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By G. L. Oldright, F. S. Wartman

"In the process of smelting copper ores and secondaries in the reverberatory furnace to produce a copper matte and a slag low enough in copper content to be discarded on the dump, it is essential to the best functioning of the process that most of the iron in the material charged into the furnace be at the end in the form of sulphide in the matte or ferrous oxide in the slag. Ferric oxide and magnetite present in the charged material should be reduced to ferrous sulphide or oxide. Ferric oxide offers no difficulty in reduction, at least to the magnetite stage, because it reacts very readily with sulphides at quite low temperatures. Magnetite is less reactive and consequently more resistant to slagging, so that the furnace man must take advantage of all factors favoring its reduction in order to prevent accumulations in the furnace.In order to determine these factors more definitely, the Bureau of Mines in cooperation with the Department of Metallurgy, University of Arizona, has undertaken at the Southwest Experiment Station an investigation of the effect of various factors upon the rate of reduction of magnetite by ferrous sulphide. A previous paper's reported the nature of the reactions taking place and the effect of various physical factors when only pure sulphide and oxide were present. Since in the actual smelting operation, many other substances are also present, it seemed desirable to make a study of the effect of their presence upon the rate of reduction of magnetite by ferrous sulphide. Such a study has been made; the work done and the results obtained are described herewith.As will be shown later, it has been found that of the substances usually present in the smelting charge, silica and magnesia accelerate, whereas lime, alumina, and cuprous sulphide hinder the reduction of magnetite by ferrous sulphide.No report of a previous laboratory investigation of this subject has been found. Almost all furnace operators have made at one time or another at least qualitative ccmparisons of the effect of various changes in operating oonditions upon the behavior of magnetite in the furnace, but the conclusions derived from the experiments have never been published."

Mar 1, 1931

By Gabriel Esterhuizen, Tom Goodwin, Scott Schilling, Anthony T. Iannacchione

The Roof Fall Risk Index (RFRI) is a new method introduced by the National Institute for Occupational Safety and Health (NIOSH) to assist the underground stone mine operator in 1) assessing defects the mine strata and 2) rating the relative roof fall risk these defects pose. The RFRI utilizes observational techniques to identify defects in the roof strata caused by local geologic, stress, and mining conditions. Assessment values for ten defined defect categories provides the foundation for estimating a range of risk conditions between 0 and 100 that define the potential for a roof fall. This paper examines how the defect information is collected using two field verification sites and proposes methods to analyze the RFRI data. These examples provide information on how well the method replicates observed conditions and how it might be applied in practice.

Education and training research is a major component of the Bureau of Mines human factors research program. The goal of human factors research is to enhance human performance for the purpose of improving both safety and the profitability of the minerals industries. This is achieved through the design of mining equipment, work tasks, management procedures, and development of human resources. This proceedings volume presents several new developments that are helping to improve the quality and efficiency of health, safety, and occupational skills training in the mining community. Several papers address the issue of how to teach and assess miner abilities to deal with underground mine emergencies. Other papers examine practical procedures for defining and cost justifying the integration of structured training and other performance improvement strategies to enhance the proficiency of the work system.

Jan 1, 1988

By Marc Ruest

A new instrumented cable bolt has been developed by the National Institute for Occupational Safety and Health at the Spokane Research Laboratory in Spokane, WA. Although various instruments are available to measure load distribution and magnitude along a grouted cable, this instrument is innovative in that it uses strain gauges internal to the cable as load-measuring sensors. The instrument has been successfully tested in the field at FMC?s Granger Mine, Meikle Mine, and Getchell Mine. A ?split-pipe? laboratory pull test was performed on each of three cable bolts instrumented with the new device. Each test consisted of grouting a 1.83-m-long cable in two 0.91-m-long sections of schedule 80 pipe. A numerical analysis was then performed in which laboratory boundary conditions were simulated and model properties derived from textbook guidelines. The loads calculated by the model were then compared to the measured loads.

