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By J. B. Hiskey, X. H. Jiang

The extraction of gold from chloride solutions by ion exchange is examined. It is shown that at initial gold concentrations between 1 - 5 ppm, 20 g/l C1- and pH 5, the kinetics of loading on weak base resins are slightly slower than those observed with activated charcoal. Equilibrium loading of auric chloride varies considerably as a function of pH from one resin to another. For all of the resins studied, nearly complete gold extraction was achieved between pH 2 and pH 6.5. Sodium hypochlorite was found to exhibit a slight effect on the equilibrium loading of gold chloride.

Jan 1, 1990

By Wen Tao Liu, Tong Tian, Fu Sheng Niu, Xiu Man Liang

In order to address the difficulty of accurate segmentation of froth images of different sizes, a method of froth image segmentation based on highlight correction and parameter adaptation is proposed. First, a machine vision system on a single-cell flotation machine is built to collect froth images. Homomorphic filtering is used to improve the uneven brightness and shadow of the images. Fuzzy c-means (FCM) clustering is then utilized to classify similar highlights that belong to the same froth. After Otsu threshold segmentation, a parameter-adaptive morphological operation is used to extract the marker points and edge bands and correct the froth edges in the original image. Finally, the modified image is filtered by morphological reconstruction, and the highlight mark is used as the local minimum point for watershed segmentation. Three sizes of froth images are segmented in comparative experiments. The results show that the proposed method is suitable for the segmentation of froth images of different sizes. The position of the extracted segmentation line is close to reality, with average over-segmentation and under-segmentation rates for froth images of 2.6% and 6.8%, respectively. The froth image segmentation performance is stronger than that of the other methods examined.

By V. G. Grechanyuk

The paper presents the mechanical properties of Cu-Mo composite materials depending on the molybdenum content. The influence of structural defects on the mechanical-physical properties of the condensates at stretching testing as well as of the lamellar grain dimensions upon the mechanical properties of Cu-Mo composite materials is also presented.

Jan 1, 2008

By Amila Sandaruwan Ratnayake, T. Dilmi. U. Wijewardhana, H. C. S. Subasinghe

The value addition potential of ilmenite was examined using several characterization techniques. Raw ilmenite is composed of 93.65 wt.% of FeOTiO2, 3.55 wt.% of SiO2, 1.22 wt.% of Al2O3, and the remainder being other minor oxides. Ilmenite and powdered carbonized coconut shells were mixed in the weight ratio of 4:1. A separate fraction of the same mixture was added with powdered seashells in the weight ratio of 4:1:0.5. Six fractions of each mixture were distinctly milled from 1 to 6 h in a planetary ball mill. XRD spectra (broadened and diminished reflections of ilmenite) and FTIR observations (Ti―O―Cbonding) of milled samples indicate the possible incorporation of carbon into the ilmenite structure. Any clues of an occurrence of new rutile peaks were not observed in XRD spectra of milled samples. Consequently, the carbothermic reduction has not been initiated during mechanical activation. In this case, samples powdered for 6 h in a mill were isothermally annealed for 2 h under normal airflow at temperatures of 800 °C, 1000 °C, and 1200 °C, respectively. According to the X-ray diffractograms, the annealing temperatures of 1000 °C and 1200 °C exhibited almost similar trends with rutile (R), pseudobrookite (PB) and elemental iron (F), and a very few ilmenite (I) peaks. Consequently, 6 h of milling and 1000 °C annealing were concluded as the optimum conditions for the carbothermic reduction. Moreover, this study indicated seashells as a potential rate raiser for the carbothermic reduction of ilmenite at 800 °C. Therefore, this process is applicable to upgrade ilmenite into a mixture of synthetic rutile and elemental iron.

