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By A. Martikainen, S. GYAMFI

Luossavaara-Kiirunavaara Aktiebolag’s (LKAB) Konsuln iron ore mine, located just south of the famous Kiruna iron ore mine in Malmfälten in northern Sweden inside the Arctic Circle, was developed as a test mine between 2018 and 2020 for the Sustainable Underground Mining (SUM) project [1]. Besides functioning as a test mine, Konsuln also contributes to ore production. The existing mine ventilation system was designed for the current production rate of 0.8 Mtpa using conventional diesel machines. The design was created by Kiruna mine ventilation team, Stina Klemo and Joakim Jonasson, in cooperation with a consultant, Tomas Bolsöy from EOL Vent Mining AB. There is a plan to increase this rate to between 1.8 and 3 Mtpa in the future, and this requires the primary fans to be upgraded. Therefore, a study was carried out to determine whether using ventilation on demand (VOD) could avoid this fan upgrade and reduce Konsuln’s ventilation and heating power costs in the future. The study also investigated whether using battery electric vehicles (BEVs) along with VOD or as a standalone strategy could further reduce these power costs. In addition, the study analyzed the suitability of heating power reduction strategies presently or previously used in Nordic countries and Canada to investigate potential additional strategies to reduce heating power cost, the largest portion of Konsuln’s ventilation and heating power costs.

By Gill G. Geesey, Michael R. Hankins, Paul L. Wichlacz, Anita Gianotto, John G. Jolley, Randy B. Wright

Thin films of copper [2.0 nm on germanium internal reflection elements (IREs) and 3.4 nm on germanium discs] were exposed to 10% gum arabic (aqueous solution) , 2% alginic acid (aqueous solution), 1% bacterial culture supernatant (BCS, simulated seawater solution) and 0.5% Pseudomonas atlantica exopolymer (simulated seawater solution). The IRES were monitored in situ, in real time using fourier transform infrared/cylindrical internal reflection/attenuated total reflection spectroscopy as a function of time at ambient conditions. The discs were characterized (pre- and post-exposure) by X-ray photoelectron and Auger electron spectroscopies. Ancillary graphite furnace atomic absorption spectroscopy was used to monitor the removal process of the copper thin film from the germanium substrates. Results indicate that Cu was oxidized by gum arabic, alginic acid and BCS. Furthermore, Cu was removed from the Cu/Ge interface by all four polymers. The Cu was found associated with the polymer solutions.

Jan 1, 1989

By Chee S. Theng

As the 2016 president of the Society for Mining, Metallurgy & Exploration Inc., I am pleased to present the 2016 issue of the Transactions of the Society for Mining, Metallurgy & Exploration Inc., Vol. 340. A significant portion of the contribution that we make as a professional society is the publication of professional and technical papers that accelerate the advancement of scientific knowledge and enable the transfer of technology. Communication within the mining community is the key to a successful society. This technology exchange continues a tradition that dates back to the 1871 meeting of 22 mining engineers in Wilkes-Barre, PA, that resulted in the founding of the American Institute of Mining, Metallurgical and Petroleum Engineers (AIME). Those individuals envisioned that these transaction volumes “would form a most valuable and greatly needed addition to our professional literature.” This volume fulfills that pledge. The 2016 Transactions contains some of the most interesting research and insights from the past year and features an international slate of authors spanning industry, academia and government. Papers include the latest findings from the U.S. National Institute for Occupational Safety and Health (NIOSH) and special-issue articles on process development testing. The 2016 Transactions consists of a total of 65 technical papers, encompassing all 21 papers published in 2016 in the Technical Papers Section of Mining Engineering (Vol. 68) and all 27 papers published in 2016 in Minerals & Metallurgical Processing (Vol. 33). Additionally, this volume contains 17 papers that are being published for the first time in this issue. The papers presented in this volume were written by some of the most distinguished professionals in the industry worldwide. All of the technical papers were peer-reviewed. The process of review and publication requires much hard work by authors, reviewers and our publications staff. As the 2016 president of SME and on behalf of all our members, I would like to extend our gratitude to all whose volunteer efforts contributed to the publication of this volume.

