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By Luis Hoyos-Reyes, Jesus Gonzalez-Trejo, Adriana Cervantes-Clemente, Marco Gutierrez-Villegas, Manuel Palomar-Pardave, Cesar Real-Ramirez

Recent improvements on Peirce-Smith Converters (PSC) have combined numerical and physical simulations. However, most of the physical simulations have been carried out in cold-water models with only one tuyere. Several authors have proved that 2D numerical simulations do not reproduce the hydrodynamic behavior observed in physical simulations. On the other hand, most of the 3D numerical models have used a PSC thin slice with only one tuyere, but symmetric boundary conditions on the virtual walls have been imposed in order to reproduce the behavior of the whole converter. Therefore, there is no coincidence with the rigid walls of the physical models. The aim of this work is to quantify the effect of the virtual walls boundary conditions of a PSC thin slice and to determine the minimum number of tuyeres to characterize the fluid flow behavior of the entire converter.

Jan 1, 2009

By J. H. E. Jeffes, K. T. Jacob

The activity coefficients of oxygen in liquid Pb-Sn alloys have been measured between 550 and 1100°C by use of solid oxide galvanic cells: Pt, Ni-NiO | Zr02 Solid electrolyte | O (Pb + Sn), Cermet, Pt; and Pt, Fe-FeO | Zr02 Solid electrolyte | 0(Pb + Sn), Cermet, Pt. Alcock and Richardson's quasi-chemical equation, with the coordination number of atoms set to 2, is found to predict successfully the activity coefficients of oxygen in these alloys. The relative partial molar enthalpy and entropy of oxygen at 1 atom per cent in the alloys have been calculated from the variation of the activity coefficient with temperature. The addition of Sn to an unsaturated solution of O in Pb is shown to decrease significantly both the partial molar enthalpy and entropy of O. As the measurements were restricted to a narrow range between 750 and 1100°C in Pb-rich alloys, however, the pronounced variation of the partial molar enthalpy of O with temperature at constant alloy composition predicted by the quasi-chemical model could not be verified.

Dec 1, 1971

By R. Karl Zipf, Francois E. Heuze

Stress analysis programs such as MULSIM/NL, LAMODEL, MinSim 2000, and EXAMINETAB are used in the mining industry to analyze stresses and displacements in coal mines, platinum mines, gold reefs, and tabular-type deposits. These relatively simple numerical models can efficiently simulate yielding and failure of a rock mass near a mine opening and subsequent stress transfer. The main input parameters for these models are a family of nonlinear stress-strain curves for the in-seam material. For many applications of these models, such as in coal mining, extensive field measurements and observations exist from which to estimate these stress-strain curves and calibrate the numerical models; however, such measurements are lacking for other types of mines. A three-step method is presented to determine nonlinear stress-strain curves for boundary-element (BE) programs used in many mining applications. The method requires a suite of laboratory-scale strength tests at various confining pressures. Note that this analysis uses laboratory-measured strength and modulus properties of alluvium. The dependency of the mechanical properties of alluvium on scale has not been established, although more tests are being planned. However, it is believed that the relative comparisons performed are valuable regardless of scale effects. First, the FLAC2D computer program is used to model the laboratory tests and determine cohesion (c) and friction angle () for a Mohr-Coulomb material model. Second, another FLAC2D model uses the c and values to calculate vertical stress and strain around a single opening in the rock mass. This model calculates the stress-strain path of points at various distances from the opening boundary. Finally, based on these stress-strain paths, the stress-strain curves needed for a BE analysis are derived. This three-step method was demonstrated in a large, flat-lying underground test facility in very weak rock. The BE analyses agreed well with observations of failure at the test facility and provided a basis for evaluating the behavior of alternative layouts.