May 1, 2002

By N. D. L. Burger

An effective prototype face support system to minimize rockfalls in rockfall-prone mines was developed and patented during a project sponsored by the Mine Health and Safety Council (MHSC). An experimental development model (XDM) roof support unit was developed and evaluated. Mines with rockfall problems in the face areas can use the roof support system to reduce fatalities and injuries in the face area of stopes. The roof support system consists of two similar support units connected to each other via two crank mechanisms. Each unit consists of a headboard supported by a ?wishbone? structure (top and bottom leg). In the first design a threaded bar with struts similar to a scissors jack keeps the legs apart. (In the final version that was field trialed, the threaded bar mechanism was replaced with a hydraulic cylinder). All the components are manufactured from steel. To move the system forward the first support unit is collapsed, the second remaining in the loaded position. The first unit then hangs from the second unit to which it is connected. The first collapsed unit is then manually cranked forward and prestressed. If the required position is still not achieved, the other unit is released and moved forward. The specification for the system was determined and presented at a workshop with industry participants. Different concepts were developed and evaluated against the system specifications. A technology demonstrator was then developed and tested on surface. The technology demonstrator development process included detail design, building and testing of components and subsystems, design reviews and the building and commissioning of the technology demonstrator. The testing of the technology demonstrator was done in a 500-ton hydraulic press, in a mock-up stope and underground. A risk analysis, in which technical, logistical and economic aspects were assessed, was done to determine the critical areas of the system. During the next phase of the project working prototypes were developed for underground tests and evaluation. This process indicated that it was necessary to adjust the system specifications and a redesign was called for. In an iterative process test units were built for purposes of evaluation, specification verification and field trialing. After the successful conclusion of the trials the equipping of a complete production stope started for purposes of integrating the system into the current mining process.

Jan 1, 2008

By H. Boghosian

This paper presents the design and construction of a deep basement in a steeply sloping site in glacial till in Glasgow city centre. Existing foundations, adjacent structures and services, in tandem with asymmetric loading, presented particular challenges in the planning, execution and design of the project. The construction methods and temporary works, analysis by the Finite Element method and monitoring carried out are all described.

Jan 1, 2006

By D. S. Choi

This paper presents a theoretical analysis of the effect of shape and size on strength of geologic materials. The results indicate that the shape effect is caused by the development of confining pressure at the interfaces. The linearization of the obtained formula is of the same form determined by experiments. The size effect is attributed to the fact that the geologic materials contain discontinuities in the form of fractures, bedding planes, and cleats. The maximum reduction factor for the size effect is the one-sixth power of the volume of a cubic test specimen. The results of this work are particularly useful in determining the strength of coal pillars in underground mines.

Jan 1, 1989

By Lawrence P. Goldfarb

The City of Alexandria, Virginia, Public Safety Center (PSC) is a 64,000 square foot facility that houses the Police Department, Office of Sheriff and the Office of Magistrate. In addition, the center includes a detention facility for local and federal inmates, operated by the Sheriff. The PSC is composed of a 3-story building to the west and a 6-story building to the east constructed on a landfill in a wetland area in the flood plains of hunting Creek. The existing ground floor of the 3-story building is a floating slab-on-grade, with the interior and exterior columns, exterior walls and upper floors all supported on belled, drilled shafts. Portions of the floating first floor slab have undergone excessive settlement due to the apparent consolidation of the underlying organic soils. The magnitude of the settlements of the floating first floor slab is sufficient to require replacement of the slab and relocation of a portion of the facility. The rehabilitation was complex and required staged construction, consisting of constructing Auger Pressure Grouted (APG) Piles in low overhead conditions. This paper summarizes the geotechnical conditions that lead to the excessive settlement of the floor slab, the construction of the (APG) Pile foundations in low overhead conditions and the evaluation of potential future settlements.