Mar 29, 2021

By M. Superfesky, P. Michael

Introduction The US Office of Surface Mining (OSM) is proposing changes to the Code of Federal Regulations in the interest of minimizing the adverse effects of excess-spoil-fill construction on the “prevailing hydrologic balance, fish, wildlife and other environmental values” (70 FR 35112). The proposed changes will require: (1) minimization the amount of excess spoil generated at a mine site; (2) minimization of the size of the fills constructed; (3) consideration of alternative configurations for disposal; and (4) development of a disposal plan that would minimize adverse impacts to the environment.1 To achieve those objectives, mining companies operating in steep-sloped Appalachia will likely build excess spoil fills (also called valley fills) that toe out at higher elevations in the hollows (i.e. to prevent or limit burial of streams). Consequently, the slopes of fill foundations will generally be steeper. Whereas the authors of this paper support these measures to protect the hydrologic balance and general environment, we wish to point out that placement of fills on steeper foundations can negatively impact the stability of the fills if proper care is not taken during their construction. It is important to note that in addition to impairing human safety, valley fill instability can negatively impact streams, the riparian habitat etc., and thus defeat the very purpose of the spoil minimization measures proposed. We do not, however, propose additional regulatory requirements pertaining to valley fill stability. Rather, we intend to emphasize the importance of engineering requirements already on the books, especially as they apply to the predominant type of valley fill constructed: the durable rock fill. We believe that the practice of restricting valley fills, to higher elevations in the watershed leaves less room for error in the design and construction of stable structures. This paper gives a quick review of the nature of excess spoil generation; methods and requirements of excess spoil fill construction, and the to-date stability record of the fills. The interest in excess spoil minimization and how it affects valley fill construction is also discussed. Most importantly, we will review long-standing issues pertaining to proper design and construction measures with respect to durable rock fills and discuss how they will become more critical as spoil minimization is practiced.

Jan 1, 2007

By Bradley V. Johnson, Robert J. Timko, Edward D. Thimons

Water-jet-assisted cutting involves the use of a mechanical cutting bit in combination with a high-pressure water jet directed just in front of the bit tip. Such a jet can offer benefits in terms of improved cutting, reduced dust and fines, and improved bit wear. The Bureau of Mines, through a contract with the British National Coal Board, has researched the use of water-jet-assisted cutting on roadheaders. After several engineering design problems were overcome, this program led to the successful underground testing of these roadheaders. Today, more than 60 water-jet-assisted roadheaders are in operation around the world and numerous others are on order. This paper details the evolution of these machines and the benefits to be gained by their use.

Jan 1, 1987

By Jens Classen, Martino Gatti

"GENERAL PROJECT DATAThe Sparvo Tunnel is part of the “Variante di Valico” project, a new 65km (40mi) highway link between Bologna and Florence, designed to renew the existing A1 route which connects Bologna and Florence. It is composed of 2 x 2,5km (1,55mi) twin tunnels excavated inside a complex geological context, characterized by the presence of a series of surface landslides and methane gas.The inclination is 2,6 % and the minimum radius is 1.400m (4.600ft). The two tunnel tubes were excavated by a 15,6m (51ft) diameter EPB-TBM from summer 2011 to summer 2013. The internal diameter of the concrete lining is 13,6m (44,5ft), made up of precast concrete segments 2m (6,5ft) long and 70cm (28”) thick, being the largest and heaviest segments ever produced. Excavation went smooth apart from initial problems concerning clogging problems and a main bearing damage of the TBM, which are discussed in a further paper during the congress. No structural damage was observed until the end of the TBM drives.SITE OBSERVATIONS DURING THE POST-EXCAVATION PHASEThe first evidence of the stress state of the segmental lining appeared on November 20, 2013 inside the northern tube (1st drive). Ring No. 884 showed obvious signs of overstress, resulting in spalling and crushing of the concrete, and the subsequent bending of the reinforcement, as visible in figure 1.At this time the tunnel invert was already partially backfilled, and construction traffic was running through the tunnel. First safety measures included closing of the tunnel, and initial measurements of the displacements."

