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By G. Wang, L. R. Moore, Y. Xiong, A. Gorken

"Feldspar may represent 60% of the earth’s crust, but the mineral does not exist in a pure state. It is generally associated with quartz, iron containing minerals such as mica, and titanium containing minerals such as rutile. Feldspar itself can even exist in different lattices from those containing sodium to various divalent ions. As such, its beneficiation has become a process that is quite complicated, when compared to the beneficiation of other minerals. It is this complexity that has made feldspar beneficiation dependent on tailor made reagents to successfully yield the industry specified feldspar products. This paper reviews the mineralogical variations found from two feldspar mines and the development of collectors to specifically target a Fe+Ti concentration of < 0.05%, while maintaining a feldspar recovery greater than 90%.INTRODUCTION Feldspar is a class of aluminum silicates that represents the most abundant mineral on earth (Vidyadhar, 2002). This class of mineral can further be defined by the types or concentrations of cations present in the crystal lattice, MAlSi3O8 (M = K, orthoclase and microcline; M = Na, Albite; M = Ca, Anorthite) (Heyes, 2012). Feldspar is most commonly mined and processed for either the alumina used in glass making or for the alkalis used in ceramics. The alumina is known to improve product hardness, durability, and resistance to chemical corrosion. The alkalis act as flux, which means they not only lower the melting temperature of the mineral mixture, but also assist in connecting the other components present in ceramics. It was stated in 2009 that the world production of feldspar was in excess of 18.3 million tons produced, with the majority coming from China, Italy, and Turkey. Raw feldspar is typically found with quartz, iron containing minerals such as mica, titanium containing minerals such as rutile, and other feldspar minerals (Celik, 2001). Quartz is stated as having a negative effect on the melting point of the feldspar, whilst the iron and titanium based mineral contaminants are known to have negative effects on color and quality of the product produced; these mineral contaminants must therefore be separated prior to application (Barns, 1997 & Celik, 2001). Mineral flotation and magnetic separation are the most common means of feldspar beneficiation. However, conditions vary greatly from mineral contaminant to mineral contaminant (Table 1). Some literature suggests feldspar can be floated with an amine, but this generally yields lower than acceptable recoveries and often still requires the magnetic separation of iron based minerals to achieve the desired grade (Amarante, 1997 & Heyes, 2012). Feldspar flotation can be further improved with the addition of hydrofluoric acid (HF) as a silica depressant and feldspar surface modifier, but this still requires the removal of some of the other minerals first. Rutile can be floated with an anionic fatty acid collector at a pH range of 7-8 or with a petroleum sulfonate at a pH < 4 (Celik, 2001), while mica can be floated with a petroleum sulfonate or an amine collector at a pH of 3.5."

Jan 1, 2016

By William L. Carter

Through your presence here this morning and your membership in the Society of Mining Engineers, you have shown that you are interested in keeping abreast of the latest technology and mining procedures, want to be part of the continuing progress made by those in your profession, and are looking for ways to participate in expanding your professional and personal experiences and skills. All of these factors are part of your continuing education, the need for peer identification or recognition, and the desire to make a specific contribution to strengthening your profession. However, you may be here with or without your company support and financial backing, unless you are self-employed. Whether you are here for the above reasons, or for many others, your presence reflects a recognition of the importance of participating in the organizational structure of your profession.

Jan 1, 1981

By ANA E. BOHE, MICCO GEORGINA DE, GASTON G. FOUGA, JUAN P. GAVIRIA, FEDERICO J. POMIRO

To the best of our knowledge, this paper comprehensively summarizes a thorough study to determine the thermodynamic viability of the reactions between light rare earth oxides and chlorine with and without carbon. The kinetics and mechanisms of light rare earth oxide chlorination and carbochlorination reactions are analyzed and discussed according to results in the literature. Lanthanides between lanthanum (La) and gadolinium (Gd) are considered as light rare earth elements (LREEs) in agreement with previous literature and the results detailed in this review. Both laboratory- and industrial-scale light rare earth chlorinations and carbochlorinations, starting from oxides and ores, are reviewed.