By Ernest Davis

WATER power, until developed, produces nothing, but when harnessed it continues to produce, it might be said, indefinitely. Hence the importance of developing all feasible water powers. British Columbia, like the western states of America, is subject to variable meteorological conditions which cause most streams to be erratic in their flow. The wet season, usually commencing in October and continuing to March or April, together with the melting of the snows during the early summer, produces a heavy run-off which diminishes considerably during the later s1.1,mmer months, with the result that storage is essential on practically every stream in order to regulate the flow to obtain a discharge which will meet the requirements of the load of the markets the power is to serve. Storage sites of sufficient capacity to equate the flows are not always present and it follows that, where such a deficiency exists, the difference must usually be met by burning fuel in steam plants. Fortunately, there are within the Province deposits of high-grade coal, suitable for the operation of such auxiliary steam plants. One of the strongest reasons for the development of water powers is the conservation of fuel. All use of coal or oil depletes resources that can never be renewed. Every water power developed means a saving in fuel and, even if at first it does not possess an over-powering financial advantage, it must become of ever increasing value as fuel resources become depleted. However, sight must not be lost of the inter-relation which should exist between the two methods of generating electrical energy, as each makes an admirable supplement to the? other with respect to suitability for carrying different types of load. In general, it can be said that the fixed charges of a water power development are usually high in relation to the operation costs, while those of fuel power plants are usually the reverse, so it is sometimes possible to combine the two methods of generation for the more efficient production of energy.

Jan 1, 1942

By A. T. Iannacchione

Recent fatal injuries occurring during pillar retreat coal mining call for better identification of the hazards and recognition of risks. Ground control hazards associated with room-and-pillar retreat mining tend to intensify with depth, requiring extra precautions in the form of additional controls. In many locations these activities are further complicated by local complexities often associated with unique or novel circumstances, such as over-mining or under-mining. One technique recently studied by NIOSH, Major Hazard Risk Assessment (MHRA), may help mine operators to mitigate the risks associated with pillar recovery operations. The approach was trialed at two underground coal mines in southern West Virginia that are currently practicing pillar recovery. The first step in the MHRA process involved reviewing the segments or parts of the pillar extraction mining system and identifying associated hazards and threats to the operation. Some of the high risk hazards at these two sites included: ? Rock fall during pillar extraction covers equipment and injury ? occurs during recovery operations, Rock fall above the roof bolt horizon, potentially injuring ? workers and/or requiring recovery action,Rib fall under deep cover, potentially injuring workers, and; ? Strata instabilities associated with subsidence of the ? interburden due to simultaneously mining two seams in close vertical proximity to one another. The mines? risk assessment teams then considered each threat individually in order to systematically identify potential unwanted events. The top unwanted events were examined individually using structured risk analysis tools. The output from the process includes a list of priority existing controls for monitoring and auditing, and a second list of potential new controls. These controls consisted of: ? Examples of best practices, ? Enhanced communication, ? Implementing standard operating procedures (SOP), ? Protocols for emergency response actions, ? Effective layouts, ? Efficient monitoring, and; ? Successful audits. This paper documents the process as it unfolded at the two mines, and analyzes the strengths and weaknesses of the MHRA technique as it applies to pillar recovery operations. This work was part of a larger NIOSH research project. NIOSH was responsible for: 1) facilitating the risk assessment process known as Major Hazard Risk Assessment (MHRA), 2) documenting the risk assessment process, and 3) providing mine management with a written draft summary of the risk assessment process. The results of the risk assessment represent the thoughts and opinions of the individual risk assessment teams and should in no way be construed as an endorsement of the risk assessment output by NIOSH or the University of Pittsburgh.

Jan 1, 2009

Obtaining correct assays for gold determinations relies on the correct methods being chosen and the assayer being made aware of the mineralogy of the sample and its general origin. Usually when a geologist or metallurgist obtains "incorrect" gold assays the problem can be traced to poor communication between the geologist or metallurgist and the assayer.

Jan 1, 1986

By John N. Cunningham

Despite the wide use of micropiles for rehabilitating and retrofitting existing structures, little is known regarding the load-transfer distribution of grouted micropiles in various soil deposits. The rehabilitation of a concrete-frame warehouse in Portland, Oregon, required provisions for the seismic restraint of a new shear wall; the installation of two micropiles was specified to meet project requirements. The micropiles were uncased, 19-m (63-ft) long, 200-mm (8-in) nominal diameter, and reinforced full-length with a 64-mm (No. 20) diameter hardened steel threadbar. Due to space limitations, a sacrificial, instrumented micropile was installed near the two production piles to verify design assumptions. This paper describes the geologic setting of the project within the unsaturated Missoula Flood deposits, instrumentation, load-displacement behavior, load transfer, and Beta-coefficients for the sacrificial micropile.