Jan 1, 2016

By Thomas C. Shapiro

Introduction In recent years - even months - the number of articles on computers has increased rapidly. One can hardly pick up a newspaper or magazine without seeing a computer-related article. The article usually explains how the computer will change our lives. Many of us have some concern about the nature and type of change. For most of us, though, the problem is lack of information and understanding about how computers work. In other words, how do we make cost-effective decisions about computers? This three-part series will explain, simply, what a microcomputer is, how it works, and how to decide if you need one. This first article will define terms and briefly discuss areas where computerization might be economic. The second article will discuss geology and mining applications. The third article will discuss plant, administrative, and geotechnical areas as well as the future of software development in the minerals industry. Terms and Concepts All computers have input and output devices and a central processing unit (CPU). Information - instructions and data - is communicated to the computer by means of input devices. These instructions to the computer are converted into language that the computer understands. This causes the instructions to be carried out in the CPU. The result of these operations is translated back into language that we understand. This information is then sent to output devices such as printers and video display tubes. Traditionally, peripherals were devices separate from the main-frame (the CPU and memory) and were used to input, output, and store information or instructions. Today, peripherals perform the same functions though they may be housed in the same cabinet as the CPU and memory. Historically, peripherals included all input and output devices not part of the mainframe. Input devices include keyboards, magnetic tape, and card readers. Tapes and disks are input as well as output devices. Output devices are printers, CRTs (Cathode Ray Tubes), and any mass storage device capable of storing data when directed to do so by the computer or the program. In fact, any mass storage device that can give the computer data when requested is an input device. Mass storage devices include floppy disks (thin, round sheets of plastic covered by metal particles), and hard disks. The latter are thicker and more densely coated with metal particles. This allows much more information to be stored. Another type of mass storage is magnetic tape. Its type and size varies widely. Processing and Storage Any computer understanding must include how instructions and data are processed and stored. Information is stored as a positive or a negative field known as a "bit." There are eight bits in a byte. The bits can be represented as either a one or a zero. Thus the code for a byte representing the numeral one is 00110001. The byte representing the letter A is 01000001. These codes are from the American Standard Code for Information Interchange (ASCII). ASCII defines the standard set of characters including alpha, numeric, and special characters. The computer's memory has allocated locations where instructions as well as incoming information can be stored. All information and instructions are stored as binary numbers bit by bit - zeros and ones. The amount of data that can be stored is referred to as either thousands or millions of bits or bytes. The letter "K" is used to designate one thousand units. The letter "M" is used to mean one millon units (one meg). Disks Thus, a 113-mm (5 1/4-in.) floppy disk - double sided and double density (DSDD) - contains 320,000 bytes (characters) or 320K. This is about 164 double-spaced, type-

Jan 2, 1984

By Y. K. Yen, J. D. Miller, C. L. Lin

The image-based On-line Particle Size Analyzer (OPSA)system has been developed at the University of Utah to measure particle size distributions under plant conditions where overlapped and segregated particles are being transported on a moving belt conveyor. Evaluation of the OPSA system at several plant sites has been completed. The results show a consistent agreement between the particle size distributions obtained from the OPSA system and those obtained from laboratory screen analysis of belt samples. These results and the stable performance of the OPSA system during the field tests suggest that continuous quality control of crushed products is possible using the OPSA system.

Jan 1, 1999

Arizona copper mines produced nearly 67% of the nation?s copper in 2000, according to a report released by the Arizona Mining Association (AMA). This was a slightly larger share than in 2000 despite large reductions by one major copper producer and production cutbacks at several other facilities. In 1999, Arizona mines produced 64% of the nation?s copper. The report was prepared by economist George F. Leaming of the Western Economic Analysis Center in Marana, AZ. It also showed the copper industry had a $4.6-billion impact on the Arizona economy in 2000, a 26%decline from 1999. This is the lowest financial impact since 1973 and less than half the record reached in 1981of $9.6 billion. The decline is primarily due to a sustained low copper price and a slow-down in the US economy. The mining industry?s impact included combined direct and indirect contributions of $1.283 billion in personal income for Arizona residents, the equivalent of 43,000jobs. More than 5,000 of those jobs were in state and local government and more than 18,000 were in trade and ser-vice businesses. The copper industry directly employed fewer than 8,000 people statewide in 2000. This was down about 23% from 1999.