By P. N. Psarropoulos

During many strong earthquakes in the past, a significant number of tailings dams failures has been recorded, leading in some cases to human life losses. However, over the last decades, seismic design of tailings dams has drawn much attention mainly due to the high environmental hazard. Although the stability of such geostructures under dynamic loading is mainly related to their liquefaction potential, there exist several technical issues that have not been adequately investigated. One of these issues is the impact of local site conditions on the dynamic earthquake stresses developed, and therefore on the inertial instability of these dams. Based on the models examined in the first part of the present study (Stability of Tailings Dams ? Part I: Static Loading), two-dimensional numerical simulations are performed in order to examine the effects of local site conditions in the dynamic response of tailings dams. Imposing dynamic loading via characteristic pulses and real earthquake records, the most commonly used types of construction methods are studied at their final stage. Emphasis is given on the special characteristics of the ground motion, while the material nonlinearity of both soil and tailings is taken into account by an equivalent-linear procedure. The results obtained indicate that local site conditions may have a significant impact on the seismic response of a tailings dam.

Jan 1, 2005

By M. A. Sochocky

Rod mills were developed, as a logical substitute for the rolls crusher when larger tonnages had to be handled, on a continuous basis. Today, with even larger tonnages to process, the trend is to install larger equipment, automate the plant and develop the highest availability possible, in order to cut costs. The rod mills, because of design limitations in size and speed 1&apos;2, are not able to meet these new requirements. The autogenous mill was a timely development and serves as an excellent alternative for ores that are suitable to this type of grinding. When ores are not amenable to autogenous grinding, selection of a flowsheet is dictated by liberation characteristics and unit operations to be used for mineral recovery.. The following alternatives are available: (a) Multiple rod mills, capable of drawing no more than 2000 HP each, followed by ball mills. (b) Gyradisc crusher followed by two stages of ball mill grinding.3 (c) Tertiary crushing followed by closed circuit single stage ball mills grinding to approximately -100 mesh, as in the copper industry. (d) Tertiary&apos; crushing followed by two-stage, ball milling. Each stage will operate in closed circuit with either screens or cyclones. It is this last alternative, particularly as it

Jan 1, 1972

By A. E. J. Gallagher

There are many influences which have a bearing on the economics of industrial minerals production. The purpose of this paper is to discuss briefly three factors which have economic significance in the production of these mineral commodities. The three items of discussion include 1) the nature and relative value of the industrial minerals group, 2) project planning, and 3) market analyses. General aspects of these factors are familiar to most of us. However, an attempt will be made to give some current details regarding each. Also, in reality, project planning and market studies are usually so closely associated that they will be discussed jointly, rather than separately. This will be done by way of examples which show how these two activities actually evolved for two industrial minerals projects.

Jan 1, 1984

By A. Podlesny, E. N. Rubinstein, J. J. Sammarco, B. Demich

Roof bolting typically follows the extraction of a commodity to help keep the roof from collapsing. During 2004 to 2013, roof bolter operators had the highest number of machinery-related injuries, accounting for 64.7 percent, at underground coal mines. This paper analyzes U.S. roof bolter fatal and nonfatal lost-time injury data at underground work locations for all commodities from 2004 through 2013 and determines risk indices for six roof bolting tasks. For fatal and nonfatal incidences combined, the roof bolting tasks in order of the highest to lowest risk index were bolting, handling of materials, setting the temporary roof support (TRS), drilling, tramming, and traversing. For fatalities, the roof bolting tasks in order of the highest to lowest risk index were handling of materials, setting the TRS, bolting, drilling, traversing, and tramming. Age was found to be a significant factor. Severity of injury, indicated by days lost, was found to increase with increasing age as well as with increasing experience, largely due to the confounding of age and experience. The operation of the roof bolting machine used in underground mining should be a research priority given the high frequency and severity of incidents. The results also suggest that temporal factors may exist, so additional research is warranted to better understand these factors and potentially develop interventions. This research provides a datadriven foundation from which future research can be conducted for safety interventions to reduce the frequency and severity of incidences involving the roof bolter activities of bolting, handling of materials, and setting the TRS.

Jan 1, 2016

By C. A. Young, R. G. Robins, E. J. Dahlgren

The formation of copper thio-complexes in sulfide solutions has been recognized for many years and the measured solubilities of certain copper sulfide minerals attributed to these complexes. Attempts to model this system have proposed either copper(I) or copper(II) thio-complexes, and these have been incorporated into computer programs for generating stability diagrams for the copper-sulfur-water system in order to delineate the region where the reductive dissolution of copper sulfide minerals is likely. In this paper it is proposed that the dissolution of copper from both ore bodies and sulfide tailings can be explained by the formation of the cupro-thio-complexes under anaerobic conditions. Stability diagrams are presented to depict the region and extent of the solubility.

