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By Kurt Oakes, Paul Worsey, Braden Lusk, Tony Brasier, Scott Crabtree, Randy Wheeler

Theoretical description of destructive wave interference and the use of sacrifi cial holes is included and is supported by data collected at Springfi eld Underground. Finally, the process by which the reduction in vibration was achieved in practice is described. Results are discussed for several production blasts taking place over a one year period.

Jan 1, 2008

By Wilson D, Kirkland J

Compressed air energy storage (CAES) uses low cost off-peak energy to compress air and pump it into pressurised underground storage. Expanding the air through a modified form of gas turbine generates electrical energy when required. While generating power, a CAES station consumes approximately one-third of the gas required for the equivalent installed capacity of a conventional gas turbine. Air can be stored in underground rock caverns, caverns in salt domes, or in aquifers. Existing CAES power stations use caverns mined out of salt domes. Aquifer storage for CAES has been proposed, but not yet implemented. The groundwater in the aquifer would be displaced during air injection and when required the air would be extracted using the natural hydro-static pressure. Victoria has no salt domes, but has aquifers onshore in the Gippsland Basin with geological dome structures of suitable depth, discovery pressure, porosity, permeability and caprock for CAES development. Field tests costing several million dollars would be required to prove the suitability. The most suitable aquifer is near Seaspray, where several dome structures exist. The aquifer, comprising of coarse sands capped by coal and mudstone, is some 600 metres deep with a hydrostatic pressure of 6.3 MPa. Computer simulation of injection and extraction of air from the aquifer under various combinations of horizontal and vertical wells, permeability and tubing head pressures indicated the largest aquifer structure had the capacity to sustain a 300 MW station. A well field comprising of 24 directionally driven wells with a horizontal exposure to the aquifer would achieve the air flow rates required. Using plant similar to that recently installed at McIntosh Alabama USA, would mean high capital costs compared to standard gas turbine plant. However, a review of modem gas turbines indicated that they could be easily and economically adaptated to CAES duty. Adapting a 120 MW gas turbine would give 344 MW output. A separate air compression plant would be used. Economic evaluations indicate that, for gas prices above $1.95 per GJ, a 344 MW CAES plant is more economic for intermediate/reserve load duty than simple cycle gas turbines.

Jan 1, 1992

By Brendan Demich, Brendan Macdonald, Timothy J. Orr, Jason Navoyski, Jennica L. Bellanca, William J. Helfrich

Recent advances in computing, rendering, and display technologies have generated increased accessibility for virtual reality (VR). VR allows the creation of dynamic, high-fidelity environments to simulate dangerous situations, test conditions, and visualize concepts. Consequently, numerous products have been developed, but many of these are limited in scope. Therefore, the National Institute for Occupational Safety and Health researchers developed a VR framework, called VR Mine, to rapidly create an underground mine for human data collection, simulation, visualization, and training. This paper describes the features of VR Mine using self-escape and proximity detection as case studies. Features include mine generation, simulated networks, proximity detection systems, and the integration and visualization of real-time ventilation models.

By Peter J. Nicholson

A new method of constructing retaining walls, in-situ, prior to excavation has been developed. This "Vertical Earth Reinforcement Technique" VERT, has been demonstrated at a full scale test wall at the National Geotechnical Experimentation Site at Texas A&M University. This 10 meter high wall, was constructed of elements of soil mixing in an array that forced composite behavior between the soil mixed elements and the in-situ soils. Inclinometers and extensometers were used to verify the performance of the wall. The construction and results of the testing are presented.