Jan 1, 2001

By V. B. Menon, L. D. Michaels, M. E. Mullins

Introduction The cleaning of coal to remove sulfur and inorganic impurities has, in recent years, become an essential operation in any coal utilization process. US coals, on average, contain about 3% total sulfur, of which more than 60% is generally inorganic or pyritic sulfur. Existing technologies such as heavy media cycloning, selective agglomeration, and electrostatic separation have the potential for removing about 80% of the pyrite from coal (Khoury, 1981). In view of the large volumes of coal being used today, there exists a need for the development of new processes to further improve the separation of pyrite from coal. Colloidal particles in suspension possess surface charges that are related to the chemical composition of the particles. In aqueous suspensions, the surface charge is a function of pH. For coal-pyrite mixtures, it is possible, by an adjustment of the pH (also a function of polar molecules), to reach a state where the charge on coal is very close to zero, but the charge on pyrite is still substantial. The introduction of collector particles with a charge opposite that of the pyrite should then result in the selective flocculation of pyrite and collec¬tor. These flocculates should settle out much faster than coal and could be removed from the bottom of the settling column. This note discusses our preliminary observations of the effect of clay-based collector particles, especially bentonite, on the settling behavior of coal and pyrite. These experiments were conducted with a view to developing a new electrokinetic flocculation process for separation of coal-pyrite mixtures. Experimental The objective of the experiments was to determine the effects of clay-based additives on the settling rates of clean coal, pyrite, and coal-pyrite mixtures. Illinois Colchester (No. 2) coal was obtained after processing in an existing coal cleaning facility. This coal was reported to contain less than 0.3% pyritic sulfur, which was in the form of a fine powder with an average particle size of 5µm. Pyrite (of average particle size 5 µm) was also obtained from the same facility and reportedly contained less than 0.1% coal. The zeta potentials of coal and pyrite in water were measured as a function of pH using a zetameter. The pH was adjusted by adding sodium hydroxide or hydrochloric acid to the suspensions. Sedimentation experiments were conducted in 50-mL glass cylinders, and settling rates were measured by noting the height of clear liquid above the settling front as a function of time. Settling behavior was also charted by periodically taking photographs of the system. The following systems were investigated: •a slurry consisting of 2.5 g of clean Illinois Colchester coal in 50 mL of water of pH 6.0, with and without the addition of 0.5 g of bentonite (Fisher, purified grade) ; • a slurry consisting of 2.5 g of pyrite in 50 mL water of pH 6.0, with and without the addition of 0.5 g of bentonite ; and • a slurry consisting of a mixture of 1.25 g clean coal and 1.25 g pyrite in 50 mL water of pH 6.0, with and without the addition of 0.5 g of bentonite. In addition, experiments were conducted with kaolinite (Bath, South Carolina) and alumina (Fisher, purified grade) as collector materials to verify the observed effects. Results and discussion Figure 1 shows the zeta potential values for the Illinois coal and pyrite as a function of pH. The zeta potentials of coal and pyrite decrease with increasing pH, changing from an initially positive value at low pH to a negative value at high pH. The point of zero charge (PZC) for the coal is at a pH of 6.2, while the PZC for pyrite occurs at a pH of 10.3.

Jan 1, 1988

By Doug Harding

The Niagara Tunnel Project (NTP) is a 10.4 km (6.5 mi) long, 14.4 m (47.5 ft)bored tunnel that will run under the City of Niagara Falls from the Upper Niagara River to the Sir Adam Beck Power Station. The completed project will enhance the capacity of the Sir Adam Beck Power Station by adding 500 m3 (17,657 ft3) of water per second through the tunnel. The paper describes the project in which the world’s largest hard rock TBM at14.4 m (47.5 ft) in diameter is being used to excavate the tunnel. Features of the project include the use of a High Performance (HP) Main Beam TBM, state-of-the-art ground support and tunnel logistics systems. A continuous conveyor is used for muck transport from the TBM to the disposal area. The paper will also discuss the optimization of the TBM system as the tunnel advances through the varying geology. In June 2004 the Ontario Government announced that Ontario Power Generation(OPG) had been given approval to proceed with the third tunnel under the city of Niagara Falls—the first two tunnels were constructed in the 1950s using drill and blast techniques. The third tunnel, appropriately named The Niagara Tunnel Project (NTP), consists of a 10.4 km (6.5 mi) long TBM-bored, concrete-lined tunnel with a finished diameter of 12.5 m (41.1 ft). In August 2005, OPG announced the selection of Strabag AG of Austria, one of the largest construction companies in Europe, as the contractor to build the NTP Project at a price of CAN $600 million. In September 2005, Strabag A.G. selected The Robbins Company of Solon, Ohio to design, manufacture and deliver a new 14.4 m (47.5 ft) diameter High Performance state-of-the-art Main Beam Hard Rock TBM to be used in the excavation of the tunnel. In order to meet the aggressive construction schedule as requested by OPG/Strabag, the TBM needed to be supplied as “ready to bore” within a 12 month period after the contract was awarded to Robbins.

Jan 1, 2007

By Christian Wawrzyniak

An analysis method for modeling compensation grouting based on the finite element method is presented. By this method the design parameters of compensation grouting, grouting pressure and grouting volume, can be evaluated. Also the subsidence of a building due to tunnel driving as well as the lifting of the building by compensation grouting can be simulated. The stress changes in the tunnel lining and in the foundation of the building are computed as well. The application of the analysis method is demonstrated on two examples for compensation grouting in combination with construction of tunnels.