Jan 1, 2011

By Michael E. Berndt

Asbestos first became an issue to Minnesota?s iron industry when it was revealed that mineral fibers similar to those in Reserve Mining?s tailings were being found in drinking water for several communities that used Lake Superior as their primary water source. This discovery turned what had largely been an environmental court battle into a case concerning public health. The courts listened to much conflicting and uncertain scientific testimony on the size and distribution of the mineral fibers and on the potential health effects imposed by them. In April 1974, the plant was ordered to shut down by a federal judge but the company quickly appealed the decision. The appeals court granted a stay and ultimately ruled that the plant?s closure could not be justified based on the unknown health effects of the mineral fibers since the consequences of such an action would have immediate and severe social and economic impacts. The plant was allowed to continue operation, but ordered to abate emissions to air around the plant and to switch to a land-based tailings disposal system. Much of the scientific uncertainty and public concern over mineral fibers in Minnesota?s taconite industry remain today. ©2007 Elsevier Inc. All rights reserved. Keywords: Minnesota; Iron ore; Taconite; Asbestos; Amphibole; Reserve Mining; Tailings; Mesabi Iron Range

Jan 1, 2007

By I. R. Taylor

Vanadium has recently joined the growing list of mineral commodities being exploited by surface mining methods. Union Carbide Corp. controls several vanadium deposits in central Arkansas near the city of Hot Springs in Garland County and the community of Magnet in Hot Spring County (Fig. 1). Two open pit mines, located approximately five miles southeast of the city of Hot Springs in the Wilson Springs area, have been developed for production during the past two years. Adjacent to the mining area the company has recently completed a 1,600-ton-per-day (tpd) processing plant to treat the Wilson Springs and Magnet Cove ores (Fig. 2). Although this operation constitutes the largest vanadium mining project in the United States, the open pit mines are of moderate size. A number of small to medium-sized surface mines will be developed during the life of the operation. This chapter describes the methods and practices used to bring these recently discovered vanadium deposits into production. PRELIMINARY EXPLORATION The vanadium potential of the deposits near Hot Springs and Magnet Cove was first investigated by Union Carbide Corp. in 1960. These areas have long been of interest for their varied mineral content and were previously explored by government agencies and private interests for titanium, columbium, molybdenum, and uranium. No sustained operations resulted from this early work, although the rutile deposits of Magnet Cove were worked intermittently between 1911 and 1944.l Significant vanadium concentrations were reported in a U.S. Bureau of Mines publication describing the investigation of a titanium prospect

Jan 1, 1969

By J. G. Pippenger

The mining industry has been Australia?s major economic driver over the past decade, contributing 8% to Australia?s Gross Domestic Product and 26% of Australian Stock Exchange Market capitalisation. Australia is the world's leading exporter in coal, iron ore, alumina, lead and zinc; and second largest in gold and uranium. While driving the economy, this resource boom has also created a demand for professional and operating talent that has far outstripped the capacity of Australia?s 21 million residents. I moved to Australia some 10 years ago and have not looked back. This unique island continent with its mix of Indigenous and diverse immigrants ? many still proud of their convict ancestry ? has offered life long memories both professionally and personally.

Jan 1, 2011

"AQUILA Mining Systems Ltd. is a Canadian company that designs and develops monitoring, control and navigation systems for the surface and underground mining industries. In 1992, AQUILA Mining Systems began the development of technology for monitoring, controlling and positioning mobile mining equipment. In 1993, AQUILA completed its first field test with GPS receivers onboard ablasthole drill, and thus demonstrated the viability and strategic relevance of this technology in surface mining. Since then, AQUILA has installed GPS-based technology on drills and shovels in several Canadian mines. This paper will review the development of these systems and discussthe benefits the mining industry could realise through their production implementation."