Jan 1, 1998

Chelopech Mining EAD and Best Available Techniques for Management of Waste Rock in Mining Activities

Sep 13, 2010

By Isaac Girón

Dado que se descubrieron grandes depósitos de fosfatos de Bayovar en Piura, se anunció la creación de la reserva subterránea de salmueras, donde sobresale el potasio, la sal común y el magnesio. Posteriormente, se relacionó la explotación de los fosfatos a la recuperación de sal y KCL. y la presencia de salmueras se convirtió en la única reserva de potasio del pais. En ese sentido, el presente texto describe la importancia del magnesio en dichas salmueras en tanto permite recuperar el magnesio a partir del proceso de evaporación y concentración. De forma que es posible la obtención de magnesio por el tratamiento térmico de los amargos y así fabricar el fosfato dicálcico mediante el proceso convencional, sin necesidad de usar el agua de mar.

Sep 13, 2001

By T. Celik, B. Genc, C. Musingwini

"Mine planning software continues to be an important factor when it comes to the development of the South African mining industry. To contribute to this development, a new methodology to define and measure mine planning software utilization in the South African coal mining sector within an evolving data-set framework was developed. An initial data-set showing the mine planning software providers, their corresponding software solutions, as well as the software capabilities and information on the number of licences was collected and compiled in 2012 in an online database for software utilized in the South African mining industry. Details of the database development and implementation were published in the Journal of the Southern African Institute of Mining and Metallurgy in 2013. In 2014 the data-set was updated with additional and new information.In this paper, using the 2012 and 2014 time-stamps, a methodology for estimating the software utilization is developed. In this methodology, three variables: commodity, functionality, and time factor are used to define and measure the software utilization in order to ultimately inform decision making strategies for software utilization. Utilization in the coal sector was measured according to six different functionalities, namely Geological Data Management, Geological Modelling and Resource Estimation, Design and Layout, Scheduling, Financial Valuation and Optimization. The methodology is useful for stakeholders reviewing existing software combinations or intending to purchase new software in the near future and wanting to estimate the comparative attractiveness of a certain software package. These stakeholders include mining companies, consulting companies, educational institutions, and software providers. The work presented in this paper is part of a PhD research study in the School of Mining Engineering at the University of the Witwatersrand."

Jan 1, 2016

By Jean-Marc Simard, Vincent Jourdain, Denis W. Roy

"Seven lithologic units, informally characterized, were recognized in the vicinity of the Montauban orebody. The first five lie in stratigraphic order. From structural bottom to structural top these are: (1) grey composite gneiss; (2) dark grey quartz-biotite gneiss; (3) quartz-biotite-garnet gneiss hosting several calcareous, aluminous and magnesian members and gold mineralization; (4) light grey quartz-muscovite-(sericite)-biotite gneiss; and (5) metabasafts. The last two intrude the sequence: (6) amphibolite dykes and (7) pegmatite veins. The orebody lies on the inverted limb of an overturned synform verging to the west with the metabasafts marking the core of the fold. As the foliation is folded, this fold is attributed to deformation ""D2""; deformation ""DI"" being responsible for the formation of the foliation. A late brittle deformation developed shear zones with probable strike-slip motions. The refined stratigraphy and the identification of the structural position of the orebody provide new tools for regional interpretation and prospecting.RESUMESept unités lithologiques ont été définies informeffement à proximité du gisement de Montauban. Les cinq premieres reposent en ordre stratigraphique; ce sont de la base au sommet structural: (1) le ""gneiss mixte gris""; (2) le gneiss gris forcé à quartz biotite; (3) le gneiss a quartz-biotite-grenat comprenant plusieurs membres calcareux, alumineux et magnésiens ainsi que la minéralisation aurifère; (4) le gneiss gris clair à quartz muscovite- Isericitel-biotite; et (5) les métabasaltes. Les deux autres unites sont intrusives dans la sequence: (6) les dykes d ‘amphibolite et (7) les veines de pegmatite. Le gisement se sitlie sur le flanc inverse d'un synforme déverse vers I' ouest dont les métabasaltes occuperaient le cœur. Comm e la foliation est plissée, ce pli est considère appartenir d la deformation ""D2""; la deformat ion ""DI"" etant responsable de la formation de lafoliation. Une deformation cassante tardive se traduit par des zones de cisaillement, d rejet apparemment directionnel. Cette stratigraphie plus précisé et l'indentification de la position structurale du gisement fournissent de nouveaux omits de prospection et d'interprétation regionalé."