By C. Treworgy, C. Chenoworth

Geologic and technical factors such as coal seam thickness, stripping ratios, roof conditions, partings, faults, and size and geometry of the reserve block greatly impact the availability of Illinois coal for mining. Residential and commercial developments also restrict access to coal reserves in some areas. Despite the collective effects of these factors, large blocks of bituminous coal reserves suitable for efficient, low-cost underground mining remain available in Illinois.

Feb 24, 1997

Introduction The Homestake Mining Co. has always been big on gold. After 108 years in the business, the company and its principal product are almost synonymous. The relationship continues. On Sept. 28, 1985, Homestake held formal dedication ceremonies for its newest gold mine - McLaughlin. The McLaughlin open-pit operation is located in northern California, some 113 km (70 miles) northeast of San Francisco. It lies near the boundaries of three counties - Napa, Yolo, and Lake - and a portion of its facilities are located in each. McLaughlin was originally the site of the Manhattan mercury mine that produced nearly 80,000 flasks of the quicksilver from the 1860s to 1978. At the September dedication, Homestake renamed the mine in honor of the late Donald H. McLaughlin. McLaughlin was with Homestake for nearly 60 years. He rose from exploration geologist to his ultimate positions of chief executive officer, director, chairman of the board of directors, chairman emeritus, and chairman of the executive committee. The discovery of the McLaughlin deposit occurred in 1978, the last year of operation for the Manhattan mine. Homestake geologists used a newly developed model and found surface gold at the mine site. That same year, Homestake signed an agreement with the property owner and began a two-and-a-half year exploration program. An initial discovery announcement of 31.1 t (1 million oz) of gold was made in 1980. In 1981, this was revised to 93.3 t (3 million oz), or 18 Mt (20 million st) of ore grading 5.2 g/t (0.152 oz per st). Expected mine life is 20 years. Construction began in September 1983, following the issuance of stage one permits. Start-up of operations took place in early 1985 and the first gold-silver dore bar was poured on March 4. Since then, more than 540 kt (600,000 st) of ore has been milled, producing about 1.6 t (50,000 oz) of gold. Of special interest at McLaughlin is the use of three autoclaves for gold extraction. According to Homestake, this is a first. The autoclaves are designed for a 90% gold recovery rate. Early results have proven yields at this rate and higher. Geology The McLaughlin deposit is about 1.5 km (5000 ft) long. It occurs as a wedge-shape, narrowing to a verti-

Jan 1, 1986

By Paul H. Johnson

Resource Engineering and Development, Inc. is desigining and building a portable 150 to 225 tpd, flotation-cyanide leach plant with unitized, skid-mounted components. This plant design, with its portability, low capital investment, and high recovery of silver and gold from many partially oxidized ores, is well suited to treat many small, highgrade deposits, old waste dumps, and old mill tailing piles. A description is given of flotation and/or cyanide leach tests run on 18 partially oxidized, newly mined ores; waste dump materials; placer slimes; and old mill tailings.

Jan 1, 1981

By R. W. Chappell, M. W. Hills, R. L. Olsen

A stochastic approach was developed and applied to the Butte, Montana Hillside abandoned mining site for modeling stormwater runoff and subsequent receiving stream loadings. This approach enabled capture and quantification of the uncertainty associated with stormwater quality data and allowed the prediction of copper and zinc concentrations in the receiving stream caused by runoff from the Butte Hillside during storm events. Runoff flows and stormwater concentrations were input to the model as probability distribution functions. Monte Carlo simulation allowed prediction of expected instream concentrations in the form of cumulative distributions functions. The modeling results allowed evaluation of current best management practices (BMPs), targeting of future BMPs, and identification of key data gaps to fill during future sampling activities. This modeling approach is considered extendable to other active and inactive mining sites. Output from a model of this type is easily understood and can be used to communicate effective stormwater management to site regulators. Furthermore, application of this modeling approach will facilitate the development and implementation of a site-specific stormwater management plan and will optimize efforts to achieve standards for compliance with stormwater discharge permits.