Jan 1, 2009

By Kanchan K. Sen

The North Shore Connector (NSC) project will extend the Allegheny County Port Authority?s Light Rail Transit System from downtown Pittsburgh below the Allegheny River to the North Shore via twin bore tunnels. Jet grouting, diaphragm walls, and soil mixing were selected as cost-effective technically viable ground improvement and support of excavation techniques. Jet grouting was specified to provide break-out (egress) and break-in (ingress) block sections at the tunnel boring machine (TBM) launching and receiving pits. Jet grout treatment was also used adjacent to buildings with shallow foundations and below retaining walls along the tunnel alignment. A new method for measuring jet grout column diameter based on electrical resistivity was employed on the project. New equipment was introduced in the U.S for constructing soil mix temporary support of excavation using a soil-mix technique termed Cutter Soil Mixing (CSM) due to the use of two vertical cutting wheels that have evolved from diaphragm wall trench cutter technology. The system allows for continuous water tight soil mix panel construction including steel beams. This paper highlights some applications of jet grouting and various support of excavation systems (e.g. slurry walls, cement bentonite walls and CSM walls), including new innovative techniques (e.g. Cyljet and CSM) used under the constraints of an urban environment.

Jan 1, 2010

Provide improved permanent stoppings designed specifically for use in mines with large cross-sectional entries. Approach The large entry sizes in many mines, such as oil shale, salt, and limestone, make the conventional stopping construction techniques used in smaller opening mines unacceptable. The Bureau of Mines and Colorado Mining Association jointly sponsored a contract to design and test new or modified stopping concepts for these mines. The most promising concepts were then tested in an oil-shale mine having 30-foot-high by 55-foot-wide mine entry openings. All stopping designs tested were evaluated in terms of cost, air tightness, and resistance to blast damage.

Jan 1, 1987

By Wayne N. Marchant

Introduction The issue of coal mining safety plays an important role in the United States' growing dependence on coal to supply its future needs. This article will address the federal government's role, principally the US Bureau of Mines, in meeting this challenging growth and demand while reducing the social and economic costs attributed to injuries and fatalities in underground mining. Some interesting facts and projections with respect to the nation's energy picture will be discussed. This includes the distribution of its reserves and the projected role of coal in the energy and economics of the nation's future. Underground mining will continue to be an important means of providing this coal. The author will discuss how the Bureau of Mines' research program addresses the problems of health and safety that grow out of the demand for more coal. Future projections First, a synopsis of salient facts and projections concerning the US's situation with respect to energy and the economy. Figure 1 depicts the relative quantities of recoverable energy reserves in the United States by their type. Most people are aware of the nation's use of oil. We hear a lot about natural gas. And we are aware of the controversy over the use of nuclear energy. But, while looking at Fig. 1, the question becomes, "Where will our fuel to meet the demand for energy in the future most certainly have to come from?" With 82% of the nation's recoverable fuel reserves being coal, the answer is irrefutable. Coal will be that source. Figure 2 is the present market for coal. It shows that 77% of the coal mined goes to supply electric utilities. Therefore, the coal industry as a whole is most sensitive to the trends and demands for electricity. It is less affected by what happens in other markets, such as export and direct industrial use. In fact, the coal industry is three times more sensitive to the electric utility market than to all other markets combined. Therefore, the trend in the demand for electricity must be examined. Electricity demand is expected to increase steadily over the next 15 years. It is projected to grow from its present 2.3 trillion kWh per year to 3.5 trillion kWh per year by the year 2000. The fuel to supply this increase in demand must come from somewhere. The question is "How much of this extra fuel will be coal?" Although the demand for electricity is predicted to increase, the demand for coal does not necessarily follow. Coal must maintain its fraction of the energy sources used for electricity generation if its demand is to increase at the same or greater rate as electricity. Except for a near-term dip in demand due to a slight increase in nuclear capacity, the domestic electric generation accruing to coal will go from 56% in 1985 to more than 60% in 2005. Thus, the predicted trend is for coal to become a larger part of the fuel mix for electric power generation. Similarly, looking at the most recent forecast for total coal consumption trends, it can be seen that for electric power generation alone, the coal industry must be able to supply an additional 316 Mt/a (348.5 million stpy) by the year 2000 (Fig. 3). It must be stressed here, though, that without significant improvements in mining safety, it can also be easily predicted that injuries and fatalities will increase in proportion to the increase in coal production. Will society consider that acceptable? This author does not believe so. Figure 4 examines the effect of coal prices on the price of electricity. The projections show that the already high proportion of fuel cost will become a greater fraction of the consumer price for electricity. Specifically in 1985, 36% of the price of electricity was the cost of the fuel. In 1995, 46% of the price of electricity will be the fuel cost. That implies that the price of coal will have an increasing influence on the consumer price for electricity. Thus, as coal is used more to generate electricity and as fuel becomes a greater