Jan 1, 1987

The oxidation of sulphide minerals in aqueous suspension is discussed from several viewpoints. Limitations of our present knowledge are pointed out, and several points where further information would be of special interest are mentioned.Firstly, some properties of minerals and their effect on oxidation are discussed. Properties of different species, such as crystal structure, lattice bonding, and "metallic" properties are mentioned, and then the effect of variation within a given species is discussed. The effect of physical factors, especially particle size, is also considered. Other variables discussed include the importance of solution composition, and its effect on the nature and rate of reaction, and the use of various oxidising agents. Some factors concerned with the whole system, such as temperature, pulp density and stirring rate are then considered.Finally, the nature of various oxidation products is discussed with reference to the kinetics of reaction and the nature of the rate limiting step. It is suggested that more attention should be paid to electrochemical explanations of the reaction mechanism.INTRODUCTIONKnowledge of the factors governing the rate of oxidation of sulphide minerals in aqueous suspension is a prerequisite for the effective control of many ore treatment operations. Rapid oxidation of sulphides is usually desired during the leaching of sulphide ores and concentrates, but in the cyanidation of gold ores, or in the leaching of uranium ores, any oxidation of sulphides may be regarded as an undesirable side reaction. Knowledge of many of the factors involved is also of interest in connection with the oxidation of sulphides in flotation circuits and in natural ore forming processes.Systems for which some reasonably quantitative data have been published are listed in Table 1. Qualitative...

Jan 1, 1961

By D Vickers, N C. Fowke

The reduction of geological risk for planning of high production longwall faces is essential. Geological and geophysical techniques applied at Huntly West Mine before 1989 were unable to reduce the geological risk to an acceptable level. The success of a trial long-hole directional drilling programme at Huntly West Mine (Fowke et al, 1989) has encouraged the Coal Corporation of New Zealand to use the technology long-term, for seam definition. Initial drilling in 1989 completed a total of 3543 metres, with the longest borehole length being 369 metres (limited by number of rods available). A major re-interpretation of seam structure resulted from the drilling, which was able to fill in seam details between surface exploration boreholes. The undulating thick seam conditions at the mine require a refinement of drilling strategies used overseas. Long-hole directional drilling also displays potential for inseam gas drainage. Gas flows of the order of 1000 L/min were initially indicated in individual boreholes. Other gas parameters of the seam have been studied by Beamish et al (1991), and highlight the significance of the natural gas resource in the Huntly Coalfield.   The continued development of drilling technology will be of major benefit sustainable development, particularly in policy.

Jan 1, 1991

By Thomas M. Barczak

With the development of the shield support, the primary requirement for successful ground control in longwall mining is to provide stable gate road and bleeder entries. Wood cribbing has been the dominant form of secondary support. However, the cost and limited availability of timber, along with the poor performance of softwood crib supports, has forced western U.S. mines to explore the utilization of other support systems. The recent success of cable bolts has engendered much interest from western operators. Several innovative freestanding support systems have been developed recently including: (1) "The Can"' support by Burrell Mining Products International, Inc., (2) Hercules and Link-N-Lock wood cribs and Propsetter by Strata Products (USA) Inc., (3) Variable Yielding Crib and Power Crib supports by Mountainland Support Systems, (4) the Confined Core Crib developed by Southern Utah Fuels Corporation; and (5) the MEGA prop by MBK Hydraulik. This paper assesses design considerations and compares the performance and application of these alternative secondary support systems.

Jan 1, 1996

By Jim Baumann

Deposited millions of years ago in irregular paleokarstic channels, Jamaica’s extensive bauxite deposits provide good quality ore for alumina production and subsequent aluminum smelting. Bauxite mining operations are critical to the Jamaican economy. It accounts for a large percentage of Jamaica’s export earnings. Bauxite production in Jamaica accounts for about 10% of the world’s output each year. Bauxite deposits in Jamaica lie close to the surface. They can be extracted using standard surface mining techniques. The deposits occur in scattered pockets across the country’s rugged landscape. So it was necessary for two of the country’s major mining and refining operations to implement cost effective methods for the acquisition and management of bauxite reserves and surface ownership distribution rights.