Jan 1, 2002

By J. A. Dos Santos

High angle conveyor (HAC®) systems in open pit mining offer many advantages over the traditional, truck only, haulage systems, including: (1) superior energy efficiency, (2) less dependency on petroleum products, (3) less sensitivity to inflation, (4) less labor, (5) less excavation for the amount of ore recovered, and (6) less ramp construction and maintenance costs. Previous studies had revealed the technical and economic feasibility of high angle conveyors. This paper presents the Sandwich Belt HAC® as the vital link to optimization of in-pit conveying systems. HAC development to date is discussed, beginning with studies in 1979, to the first large scale prototype in 1983, to the first commercial unit in 1984, into "the latest commercial installations. Discussion continues with the HAC systems to suit the various open pit mining operations and the corresponding characteristics of the system components, particularly the high angle conveyor. The range of HAC systems from the low capacity (up to 1,814 t/h), low lift (10.7 to 36.6M), highly mobile to the moderate capacity (1,814 to 3,629 t/h), moderate lift (36.6 to 76.2M), intermittently mobile to the high capacity (greater than 3,629 t/h), high lift (greater than 76.2M), semi-mobile, are discussed along with some possible combinations of these.

Jan 1, 1989

By Charles H. Minott, Michael J. Markow, Robert D. Wyatt, Fred Moavenzadeh

The substantial investment in tunnels anticipated in the next twenty years has focused new attention on the economics of tunnel construction itself and on some costly problems associated with underground work: the uncertain geologic conditions, the performance and adaptability of men and equipment, and the need for quicker, more efficient excavation methods. There also exists a need to develop better ways of estimating tunnel construction. Inaccuracies in current bid estimates stem from a number of causes, among them (1) the effects of geologic conditions, which are not adequately known prior to construction, (2) the dependence of actual cost on the construction method used and on the interactions among the operations occurring underground, and (3) the reliability of tunneling equipment. Inability to estimate final costs for conventional tunneling more accurately has in turn caused difficulty in gauging the costs and benefits attributable to new tunneling technologies either under development or for which R&D programs are planned. ATTRIBUTES OF THE TUNNEL COST MODEL This paper presents a computer based Tunnel Cost Model (TCM) which quantitatively assesses the uncertainties inherent in underground work, and is detailed enough to aid in preparing estimates or bids. The model employs appropriate techniques of subjective (or "degree of belief") probability and computer simulation of tunnel construction operations to estimate distributions of total tunnel

Jan 1, 1974

By Thomas P. Meloy

Theoretical development of comminution models has come about in the last 10 years. These models assume that the material being broken is homogeneous and that the compression or energy wave is uniform throughout the specimen. Obviously, this is not the case because most comminuted materials are rocks with either many phases and/or definite grain size. The mathematical models deriving the size distribution of daughter fragments resulting from the comminution of brittle, single particles are of two schools. The first model, proposed by Gilvarry in 1961, was based on the concept of volume, surface, and edge flaw activation. The second, proposed by Meloy in 1960, was based on the concept that the crack density is a function of the energy in the comminution wave. The flaw theory has run into increasing theoretical problems and is now being abandoned. On the other hand, the crack density theory has been expanded and has successfully considered the case where there are inhomogeneities in the comminutive wave. However, the main constraint of a homogeneity in the solid being comminuted has hitherto never been overcome. In this paper, a very general derivation of the crack density model is made for inhomogeneous solids by replacing the assumption of homogeneity with an arbitrary function, P(y), which describes the susceptibility of the material to comminution as a function of position. The restraints on this function, P(y), are very broad and, hence, the derivation is extremely general. General use of the equation derived necessitates a detailed a priori knowledge of both the fracture process and of the physical properties of the material being fractured; this knowledge is expressed in open form as, P(y), the linear probability density that a plane of fracture intersects at point y on an arbitrarily oriented line segment of total length xo through the original particle. From these assumptions, a general expression for the cumulative mass distribution of particles resulting from fracture is then postulated. It is: [ ] where, B(x), is a cumulative mass of material finer than size x, r is the average number of crack,, (y), is defined above and xo is the initial particle size. It is shown that suitable assumptions reduce the expression to the theoretical results of Gaudin and Meloy and to special forms of the empirical equations of Rosin-Rammler, Gaudin and Schuhmann. Semi quantitative agreement is demonstrated by Grimshaw with experimental results of a very complex fracture of heterogeneous sandstone blocks. A need is expressed for more theoretical development of P(y), and a more extensive experimental study of both homogeneous and heterogeneous fracture. The full mathematical derivation is presented for the first time in this paper. The general implications of the equation and its application are also discussed.

Jan 1, 1968