Jan 1, 1997

By E. H. Dix

The work of Merical and other investigators indicates that the phenomenon of age-hardening in alloys of the duralumin type is primarily dependent upon the variation in the solubility of copper with temperature. In addition to copper, however, these alloys contain small amounts of magnesium, silicon, manganese and iron, which may affect the age-hardening either directly or indirectly. The effect of these elements on the solubility of copper and on the manner in which this solubility varies with the temperature is of considerable interest, therefore. The effect of magnesium is of especial interest because apparently it exerts a marked effect on the natural or room-temperature aging of alloys of the type described.2 A series of investigations3 has been in progress in the research laboratories of the Aluminum Company of America to determine the functions * Metallurgist, Aluminum Research Laboratories. f Metallurgical Division, Aluminum Research Laboratories. Formerly with Metallurgical Division, Aluminum Research Laboratories. 1 P. D. Merica, It. G. Waltenberg and H. Scott: Heat Treatment of Duralumin. U. S. Bur. Stds. Sn. Paper 347 (1910). 2 M. Gayler: Constitution and Age-Hardening of Alloys of Aluminum with Copper, Magnesium, and Silicon in the Solid State. Jnl. Inst. Met. (1922) 28, 213. W. Fraenkel: Vergutbare Aluminiumlegiengen. Ztsch. Melallkunde. (1920) 12, 427. E. H. Dix, Jr.: Note on the Microstructure of Aluminum-Iron Alloys of High Purity. Proc. Amer. Soc. Test. Mat. (1925) 26, Pt. 2, 120. E. H. Dix, Jr. and H. H. Richardson: Equilibrium Relations in Aluminum-copper Alloys of High Purity. Trans. A. I. M. E. (1926) 73, 560. E. H. Dix, Jr. and W. D. Keith: Equilibrium Relations in Aluminum-manganese Alloys of High Purity. Proc. Inst. Met. Div., A. I. M. E. (1927) 315. E. H. Dix, Jr. and A. C. Heath, Jr.: Equilibrium Relations in Aluminum-silicon and Aluminum-iron-silicon Alloys of High Purity. Proc. Inst. Met. Div., A. I. M. E. (1928) 164. E. H. Dix, Jr. and F. Keller: Equilibrium Itelations in Aluminum-magnesium Alloys of High Purity. Proc. Inst. Met. Div., A. I. M. E. (1920) 351. E. H. Dix, Jr., F. Keller and R. W. Graham: Equilibrium Relations of Aluminum-magnesium Silicide Alloys of High Purity. Trans. A. I. M. E., Inst. Met. Div. (1931) 404. W. L. Fink and K. R. Van Horn: Constituents of Aluminum-iron-silicon Alloys. Trans. A. I. M. E., Inst. Met. Div. (1931) 383.

Jan 1, 1932

The Bureau of Mines has successfully used sulfur hexafluoride (SF6) as a tracer gas to measure mine air flows under conditions where conventional methods have failed. SF6 was employed experimentally to measure accurately recirculation of return into intake air caused by leakage through an old stoped area, to check for potential leakage from an adjacent mine, to trace 10,000 cfm of "lost" air from an intake airway, and to measure transit air time through uranium mines. It proved useful as a means of accurately measuring airflow volumes in airways of large cross section and very low flow velocity, and in determining the recirculation resulting from underground cooling plants.

Jan 1, 1974

Adhesion of Escherichia coli onto Oxide Minerals - Extended DLVO Theory and Flotation Behaviour

Sep 13, 2010

By Simpson JF, Murrie SJ

In determining new areas for slag disposal a foamed slag aggregate has been developed for use as a skid resistant material. The foaming of the slag does not rely on the use of water, but rather on the slag chemistry. Laboratory test results indicated that a product having good skid resistant properties has been prod- uced. A section of road is being assessed for performance of the aggregate in a surface dressing application under heavy load. The results from the test section after seven months have shown that the foamed slag is suitable for this application. Further test sections are now being considered.