Jan 1, 2002

By Takashi Sasaoka

About 200 M tons of coal were imported into Japan in 2007 and Indonesia was its second largest exporter, accounting for about 30 M tons (12% of the total imported coal). Indonesia produced about 200 M tons of coal, about 75% of which was exported in 2007. As the Indonesian government has decided on an energy policy wherein 33% of the country?s primary energy demand will be met by coal by the year 2025, the domestic demand for coal has increased dramatically in recent years. Over 99% of the coal produced in Indonesia comes from surface mines. However, the conditions of surface mines are worsening each year: the stripping ratio is increasing, approaching the economic ratio, and the infrastructure for coal from inland mining areas is insufficient for such intense mining operations. To meet the demand for coal in Indonesia and the rest of the world, underground mines have to be developed. However, mining engineers and/or miners in Indonesia do not have a lot of experiences, expertise and know-how concerning the plans and operations of an underground coal mine. In addition, the industry faces a lot of problems which include poor conditions such as a steep coal seam, groundwater problem, stability of highwall, etc. Under these situations, a mine targeted in this research attempts to develop a new underground mine from an open-cut highwall because the stripping ratio in the surface mining area has almost reached the limitation of economic value. This paper discusses the possible development of a new underground coal mine from an open-cut highwall by means of field observation and numerical analysis.

Jan 1, 2009

By M. A. Trevits, A. Ozmet, A. C. Smith, J. B. Walsh, T. P. Mucho

Improvements in remote fire fighting technology are needed to reduce miner exposure to the dangers of fires and possibly save the lives of those who may become trapped. The National Institute for Occupational Safety and Health, in cooperation with U.S. Foam Technologies, Inc1., conducted a series of experiments at the NIOSH Lake Lynn Experimental Mine to study the stability, transport, control and fire extinguishing effectiveness of nitrogen-enhanced foam technology. This paper presents a description of the mine test configurations and experimental results