Jan 1, 2001

By Barbara S. Parrish, I. S. Parrish

For two consecutive years the author and his wife have been fortunate enough to have been invited by the Peoples Republic of China to work with Chinese geologists of the Geological Bureau of the Ministry of Metallurgical Industries (MMI). Our visits, each of which lasted 7-8 weeks, took us to northwestern Sichuan, central Anhui, and much of Hebei Province, as shown in the accompanying drawing. We were asked to evaluate, criticize, and offer suggestions on the exploration and mining techniques used by the Chinese. Our commission both years was centered on gold, although we were also to visit other operations when the opportunity arose. In 1986, the visit primarily concerned with disseminated "Carlin" type gold deposits; in 1987, with "Greenstone" type gold deposits. Gold has been targeted by the Chinese as a metal of importance to the nation. Several governmental agencies have received direction and budgets to seek and develop gold properties. Besides the Ministry of Metallurgical Industry, gold is being sought by the Ministry of Geology, the China Gold Corporation, and reportedly the Peoples Army. There is considerable competition among these agencies. It is not uncommon to find two or more agencies working in the same general area. However, communication between the groups is minimal. Last year, we toured a small mine at Bambishan. We could see a diamond drill across the valley. The rig belonged to another Ministry and my guides voiced their curiosity to know what their competitors were finding. Mining, too, is not the monolithic bureaucracy that most Westerners anticipate in China. There are various levels of mining. These differ not only in sophistication, but in ownership. First, for small deposits the state allows "Peoples Mines". These can be owned and worked by individuals. The individual owner-miner may hire relatives or neighbors and give them a wage or he may turn the mine into a joint ownership situation. They

Jan 7, 1988

By K. Komnitsas

This paper presents the main environmental assessment techniques and indicators that can be used a) for the establishment of a sustainable development framework and b) for the evaluation of the environmental performance within the mining sector. Reference is made to techniques as environmental risk and impact assessment, life cycle assessment, cost benefit analysis and best practical environmental option assessment that can be used as tools to assess environmental impacts of processes, activities and products in the mining sector. In addition, the issue of environmental indicators, covering operational, management and environmental areas, that provide valuable information regarding both the environmental performance of a mining company and its efforts to influence this performance towards sustainability is discussed.

Jan 1, 2003

By B. J. Schat, A. W. O. Bots, O. S. Langhorst

Amsterdam City Council is building a new metro line, the North–South Line. The line passes under Amsterdam Central Station (a listed building) about 18m below street level. The retaining wall that has to be built underneath the existing building is an innovative construction consisting of two rows of steel piles interspersed with a solid mass of overlapping jet grout columns: a composite ‘sandwich’ wall. This paper gives an overview of the approach taken to designing (computational models) and building the retaining wall. Special attention is paid to the observational method used for the construction of the jet grout columns.

Jan 1, 2007

By A. Festa

Secondary crushing often gets good press for its increases in energy efficiency and SAG milling rates but for a project considering this option the proposed benefits soon get overshadowed by implementation concerns. Reverse engineering from the published case studies is risky unless the reader understands the drivers impacting stability and operability of the circuit. This paper discusses the features of secondary crushing for Greenfield and Brownfield SAG mill grinding circuits. It is the author?s view that secondary crushing rarely adds value to a Greenfield project and restricts future expansion. Its application is best retro fitted to Brownfield operations where the benefit gained for capital expended is excellent. Two case studies are presented to reaffirm these statements. The first case study shows that the implementation of partial and total secondary crushing increases SAG mill power efficiency and it offers substantial incremental increases in milling throughput with staged capital investments for the crushing and grinding circuits respectively. The paper provides a critical analysis of process conditions for secondary-crushed grinding circuits, with particular emphasis on Brownfield circuit retrofits. Furthermore, the second case study quantifies the economic impact of secondary crushing on circuit design for plant start up and it illustrates the limit imposed on plant expansion.

Feb 23, 2014

By Newell H. Orr

Titanium&apos;s performance characteristics in acidic oxidizing and mildly reducing environments make it applicable to numerous currently defined and many projected hydrometallurgical applications. With titanium&apos;s current and projected availability and price stability increased use in pressure leach, piping systems and electrorefining is practical.

