was assembled and used for lighting purposes. A few years later, a %inch pipe was laid to a lighthouse on Lake Erie, and the early records of the Lighthouse Service tell of the difficulties surrounding this use. With the discovery of oil in Pennsylvania, there followed further development; the town of Titusville was piped with natural gas and, some few years later, gas was made available for manufacturing plants adjacent to the oil fields. For more than a half century, the industry was concentrated in the

Jan 1, 1932

By J. B. Cheatham

The influence of friction on the force required for an idealized bit tooth to penetrate a "plastic" rock is analyzed. The rock is assumed to obey the Coulomb-Mobr yield criterion and the tooth is represented by a two-dimensional sharp wedge. At the tooth-rock interface the stress field not only satisfies the yield condition but also is such that the ratio of the shearing stress to the normal stress is equal to the coefficient of friction. The solution relates the force on the tooth to the depth of penetration, the tooth angle, the coefficient of friction between the rock and bit tooth and the angle of internal friction and compressive strength of the rock. INTRODUCTION Most rocks are brittle at atmospheric pressure but exhibit ductility and increased strength as the confining pressure is increased. In a previous analysisl the force required for a bit tooth to penetrate a rigid-plastic rock was computed for two limiting conditions: (1) a perfectly lubricated tooth-rock interface which should correspond to a lower limit for the penetrating force, and (2) a perfectly rough interface which should provide an upper limit. Experimental results2 for rock indentation under confining pressure have confirmed that the analysis generally predicts upper and lower limits for the penetrating force as a function of rock properties and tooth angle. The present analysis extends the previous work to account for the friction between the rock and the tooth. ANALYSIS The force required for incipient plastic flow of an idealized model of a rock under a bit tooth is computed subjected to the following assumptions. BIT TOOTH 1. sharp two-dimensional wedge (end effects neglected) 2. rigid tooth (elastic deformation of tooth neglected) 3. displacement of tooth is normal to rock surface 4. friction exists between tooth and rock ROCK 1. semi-infinite, isotropic and homogeneous 2. rigid-plastic (elastic deformation of rock neglected) 3. non-work hardening (horizontal stress-strain curve) 4. Coulomb yield condition* (linear Mohr envelope) 5. smooth, flat surface According to the Mohr theory of failure it is assumed that failure occurs when the state of stress is such that the Mohr stress circle becomes tangent to an experimentally determined envelope. The Mohr failure curve is frequent1y approximated by a straight line and referred to as the Coulomb-Mohr failure criterion. If the rock is under sufficient pressure to be ductile we can use the linear envelope as a yield condition. The Coulomb-Mohr yield criterion is illustrated by Fig. 1 and is expressed by the following equation:l