Jan 4, 1987

By Xu Lin Sheng

During the mining course, when the roof above coal seams is constituted by thick and hard sandstone (conglomerate), sudden roof movements often take place with great force and de¬struction which is the biggest danger to the safety and production. Such sever movements of the roof in mining directly relate to the rock mechanical properties which are the main fac¬tors that influences the regularity of hard roof movement and its destruction form. A significient work and important technical way for applying rock mechanics into mining en¬gineering is studying the rock mechanics of the hard roof and altering some of the rock me¬chanic parameters which induce the improvement of the rock properties in order to efficiently control the movement of the hard roof.

Jan 1, 1989

By O. M. McRae

The Courtland-Gleeson area is in Cochise County about 15 miles east of Tombstone in southeastern Arizona. Rocks exposed in the area range in age from Pre-cambrian to Quaternary. The Precambrian is repre-sented by the Pinal schist. Paleozoic rocks include the Cambrian Bolsa quartzite and Abrigo limestone, Mississippian Escabrosa limestone, and the Permo-Carboniferous Naco Group limestones. Rocks believed to be of Triassic and/or Jurassic age include the Copper Belle monzonite porphyry, Turquoise granite, and Gleeson quartz monzonite. The Cretaceous is represented by andesitic volcanics and various sedimentary rocks. Tertiary rocks include the intrusive and extrusive Sugarloaf quartz latite porphyry and numerous dikes of various rock types. Quaternary conglomerates cover the northern and eastern part of the area. The geologic structure is extremely complex. All rocks as old as early Tertiary have been involved in either tilting, normal faulting, high angle reverse faulting, imbricate thrusting or folding and overfold-ing. Major deformation was initiated during the first half of the Tertiary. Northeast-southwest compres-sional forces caused thrust plates containing lower Paleozoic rocks to override Cretaceous rocks. Subsequently, two large slide blocks of lower Paleozoic rocks, acting under the influence of gravity, moved eastward. The imbricate structure and the gravity slide blocks were then broken by late Tertiary normal faults. INTRODUCTION The Courtland-Gleeson area, or Turquoise Mining District, has long been recognized as an area of extreme structural complexity. Gilluly 2 referred to the entire district as a "gigantic thrust breccia". In 1962, Bear Creek Mining Company completed a two year program of detailed geologic mapping supported by exploration drilling. The purpose of this paper is to present some of the results of this investigation and to provide a structural interpretation based on these results. The geologic map that accompanies this report is generalized and shows only the major and significant features. The area was initially mapped on aerial photographs on a scale of 1 in. equals approximately 500 ft. These data were transferred to a planimetric base using a vertical sketch master. LOCATION The Courtland-Gleeson area is in central Cochise County, about fifteen miles east of Tombstone, and about twenty-two miles northeast of Bisbee in southeastern Arizona (Fig. 1). The area is readily accessible over graded gravel roads from both Tombstone and Elfrida. GENERAL GEOLOGY Rocks exposed in the area range in age from Pre-cambrian to Quaternary. wilson3 and Gilluly2 have published very detailed descriptions of the principal rock units exposed in the area. Only a summary description is provided in Table I. A great number of previously unmapped narrow Tertiary dikes and small irregular masses of hornblende andesite porphyry, lamprophyre, and aplite intrude the Gleeson quartz monzonite in the western part of the map area. The scale of the map prohibits showing them. The aplite dikes are related to, and bear the same structural relationships as, the Sugarloaf quartz latite dikes found in this area. For that reason, and because both the hornblende andesite porphyry and the lamprophyre are post-mineral and post-thrusting, their omission from the map is not considered significant. Because so many of the contacts in the district are fault contacts, because bedding faults appear to be prevalent but are difficult to recognize and map, and because igneous intrusions are so common throughout the sedimentary section, it is virtually impossible to measure an exact total thickness of any of the sedimentary rock units. Nevertheless, neither the field mapping program nor the diamond drilling provided any basis for suspecting that the thicknesses of the sedimentary units are significantly greater or less than what might be inferred from surrounding districts.