Jan 1, 1983

By H. Lyn Bourne

This is the sixth annual tabulation that gives mineral royalty information. This tabulation, like the previous editions, includes all of the earlier data plus more than 100 new entries. In addition to the royalty information, some entries show the cost of purchased reserves. An article in the December 1984 Kentucky Coal Journal could have far reaching applications. It explains that a banking firm examined the "reserve risk" as one of six factors for analysis when financing a coal project. The firm concluded that coal reserves in Kentucky are worth an average of $0.29/t ($0.26 per st) in-place. The banking firm based this in-place value on its examination of more than 50 leases. In-place value is especially important when trying to establish a mineral value for a given deposit. Ernie Lehman wrote to this author after last year&apos;s column appeared and he quoted the lease rates for lead and zinc on federal land. He states, from first hand information, that the leases are based on a percentage of net smelter return as follows: 4% for the first five years, 4.5% for the next five years, and 5% thereafter. The figures used in last year&apos;s column ($ per st) came from dividing reported royalty income by reported production. The information reported last year merely translates the results of the net smelter return (as written in the lease) to royalty income per ton to the US Government for the various years. Statistics from the Minerals Management Service of the Federal Government show that oil and gas account for 40% and 53%, respectively, of the Federal royalty income. Coal accounts for about 4% and all other minerals, the remaining 3%. Oil and gas leases are mostly at 12.5%. Most of the coal leases are at 12.5% for surface mining operations and 8% for underground mining. Many of the other commodities are leased at 5%, which has been true for decades. Relative to Federal leases, this year&apos;s table shows some percentages and some costs per ton. This was done to give information about the leases and also to show income produced by various commodities. Note that some commodities have a variation in $/ton even though the royalty percent is the same. These variations result from a combination of factors that influence the value of a mineral commodity. The same caveats that have appeared in previous columns relative to factors that influence the value of reserves are restated. The data in the table serve as a general reference and are not intended to present an absolute scale of reserves costs. Several factors influence the value of any mineral commodity. The factors include: • location/transportation (especially significant for most industrial minerals); • market conditions both for the commodity and the company acquiring the right to mine it; *quality or grade of the deposit as it reflects the amount of processing/beneficiation necessary to produce the finished product; and • legislative restrictions and conditions for mining a given material at a given site. These and other factors will significantly influence the cost of reserves. The table shows the range of royalties and the variations in the basis of computing the fees. In a few instances, it gives the cost of acquired reserves based on purchase price and quantitative estimates of the material in place. The table lists the commodity in column 1, and the subsequent columns give the location - either by state, US geographic area or Canadian province; the cost - R for royalty and P for purchased cost; and the year in which the lease or purchase agreement occurred. The last column offers either comments or gives a footnote number for more information. The cost column requires more explanation. The units may refer to cubic yards (/yd), cubic feet (/cu ft), tons (/T, 2000 lbs) or acres (/A). 1 cu yd = 0.7646 m3 1 cu ft = 0.2832 m3 1st=0.9078t 1 acre = 0.4047 hm or m2 In several cases, the royalty is a percentage of the sales price of the finished product and is levied against either the amount produced or the amount sold. We thank those who contributed information for the table: G. Anderson, B. Brown, R. Ganis, K. Hauser, E. Lehman, and S. Sims. Their help is appreciated as are the contributions by those who asked to remain anonymous. This column requires additional information each year. That data must come from people in the minerals industry who have royalty information. What appears in the table is only a very small fraction of the cost information relative to the various commodities and the geographic areas for which there is royalty information. If you find this column of interest and possess information write the author at the address given in the author&apos;s box or call 313-462-0005.

Jan 7, 1988

By John J. Sammarco

"The mining industry has made great strides in making mining safer and reducing the occurrence of mine disasters. Nevertheless, sometimes miners encounter smoke while trying to escape from a mine. Underground miners use different visual cues to help them escape from a smoke-filled environment. Foremost, miners look for primary and secondary escapeways that are typically indicated with reflective markers of various colors, with at least 11 colors available from manufacturers. Federal regulations require that escapeways be marked, but they do not specify the colors to be used. Thus, no standard color code exists and some colors can be more difficult to see in a smoke-filled mine.Researchers at the National Institute for Occupational Safety and Health (NIOSH) Office of Mine Safety and Health Research (OMSHR) tackled this problem by taking a human-centered approach to provide miners with better visual information that would improve their ability to see escapeway markers in smoke, thus enhancing their ability to self-escape. What marker colors does your mine use?Does your mine use blue retro-reflective markers to indicate primary or secondary escapeways? Is your mine ready to purchase new or replacement retro-reflective markers? Color is important and blue had the poorest visibility as determined by OMSHR’s recent research investigating the visibility of markers in smoke. OMSHR researchers are not alone in their interest to improve a miner’s ability to escape - specifically when their efforts are hampered by smoke. For instance, there is a LinkedIn Mining Safety subgroup called "Standardized Color Code for Escape Ways and Returns in Underground Mines," and a recent National Academy of Sciences report recommended the development of humancentered technologies to enhance self-escape from underground mines. The mining industry has a common goal of helping improve miner safety, especially when it can be done by way of a simple and relatively low-cost solution of using escapeway colors that are more visible."