Jan 1, 1979

By Brock Wallis, Steve Davidow

The following text will present the concept of rock socketed drilled shafts used to support electrical substation structures, and discuss the cost and schedule risks that traditional design responses to unforeseen shallow rock can pose to a project. Design considerations will be detailed, including rock characterization, shear strength of drilled shafts, and modeling lateral resistance of the shaft and surrounding rock. The specific case of drilled shafts installed for heavily loaded structures at the Moxie Freedom Substation will provide an example of how close collaboration between the engineer and contractor to refine designs based on site-specific feedback can provide tangible benefits to the project. In this example, value engineered designs resulted in an approximate 40% reduction in shaft/concrete volume and a 60% reduction in total rock socket depth. PROJECT OVERVIEW The Moxie Freedom Project included the construction of a new 500 kV switchyard in Berwick, Pennsylvania. The foundation contractor was selected to install both small and large diameter drilled shaft foundations to support the structures within the switchyard. The small diameter shafts were utilized to support transformers, switches, bus supports and a static mast, while the large diameter shafts were used to support one 180-foot monopole and six H-Frame structures. CHALLENGES: ROCK SOCKETED DRILLED SHAFTS Available geotechnical data at the time of bid included limited borings and seismic refraction. The borings were not located at every structure, and the contractor and design engineer were left to interpret desktop studies and geophysics to determine the probable site-specific conditions at each foundation. The data suggested substantial variability in the quality and depth to bedrock across the project area, indicating significant risk of deep embedment into bedrock at all seven large diameter shaft locations. Rock socketed drilled shafts pose unique challenges for both designers and contractors, and the topic has become a focus of national foundation organizations. Traditional design models result in deeper and/or larger diameter shafts where rock is encountered. In the case where site-specific geotechnical conditions are not clearly understood and rock is encountered at shallow depths, this can lead to significant additional rock drilling, impacting overall project cost and schedule. Rock drilling can result in more than ten times the cost of soil drilling and can easily take in excess of ten times longer to excavate.

Jan 1, 2018

By J. T. Norton, N. J. Grant, A. M. Gervais

An investigation of the creep deformation of coarse grained specimens of high purity aluminum in the temperature range 800' to 1150°F, permitted the formulation of a theory explaining the formation of kink bands. The X-ray Laue back-reflection technique was used in conjunction with metallographic studies to determine the crystallographic elements involved in kinking and to measure the rotations of the bands. THAT metals deform by the formation of kink bands was first shown by Orowan1 in 1942. He manually compressed cadmium single-crystal wires, the basal planes of which were parallel to the wire axis and to the direction of compression. He found that kink bands formed quite suddenly. Similar experiments were performed by Hess and Barrett2 on zinc with a hydraulic testing machine to permit slower more careful compression. They observed that kink bands formed progressively with increasing compression. Recently Washburn and Parker3 observed the formation of kink bands in zinc single-crystal specimens during tension creep experiments. Each of these authors observed the formation of kink bands but did not make a complete analyses of the crystallographic relationships. In addition to these studies on hexagonal metals, extensive investigations of kink bands formed during deformation of aluminum in tension at room temperature have been reported. Two types of deformation bands have been observed during the deformation of aluminum at room temperature. These are: 1—kink bands: these exhibit a sharp curvature of the lattice along certain surfaces, and 2—bands formed by secondary slip along certain regions. As has already been shown by Honeycombe,4 it is important to point out the difference characterizing the two types of deformation bands. In the first case. for moderate deformation, only one system of slip planes normally is active; in the second case, however, two slip systems are active in the deformation bands. The latter have a rumpled surface because of the action of the two slip systems. In the present work only the first type of band was studied and to avoid any confusion the term kink band will be used exclusively in the discussion which follows. Honeycombe' observed that very narrow kink bands (width, 0.01 mm) formed along the (110) planes during the deformation of high purity aluminum at room temperature. He observed narrower ones in commercially pure aluminum and found also that their width decreased with decreasing temperatures. Chen and Mathewson5 reported the formation of kink bands during tensile testing of single crystals of high purity aluminum at room temperature and pointed out that some rotation occurred about a [211] direction. The influence of the bending moment on the formation of kink bands was illustrated by the experiments of Rohm and Kochendorferl0 who used a Polanyi apparatus to obtain pure shear during tensile testing of high purity aluminum single crystals. Under such conditions only one slip system was active and no kink bands were observed; consequently, no noticeable asterism was detected after deformation. The influence of the bending moment will be discussed later. Calnan8 gave a detailed account of the work performed on kink bands obtained during deformation of aluminum at room temperature. Because no explanation of the process of kink band formation in creep was given in the previous investigations and because some of the above observations are vital to the following discussion the brief review of the literature has been given. It is proposed in the present work to provide an explanation of kink band formation during creep deformation at elevated temperatures. Results and Discussion Kink bands were observed to form during tensile creep testing of high purity (99.995 pct) aluminum specimens, having a very large grain size, in the temperature range 800" to 1150°F. These observations were made in grains which occupied the whole cross section of the specimen. The specimens were originally round (diameter, 0.187 in.; gage length, 1 in.) and had parallel flats milled to permit easier metallographic and X-ray observations. The final