Jan 1, 1967

By D. Imeson, T. Grammatikopoulos, M. Aghamirian, M. Oliazadeh

"More than 70% of potash is produced worldwide by froth flotation. Flotation of potash was developed in the early 1930s. Amines are widely used for flotation of sylvite (KCl) from halite (NaCl) and insoluble materials such as clays. Amine collector is also absorbed by clays. Therefore, clays are usually separated by scrubbing and de-sliming prior to flotation. Alternatively, slimes can be floated ahead of potash flotation. Flotation recoveries of sylvite are commonly in the range of 85%, while losses can occur in slimes, flotation tailings and make-up of process brine. Ores containing free coarse-grained sylvite are generally screened, whereas both fine and coarse fractions are conditioned and floated separately. The unique features of potash flotation include solubility of sylvite in water, the size of particles floated and fast kinetics. Particles up to 2.3 mm can be floated and about 50% of flotation feed can be removed in the rougher stage in few minutes. The main challenges in potash flotation are the recovery of potash from slimes, flotation efficiency in the presence of carnallite and recovery of coarse potash grains. A review of potash flotation shows that there is still room for improvement in both coarse and fine potash flotation. The present paper reviews the most significant flotation parameters including reagent type and dosage, flotation circuits, flotation equipment size and new developments in potash flotation. The latter include new reagents, flotation technologies (Hydrofloat, Jameson and column cells) larger flotation cells and slimes flotation.INTRODUCTION Potash is the common industrial term for potassium in various chemical combinations and minerals soluble in water. About 90% of potash produced worldwide is used as agricultural fertilizers. Flotation is the main treatment process of sylvinite (KCl-NaCl) ores for recovery of sylvite (KCl). Potash concentrate should contain a minimum of 95% KCl and be relatively free from 0.2 mm KCl fines. The flotation process for beneficiation of potash ores was developed in United States and Russia concurrently in the early 1930s. In 1934, Potash Corporation of America applied flotation process in a commercial scale (Tippin R.B. and Huiatt J.L). In the initial application, halite (NaCl) was selectively floated by employing lead chloride as an activator and soap as collector. The sylvite concentrate was reported in the cell underflow."

Jan 1, 2012

Wire rope, when used for hoisting on a mine is one of the most vulnerable units in the most expensive group of installations on the mine. With the introduction of hoisting on the Koepe sheave, a new technique was established. This innovation brought with it certain advantages which long had been recognized and which are being developed further.A need exists for the development of an infallible non-destructive testing device for wire ropes and it is axiomatic that the development and application of such a device should be coupled with the physical examination of mine hoisting systems. Therefore an integrated type of research programme is necessary in order to correlate the effect of shock loading with rope damage, which may be detected ultimately bynon-destructive means. This paper reviews certain historical aspects of investigations on this topic and it outlines a policy for research which can cope with a.c. or d.c. methods of excitation of the rope.INTRODUCTIONThe importance of wire rope in mining operations is often not fully recognized. A wire rope when used for hoisting in a mine shaft should be regarded as a "machine" forming part of a system of machines, and consequently it should be specified as such when it is purchased, it should be maintained as such during its working life, and it should be discarded only when it has done its duty and has been rendered either unsafe or uneconomic for further use.Every mine shaft, vertical or inclined, has in it one or more wire ropes which are used to transport men, material, and ore. Considering the long history of wire rope haulage and the large number of rope applications, it is a tribute to wire rope makers and to mine maintenance engineers, throughout the world, that not many serious accidents have occurred because of failure of wire rope. However, when a...