Jan 1, 2014

By James D. Nickerson

Thee Brightwater water treatment facilities, currently scheduled to be completed in 2010 and begin operating in 2011, will serve the northern part of King County, WA. The facility includes a new treatment plant and extensive conveyance system consisting of more than 21 km (13 miles) of influent and effluent conveyance tunnels and five portals. The majority of the conveyance system tunnels are mined by tunnel boring machines (TBM) and microtunnel boring machines (MTBM). Tunnel and portal construction is divided into three main contracts. The Ballinger Way receiving portal, constructed under the central tunnel contract, is the terminus for the BT-3 leg of the central contract and the BT-4 terminus of the west contract. The shaft has a 7.3-m (24-ft) finished inside diameter (ID) to accommodate removal of the central project TBM and the west contract TBM and extends to a depth of 66 m (216 ft) below grade through a complex and challenging soil profile characterized by multiple ground water tables. Vinci Grand Projects/Parsons/Frontier-Kemper Constructors (VCFK) was the joint venture team for the Ballinger Way portal. Frontier-Kemper was responsible for the shaft sinking. VCFK evaluated either slurry wall techniques or ground freezing for earth support during excavation of the portal and liner installation. The selection process took into account the vertical depth, cost, past practice, geology, water tables and a 9-m- (30-ft-) thick zone of contaminated soil at the top of the shaft. Ground freezing, which would also act as a hydraulic barrier, was deemed the better option for this project. The contract was awarded to New Jersey-based geotechnical contractor Moretrench. Typically, frozen walls, by design, key into an underlying cutoff. At the Ballinger Way portal, however, the [ ] freeze bottomed out in a substantially thick stratum consisting of predominantly clay, but with some inclusions of permeable soil that indicated significant ground water pressures. To ensure stable conditions at the bottom of the shaft, Moretrench, which also specializes in dewatering, designed and installed a perimeter array of deep wells to temporarily depressurize the permeable soils. The movement of ground water generated by pressure

Jan 1, 2009

By M. A. A. de Klaver

Functional Description Figure 1 is a typical flowsheet for a system for solid fuel addition to filter cake. Solid fuel, coal, coal breeze, or charcoal, is fed from a,stockpile to a surge hopper. The solid fuel is metered into a grinding mill. The fuel is dried and ground in a grinding mill. The on-size particles are removed from the mill by air sweeping. The ground solid fuel is separated from the air stream by a cyclone and stored in a surge hopper. The ground solid fuel is then pneumatically conveyed to a small hopper in the balling area. The fuel is proportioned into the filter cake just prior to mixing. An efficient mixer is very important to have a successful operation. The exact flowsheet would depend on a number of factors including what fuel is used, how the fuel is received, and the cnaracteristics of the fuel as received. Availability of floor space in the plant may also affect the flowsheet. For example, drying air may be supplied from the pellet furnace if the grinding mill can be located near the grate, or the pneumatic conveying system and a surge hopper may be eliminated by placing the grinding mill adjacent .to the mixing area. Also, for a multiple line plant, a ball mill rather than a roller mill may be more suitable.

Jan 1, 1980

By William F. Lawrence

Research performed by the West Virginia University Coal Research Bureau under the sponsorship of the U. S. Bureau of Mines has demonstrated that coal-ash can be converted into mineral wool insulation of a quality equal to commercial grade mineral wool. An unexpected benefit has been gained due to the discovery that the usual and costly fluxing agents employed when using conventional raw materials are not required when producing mineral wool from coal-ash. Because coal-ash sources are commonly located close to mineral wool marketing areas and because mineral wool is seldom shipped far as a result of its low weight and high volume, the use of coal-ash may offer the mineral wool producing industry profitable opportunities. Moreover, coal-ash produced from experimental limestone based air pollution control processes also yields high quality mineral wool which may aid in retarding corrosion of metals contacted by the wool. In addition, internal fluxing effects and possible sulfur oxide utilization could provide economic advantages to the use of these "modified" ashes.