Jan 1, 1954

By Ihor A. Kunasz

Lithium minerals occur predominantly in pegmatites which contain mineral assemblages derived from the crystallization of postmagmatic fluids or from the metasomatic action by residual pegmatitic fluids. They have been the traditional sources of raw materials for ceramic and chemical industries. However, with the discovery of Searles Lake, brines became new sources of lithium. Indeed, the 1960s may well be referred to as the "brine decade" because several brine bodies of significant economic importance were discovered. In the United States, the brines of Clayton Valley, Nevada, presently exploited by Foote Mineral Co., and the Great Salt Lake of Utah, to be exploited by the Great Salt Lake Chemicals Corp., have been defined as major sources of lithium. Also a lithium-bearing brine has been discovered in Chile. Following the termination of the AEC purchase program in 1959, several companies such as Maywood Chemical Co., American Lithium Chemicals, and Quebec Lithium Corp. were forced to close down their operations. Nevertheless, with the development of new applications in glass ceramics, air conditioning systems, synthetic rubber, and metallurgy (aluminum potlines), the lithium industry grew steadily, and with the potential application of lithium metal in batteries and nuclear reactors, a healthy growth can be foreseen. New products and new applications are likely to stimulate exploration for expanded reserves as well as the search for new sources from which lithium could be extracted economically. Geochemistry of Lithium Lithium is the third element in the periodic table. It is the lightest of all the metals, having an atomic weight of 6.938. Its ionic radius is 0.60A and its charge is + 1. The geochemistry of lithium has been extensively studied and has been summarized by Rankama and Sahama (1950), Goldschmidt (1937), and Hortsman (1957). The distribution of lithium in igneous rocks is controlled by its size and its charge, and by the (MgO+FeO)/Li2O ratio. In the early stages of crystallization of a magma, that ratio is very large. Consequently, both magnesium and iron are removed by ferromagnesian minerals in preference to lithium which is then concentrated in the residual magma. This results in an enrichment of lithium in silicic rocks and pegmatites (Strock, 1936). Pegmatites are coarse-grained igneous rocks formed by the crystallization of postmagmatic fluids. Minerals within pegmatites may also form by metasomatism (Jahns. 1955). Genetically, the pegmatites are associated kith neigh- boring intrusives. Mineralogically, granitic pegmatites contain feldspar, quartz, and mica as the main constituents and a variety of exotic elements such as lithium, beryllium, tantalum, tin, and cesium, which may or may not occur in economically significant concentrations. Detailed studies by numerous investigators (Cameron et al., 1949, 1954; Hanley et al., 1950; Jahns, 1953, 1955; Page et al., 1953) indicate that pegmatites often exhibit an internal zonal arrangement, with each zone containing a specific suite of minerals. The lithium minerals are usually found in the intermediate zones, and although as many as 13 zones have been recognized by Cameron, a complete zonal arrangement is rarely found. Zoning of pegmatite bodies has also been observed on a regional basis. The regionally zoned pegmatite sequences exhibit mineral assemblages and complexity according to their respective distance from the granitic bodies to which they are genetically related (Mulligan, 1965). Lithium is also found in small proportions in a variety of rocks. The average lithium