By H. Ipek

Industrial grinding machines used in the mineral processing industries are mostly of the tumbling mill type. These mills exist in various types: ball, rod, pebble, autogenous, and semi-autogenous. Balls and rods are traditionally media shapes used in the tumbling mills. In resent years, as an alternative to balls, grinding charges with various shapes are being used. Cylpebs are slightly tapered cylindrical grinding charges with length equaling diameter, and all the edges being radiused. Cylpebs of equal diameter and length have 50% greater surface area and 45% greater weight than balls of the same material. In addition, they have 9% higher bulk density than steel balls, or 12% higher bulk density than cast balls. An important advantage of cylpebs over balls is that cylpebs produce narrower granulometric distribution due to their shapes. However, some discrepancies were found in the literature regarding the milling performance of cylpebs in comparison with balls (Chi, 2004). In recent studies, Chi (2004) has provided detailed information on cylpebs and has compared these to balls in relation to media mass, size distribution, surface area, and input specific energy. Ipek (2006) has investigated the effects of cylpebs and balls with equal mass and surface area on the breakage rate of quartz, using cylpebs and balls separately. Similarly, Lameck and Moys (2006) have investigated the effects of balls and worn balls on breakage rate of material using worn balls as grinding environment. However, no study has attempted to investigate the effects of grinding environment other than balls on the brekage distribution. As indicated by Prasher (1987), the breakage distribution function is independent of the following variables in ball mills: hold-up (Mika et al., 1967; Kelsall et al. 1969), mill speed and ball load (Herbst and Fuerstenau, 1972), media load and ball density (Kelsall et al., 1973), mill diameter (Malghan and Fuerstenau, 1976), and powder charge (Shoji et al. 1980). The aim of the present paper is to compare the effects of cylpebs and balls on the breakage distribution function of quartz with respect to same mass and same surface area. BACKGROUND Comminution as a rate process is called kinetic approach. Studies on the kinetic approach are reviewed by Oner (2001). Oner states that grinding kinetics are based on studies by Kolmogorov in 1941 and that Robert (1950) is the first to suggest this approach. Later, Melzak, Loeveday, and Reid have improved the grinding kinetics equation; and, Austin and Lynch have conducted two basic studies on the analytical solutions of these equations. Considering the results of studies comparing the size reduction mechanisms, it has been accepted that breakage constitutes of two operations. These two basic operations, first defined by Epstein (1948), are those of selection of material for breakage and the distribution of breakage material to particle sizes smaller than the initial size (Lynch, 1977). Epstein defined the two operations as: ? Pn(y), the probability of breakage of a particle size in the nth step of the breakage process. ? F(x,y), the cumulative distributions by weight of particles of size x<y arising from the breakage of a unit mass of a size y. Probability of breakage is called a selection or a breakage-rate function (Si). Characteristics size distribution after breakage is called a breakage distribution or appearance function (Bi,j). Due to the difficulties in representing particle size distributions mathematically and constantly, the batch equation based on particle size fraction is suggested. Thus, as is the case in breakage distribution and specific rate of breakage, the breakage parameters were defined by batch grinding experiments conducted in laboratories (Oner, 2001). When effective breakage occurs in the mill, the breakage of material with single feed size fraction usually fits first order grinding kinetics and the specific rate of breakage values can be calculated through the slope of semi-log plot. The values of the breakage distributions are deduced from the size distributions at short grinding times where there is mainly size 1 material breaking and only small amount of smaller sizes to rebreak (Austin et. al., 1984). B values can be calculated by using BII. [ ] where j is the top size of the charge, Pi(t) is the cumulative percent undersize of i th size interval at the short grinding time which gives no more than about 30% broken out of the top size interval. Cumulative primary breakage distribution, Bi,j, is also defined in an empirical form by [ ] where xi is the top size and Bi,j is the weight fraction of primary breakage products. The parameters F, ? and ß define the size distribution of the material being ground. On plotting size versus Bi,j on log scale, the slope of the lower portion of the curve gives the value of ?, the slope of the upper portion of the curve gives the value of ß, and F is the intercept as in Fig.1. [ ]

Jan 1, 2009

The Stawell Goldfield, the westernmost of the main Victorian fields, has produced over a million and a quarter ounces of gold from one and three-quarter million tons of ore. The lodes are quartz reefs and sulphide bodies occurring in sediments of lower Ordovician or upper Cambrian age. The lodes are confined to a relatively narrow suite of weak rocks lying between stronger ones above and below and there is a definite relationship between fold structure, pitch and strength of folding and ore.LOCATION HISTORY AND PAST PRODUCTIONThe town of Stawell, situated 150 miles north-westerly from Melbourne on the main railway and road to Adelaide, is the most westerly of the main gold areas of Victoria. Alluvial gold was found at Pleasant Creek (now Stawell West) in 1853 and the usual &quot;rush&quot; followed. Numerous alluvial leads, some surface, others buried under up to 100 ft. of Tertiary sediments were worked. The alluvial gold was soon exhausted, but in 1857 gold-bearing reefs were found on the slopes of a prominent ridge on the northern edgeof the present town. Early reef mining was by small working parties mining to shallow depths only and treating their ore at public crushing plants. Some of the early returns were very high grade. The next stage was the amalgamation of claims and the formation of companies, with their own treatment plants. This stage continued till the last mine closed in 1921. These companies had, by present standards, small holdings and far too many shafts were sunk, resulting in less efficient prospecting and operation.Since 1921 there have been one or two small scale attempts to revive mining but without success. Of recent years Gold...