Jan 1, 1969

By M. A. Trevits

The explosion hazard presented by methane gas in coal is confronted daily in the mining industry. Research has developed several viable methods for gas control in addition to conventional dilution by ventilation. Such methods include the drilling of horizontal or cross-measure boreholes from a mine opening and vertical boreholes hydraulically stimulated in advance of mining or for gob gas drainage. The long-term production history of five gas drainage installations was studied. Three installations were completed in the Pittsburgh Coalbed: two in West Virginia and one in Pennsylvania. The remaining installations were completed in the Mary Lee Coalbed in Alabama and the Sunnyside Coalbed in Utah. The types of drainage methods utilized included horizontal and vertical boreholes. The length of production studied ranged from 860 days to 36 years. The cumulative production from the five sites was in excess of 155 Mm3, representing a significant volume of gas.

Jan 1, 1985

By L. G. Austin

Introduction My first contact with industrial milling was during the time I worked in the electricity generating industry in the United Kingdom. In visits to power stations to investigate either deposits in the boiler furnaces or polluting deposits settling around the stacks. I had to check the performance of the vertical coal pulverizers, since poor pulverization aggravated both problems. Naturally, then, when I came to the USA in 1957 to take a PhD in fuel technology at Penn State, I was put to work to review the science of coal pulverization. After this reviewing, I was completely confused. On one hand, there was a well-developed understanding of stress-strain equations, and a rap- idly developing knowledge of how stressed, brittle solids fractured, based on the Griffith crack theory. On the other hand, reading in the grinding literature gave me: • Kick&apos;s Law, which was clearly not correct in the light of modern fracture theory; • Rittinger&apos;s Law, which was also clearly not correct; • Bond&apos;s Third Law of Comminution, which was claimed to have something to do with the Griffith crack theory, but where the connection between the two was made by intuitive pseudo- scientific reasoning I could not accept; • the choice of mill motor power for the most common type of coal mill, the Raymond pulverizer, was calculated from the fan power required to move air through the mill. Although I could accept the empirical connection between the two, it made no sense from the point of view of fracture energy. Even today, most books or review chapters on size reduction start from these laws. incorrect statements abound in the literature, such as “the Hardgrove Index is based on Rittinger&apos;s Law," which it is not, "The Bond theory states that work input is proportional to new crack tip length produced in particle breakage," which is not true, etc. My own test work showed that these "laws" did not fit the data for grinding of coal. At about this time, Epstein (1 948) and Broadbent and Callcott (1 956), following the original work by R.L. Brown (1941) at the British Coal Utilization Research Association, proposed describing breakage as a series of fracture stages. I took their concepts and developed the basic differential equation for a batch grinding process continuous in time, analogous to a batch chemical reactor. Robin Gardner then joined the project and did his PhD on treating batch grinding in the same way as a batch chemical reactor. He found that the basic equation had already been partially derived by Sedlatschek and Bass (1 953) in Germany. We confirmed experimentally the validity of the equations for describing batch grinding (1 962) and formulated the equation describing steady-state continuous grinding in a fully-mixed mill. At about the time this work was published, Gaudin and Meloy (1962) and Filippov (1961) independently published essentially the same equations, but without experimental proof of the validity of the concepts. I will give a brief overview of what these beginnings had led to in the design of mills for size and power, and show some of the results of this more detailed understanding of grinding processes. Concepts of Fracture Mills such as tumbling ball, rod, pebble and autogenous mills and vertical mills such as the Raymond, and E-type apply compressive stress to lumps or particles relatively slowly. Compressive stress applied to a particle of an elastic brittle solid imparts overall strain energy to the solid and produces local regions of tensile stress, (Fig. 1) (Berenbaum and Brodie, 1959). Irwin (1949) showed from solution of the stress-strain solutions that a small hole in a region of tensile stress reduces stress concentration at the hole, that is, the tensile stress at the tip of a crack or flaw in a solid is much higher than the general tensile stress in the region. The longer the crack, the higher the stress concentration. Griffith (1920) hypothesized that when the regional tensile stress is large enough, then the chemical bonds at a preexisting crack tip are stretched to breaking point, as illustrated in Fig. 2. When the bonds break, the crack becomes longer, the tensile stress concentration increases, the situation is unstable and a crack opens up (propagates) a surface of tensile stress, creating its own tensile stress at the leading edge. Stored strain energy is converted to the kinetic energy of the moving stress field, which is analogous to sound propagation through the solid, so the crack tip accelerates to velocities approaching those of sound. The moving crack will pass through regions that were previously under regional compressive stress. The equations for "ideal" and "Griffith" strengths are where a is the intermolecular distance, y is Young&apos;s modulus, g is the energy

Jan 1, 1998