Jan 1, 1965

By Q. G. Reynolds

The presence of dust and fume suspended in the freeboard region is a common feature of the operation of direct current (DC) plasma smelting furnaces. This occurs primarily as a result of the use of fine feed materials together with the open-arc, open-bath operation of such smelters, and is exacerbated by the high velocities and turbulent mixing of the gas in the vicinity of the arc jet. Dust and fume losses into the furnace off-gas system can be significant in some cases and may have economic, operational, and environmental impacts on the process. A computational modelling study is presented in which the concentration of dust material was considered as a continuous field subject to a governing partial differential equation. Settling behaviour was calculated as a function of particle size, local gas/plasma temperature, and other physical properties. Development of the coupling between the concentration field and a magnetohydrodynamic description of the arc is shown, and the resulting models were used to compute various aspects of the behaviour of the concentration field in the arc region for a variety of furnace conditions. Time-averaged as well as transient models of the arc were used to generate the results presented. Qualitative case studies produced several practical suggestions for furnace operation, including increased dust capture by the bath when feed ports are located closer to the electrode, and the possible effects of feed segregation in the furnace freeboard based on dust particle size and density.

Jan 1, 2015

By Jacob Masliyah, Zhiang Zhou, Tshitende Kasongo, Jianjun Liu, Zhenghe Xu, Jeawon Choung

"Slime coating is a recognized challenge in fine particle flotation, not only in decreasing recovery, but also in reducing the selectivity and hence froth quality. In this presentation, a novel method based on electrophoretic mobility distribution measurement to study slime coatings is described. By measuring electrophoretic mobility distribution of individual minerals and their mixtures, the interactions between these minerals can be evaluated.For illustrative purposes, a model system of fine coals, or oil sands with two different types of fine clays was studied. Flotation tests showed a significant decrease in coal (bitumen) flotation recovery with montmorillonite but not with kaolinite clay addition. When electrophoretic mobility distribution of a fine coal/montmorillonite clay mixture was measured, a single modal zeta potential distribution was obtained, in contrast to a bimodal distribution for fine coalkaolinite clay mixture. This finding suggests a stronger adhesion of montmorillonite than kaolinite clays on fine coal surfaces. In the case of bitumen, the bimodal zeta potential distribution was measured for the mixture of bitumen emulsion and kaolinite or montmorillonite, indicating a weak attraction of the clays by bitumen. In the presence of calcium, however, a single modal zeta potential distribution was obtained in the mixture of bitumen emulsion with montmorillonite but not kaolinite clays. These findings are in excellent agreement with bitumen flotation results, demonstrating that the electrophoretic distribution measurement is a powerful tool to study slime coating phenomenon in a complex fine particle flotation system."

Jan 1, 2002

By Norman O. Lotter, Dominic Fragomeni, Jorge Oliveira, Dee J. Bradshaw, Rebecca Monnapula

"The role of mixed collectors in enhancing the metallurgical performance of sulphide flotation processes was reviewed in 2008, and later published as an integrated theory by Lotter and Bradshaw, 2009. The theory proposed that xanthates, dithiophosphates and dithiocarbamates could be synergistically combined in an optimal formula to deliver improved grade and recovery. The approach uses a five-step structure, viz.1. A mineralogical study of the ore to be treated, identifying and quantifying the economic minerals (with hosting and association) and gangue species present.2. Selection of candidate collectors from this mineralogical information and from the known pulp conditions of that operation (e.g. Eh, pH).3. Design and execution of a factorial experiment to estimate and test the main effects and interactions, and to model the response surface for an optimum formulation [Box et al., 1978].4. Use of a High-Confidence Flotation Test platform in the factorial to reduce overall errors and allow for clearer observations [Lotter, 1995; Lotter and Fragomeni, 2010].5. Statistical design of a plant scale trial to measure and validate the gains [Napier-Munn, 1995; Lotter et al., 2009]. Eland Platinum, which was commissioned in November 2007, appointed a team to apply this theory to formulate an optimized mixed collector suite for use in the operation. The West Pit ore (UG2 - Normal ore) was sampled at site and brought to Xstrata Process Support, Sudbury, Canada, for mineralogical and metallurgical testing in 2008. Microprobe and QEMSCAN measurement characterized the type, grain size and textural association of the discrete Platinum Group Minerals (PGM) present. From the mineralogical data, it was clear that a mixture of dithiocarbamate and two xanthates would be a likely reagent suite selection. A factorially designed set of High-Confidence Flotation Tests studying these was performed, concluding that an optimal suite using certain amounts of these collectors was a viable formulation that would advance the grade and recovery performance at Eland above the standard PIBX by approximately 2.13% 4E PGE. The plant trial, which used a form of the replicated block design after Napier-Munn, 1995, and Lotter et al., 2009, exceeded this estimate with an overall PGE recovery gain of 2.48% (absolute basis) and a concentrate grade gain of 26.4 g/t PGE (absolute basis), as well as reducing chrome in concentrate from 2.04 to 1.62% (absolute basis). These gains proved to be statistically significant using the analysis of variance method, and have validated the theory."