Jan 1, 1960

By Johnson T, Huynh D

The State Electricity Commission of Victoria is conducting a program of research and development into alternatives to the use of conventional boilers for the generation of electricity from brown coal. The objectives of the program are to reduce the cost of electricity generation and also to improve the thermal efficiency so as to reduce the emission of greenhouse gases and other pollutants. The program presently includes the following four technologies: Hydro-thermal Drying, Direct Coal Fired Gas Turbine, Integrated Gasification Combined Cycle, and Steam Fluidised Bed Drying. The Hydro-thermal Drying process produces a combustible coal-water-slurry fuel which is suitable for use in a coal fired gas turbine. The coal fired gas turbine has the potential to produce electricity at a lower cost than conventional power stations and when combined with a steam cycle, it will also use significantly less coal. The Integrated Gasification Combined Cycle process gasifies the coal, cleans the gas, and then bums it in a gas turbine/combined cycle. This process is being developed in Europe and the USA in order to meet their stringent emission regulations. It offers Victoria cleaner more efficient and cheaper electricity.

Jan 1, 1992

By G. Miller

The design of solvent extraction plants has been generally based on the assumption of steady operating conditions in both the settler and the mixers. Recent experience with both large and small plants has shown that this is not the case. Mixer transients include start up aqueous locking and partial phase separation in secondary mixers. Both of these lead to either reduced plant capacity or overflow of upstream mixers. Analysis of the hydraulic pressure profiles has generated new design methods to eliminate the effects of the partial or complete phase separation. Further, changes to the method of specification and selection of both primary and secondary mixers have been made to eliminate the onset of partial separation during operation. Observation of settler operation has shown that it is also a dynamic process, even under ‘steady state’ conditions. Four different transient phenomena have been identified that lead to internal circulating flows, poor disengagement of fine secondary haze, and erratic and high entrainment levels in the discharges. A first approximation analysis has shown that there are significant pressure differentials within settlers and these change along the length and with phase separation rates. A technique to control the effects of these transients has been developed which allows plant performance to be improved beyond ‘standard’ expectations. The design and selection of the settler internals is described.

Jan 1, 2001

By R. Katzenbach, M. Vogler, U. Adamietz

Abstract The design of deep excavation pits in rock mass is dependent as well on the mechanical properties of the rock mass as for example the orientation and the type of discontinuities like bedding planes, joints and fissures, the length of the discontinuities (persistence), the grade of weathering, the strength of rock mass, and the shear strength in the discontinuities, etc., and also on the respective boundary conditions specific for the project, and here especially the geometrical boundary conditions. The basic mutual influences and interactions between these boundary conditions are explained and exemplary presented at an excavation pit with a depth of 18,5 m, situated at a slope with a surface near groundwater table. Résumé La planification des excavations profondes dépend aussi bien de la qualité mécanique du roc, par exemple la location de la texture de la surface de moindre résistance, le degré de rupture, le degré de décomposition, la dureté du roc et la résistance limitée au cisaillement de la texture de la surface de moindre résistance que des conditions limitées spécifiques pour le projet, ici en particulier des conditions limitées géométriques. Les influences et interactions essentielles et mutuelles entre les conditions limitées isolées seront expliquées et présentées à l’aide d’une excavation 18,5 m de profondeur, située sur une pente où le niveau des eaux souterraines est près de la surface. Kurzfassung Die Planung tiefer Baugruben im Fels hängt sowohl von den mechanischen Eigenschaften des Fels wie z.B. der räumlichen Lage des Trennflächengefüges, dem Durchtrennungsgrad, dem Verwitterungsgrad, der Gesteinsfestigkeit sowie der Scherfestigkeit des Trennflächengefüges als auch von den projektspezifischen Randbedingungen hier insbesondere von den geometrischen Randbedingungen ab. Die wesentlichen gegenseitigen Einflüsse und Interaktionen zwischen den einzelnen Randbedingungen werden aufgezeigt und an einer 18,5 m tiefen Baugrube in Hanglage mit oberflächennahem Grundwasser vorgestellt.

Jan 1, 2003

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