Jan 1, 1975

By C. H. Bowen

NDUSTRY needs a generally applicable means of defining average grain size and grain size distribution. Students of sediments hade explored this field, employing methods that might also prove useful in engineering problems. Before attempting to solve specific problems it is well to review the derivation of commonly used grade scales and the reasons for their selection. This aspect of the problem seems largely to have been lost, and a review of basic factors may suggest causes for failures in using size analysis data. Three facts are implicit in selection of a grade scale: 1) Most particulate mixtures are continuous distributions of sizes, and any grade scale that may be employed is an arbitrary means of visualizing that distribution. 2) For purely descriptive purposes, any grade scale, regardless of the rationality of the class intervals, will be satisfactory if it is accepted by a sufficient number of workers. 3) For analytical purposes, class intervals must be small enough to define the continuous distribution accurately. Further, where statistical studies are involved, a fixed relationship should exist between classes or grades. An argument in favor of geometrically related size grades lies in the fact that most particulate mixtures contain such a wide range of sizes that use of an arithmetic diameter scale is practically impossible. Udden, who recognized this fact in 1898,' proposed one of the first grade scales based on a regular geometrical interval. Udden used 1 mm as his basic diameter and a ratio of 2 (or 1/2) between classes. In 1922 Wentworth2 re-examined Udden's grade scale, retaining the same class interval and basic diameter, but extending the scale in both directions and renaming the classes. In 1930 (Ref. 3, p. 82) the American Society of Testing Materials proposed what is now known as the U.S. Standard fine sieve series, also based on the 1 mm diam, with a v2 ratio between sieves. This, then, is a one fourth Udden-Wentworth series in the sizes below the 4 mesh sieve. The U.S. Standard coarse sieve departs from the 1 mm base and uses inches; hence it is not a direct continuation of the fine series. The U.S. Standard series would thus seem to possess all the attributes of a good grade scale, which it is. It has a large number of classes (sieves). in fact too many for practical use in its entirety. This v2 subdivision of the Wentworth grades has led to the common use of two v2 sieve series, the half-Wentworth and the engineers' series. Geologists and sedimentologists favor the half Wentworth, or 18, 25, 35, 45 sieves, etc., whereas the engineers, preferring round numbers, utilize the other half of the U.S. Standard grade scale in the 16, 20, 30, 40 sieves, etc. The fixed geometrical ratio between classes is an advantage in statistical analysis, but the unequal classes cause some complications in calculations. This is especially true when moment measures are used. It was to simplify these calculations that Krumbein in 1934 devised the phi scale. Phi is defined as being equal to —log2 of the diameter in millimeters. Selection of logarithms to the base 2 relate the phi scale directly to the Wentworth grade scale in such a manner that the whole or fractional diameter values 2, 1, 1/2, 1/4 mm, etc., become rational whole numbers, —1, 0,1, 2, etc. Since this is an arithmetic rather than geometric series, calculations are facilitated. When the logarithm is multiplied by —1 the phi values below 1 mm become positive, those coarser than 1 mm negative. Because of its relationship to the Wentworth grade scale (and in turn to the U.S. Standard fine sieve series) it is not necessary to use the transformation equation to calculate the phi value for each individual sieve; this can be done graphically as shown in Fig. 1. It should be noted that this graph may be extended in either direction to include the range of sizes most commonly used by the individual worker. Application to Statistical Analysis Any attempt at systematically relating size analysis data to properties involves a statistical study whether it is recognized as such or not. Since this is true it would seem more logical to use measures and devices related to the general body of statistical theory. Several methods are available for studying particulate mixtures. One of the most commonly employed, and also the most often misused, is the histogram or block diagram. If its limitations are recognized and provided for, the histogram is a very useful tool. According to conventional practice, the bars of equal width are plotted and the values noted in terms of diameters, when in point of fact, log diameter is implied by such notation. Further, the histogram is sensitive to choice of grade scale and size of class interval, either of which may color the result. Grade scales whose classes are not related by fixed intervals are particularly difficult. Another basic weakness of the histogram is that it pictures a continuous distribution as a series of discrete grades.

Jan 1, 1957

A case history is presented where a variance was permitted by the court to change a 500 foot limit to 250 feet for blasting overburden at a surface coal mine in the proximity of a historic structure.

Jan 1, 1991