Jan 1, 2011

By J. Gurland

A method of measuring the degree of contact between grains of 1 phase in multiphase alloys is derived. It is shown that the number and the areas of contacts between grains can be determined by metallographic analysis. Relations between the area of contact, the dihedral angle, and the mean free path of spherical grains are developed. It is often desirable to interpret the mechanical behavior of alloys in terms of structural features observed under the microscope. A quantitative description of microstructures of multi-phase alloys requires consideration of geometrical and topological factors such as the amount, size, and shape of grains and the continuity of the constituent phases. The number and dimensions of grains may be metallographically determined by applying the methods described by Smith and Guttman1 and by Fullman2 in their papers on the measurement of particle size and internal boundaries in opaque bodies. The present work intends to show that the same methods can be used to evaluate some of the parameters of phase continuity; namely, contiguity, number of contacts, and areas of contact of grains of 1 phase. Application of these concepts may be found in such problems as the calculation of electrical conductivity of 2-phase alloys, or the evaluation of the length of fracture path through grains of a brittle phase more or less dispersed in a matrix. I. DEFINITION The following definitions and derivations are based on 2-phase alloys, of which the units of the microstructure are grains. Contiguity is defined as the average fraction of surface area shared by 1 grain of a phase with all neighboring grains of the same phase. In a 2-phase alloy of constituents A and B, the contiguity of phase B is given by: where Cb is the contiguity of phase B aBß is the average area of contact between a grain of phase B and adjacent grains of phase B, aAB is the average area of contact between a grain of phase B and adjacent grains of phase A. The contiguity is a measure of the average degree of contact between grains of phase B in the 2-phase mixture. The ratio varies from 0 to 1 as the distribution of phase B changes from a completely dispersed to a fully agglomerated structure. Smith and Guttman1 have shown that the relative areas of 2 kinds of interfaces in a volume are directly proportional to the number of interfaces of each type intersected by a random line. The lines can be drawn on metallographically prepared surfaces as long as these are random sections through the sample. The contiguity ratio of phase B then becomes: Cb = 2NBB/NAB + 2N BB [2] where: NBB is the number of interfaces between grains of phase B intersected per unit length of random line. Nab is the number of interfaces between grains of phase B and grains of phase A intersected per unit length of random line. The factor 2 arises in Eq. [2] because each interface B-B is associated with 2 grains of B-phase, whereas the interface A-B involves only 1 grain of B-phase. The calculations of contiguity do not require any assumption as to volume fraction, particle size, or particle shape. Fullman2 gives an expression for the determination of the mean free path between particles. The mean free path PB between grains of phase A, i.e., through grains or agglomerates of phase B, may be found from the relationship: PB =2fB/NAB [3] where fB is the volume fraction of phase B. The calculation of the mean free path is independent of grain shape and grain size distribution. The calculation of the number of contacts and of contact area requires assumptions of grain shape, grain size, and contact shape. In the case of uni-

Jan 1, 1959

By Arturo Ressi di Cervia

From the times when men in lacustrine environments drove wooden piles into the mud to elevate their dwellings, until the beginning of the twentieth century builders reacted to the conditions found in the location of their proposed structures by attempting to distribute their loads in ways that could be supported by the foundation's soils; or, if those were unsuitable, by moving the structure, whenever possible. While many major structures were built on stable ground (the pyramids were founded on rock), others were built on [ ]

Jan 1, 2000