Jan 1, 2016

By M. R. Yalamanchili

The in-situ FTIR/IRS technique has been used to spectroscopically characterize interfacial water near a hydrophilic surface. Interfacial water was examined spectroscopically over known distances from the surface of a silicon single crystal by appropriate design of the geometry and optics of the internal reflection system. The in-situ FTIR/IRS spectra of interfacial water were examined by consideration of the 0 -H stretching region (3000 -3800 cm-1) associated with the vibrational spectra of water. The broad peak: in this region which describes the interfacial water structure was deconvoluted in order to isolate the overlapping spectral features of the interfacial water. Preliminary spectral results indicate the prevalence of an ice-like water structure (-3200 cm-!) at the silicon surface. Importantly, it appears that the interfacial water structure may extend a considerable distance (several tens of molecular layers) from the surface as established from the spectroscopic depth profile measurements which show that the free OH stretch at 3600 cm-1 becomes very significant at distances from the surface exceeding 400 nm.

Jan 1, 1995

By Paul Cameron Gilmour

Geologically, as distinct from economically, "porphyry copper (molybdenum, gold, silver, etc.) deposits" might be defined as large, disseminated and/or stock-work occurrences of copper-minerals, generally averaging less than 1 per cent cop-per. They are normally associated with small plutons which range in composition from granite to diorite, although, typically, they consist of quartz monzonite or granodiorite. Circumstantial evidence indicates that these "minor" granitic intrusions may represent the intrusive phases of post-orogenic, calc-alkaline volcanism, this conclusion being suggested by: 1. Texture and grain size. 2. Prevalence of intrusive breccias. 3. Relationship to unconformities and estimated depth of emplacement. 4. Spatial distribution in relation to orogenic zones. 5. Age of mineralization and igneous episodes

Jan 1, 1972

By Marcelo de Oliveira, Antoine Allanore, Dennis P. Chen, Davide Ciceri

Potassium fertilizers (potash) are mined in a handful of countries in the Northern Hemisphere. Potash is either expensive or unavailable to the farmers of the Southern Hemisphere. Alkaline alteration of K-feldspar rock (ultrapotassic syenite) in autoclave in the presence of Ca2+ generates a mixture of K-bearing calcium-aluminum-silicate-hydrate (C-A-S-H) minerals that potentially can be used as an alternative local fertilizer. This work investigates the effect of processing temperature (200 °C, 220 °C, and 230 °C) and time (from 0.5 to 3.0 h) on pH, mineralogy, and elemental availability of the C-A-S-H mineral mixture. Increasing temperature results in an increased conversion of K-feldspar and increased content of both the mineral tobermorite (Ca5Si6O16(OH)2·4H2O) and amorphous phase in the resulting C-A-S-H mixture; increasing time results in an increased conversion of α-dicalcium silicate hydrate into tobermorite. The amount of K leached from the mixture is relatively constant across all processing conditions. Hydrothermal alteration in autoclave of K-feldspar-bearing rocks such as ultrapotassic syenite permits the synthesis of a potential potassium fertilizer which alkalinity and mineralogy can be tailored according to soil requirements.

May 22, 2020

By J. G. Groppo, A. E. Bland, B. K. Parekh, W. F. Stotts

Many coal preparation plants discard fine coal (generally minus 100 mesh) because it is difficult to beneficiate economically. At the Kentucky Energy Cabinet Laboratory (KECL), the waste streams from several Kentucky preparation plants were evaluated for cleaning with counter-current column flotation. A series of performance evaluations were conducted using a 0.05 m (2 in.) internal diameter (I.D.) 7.9 m (26 ft.) high laboratory column. The objectives of these tests were to assess the performance in terms of recovery and percent ash in clean coal and to optimize the operating parameters relative to combustible recovery and grade. Refuse streams containing 30-50 percent ash were upgraded to 2-8 percent ash with Btu recoveries of nearly 90 percent. A pilot scale column flotation cell was installed at the Bell County Coal preparation plant. This pilot plant utilized a 5.79 m (19 ft.) high and 0.15 m (6 in.) I.D. column to verify the performance data of the 0.05 m (2 in.) I.D. column for two different waste streams. Performance evaluation and pilot plant testing results related to scale-up are discussed.

Jan 1, 1988

By Phil Rice, Mohammed Nasim, Richard Flanagan

"The Gateway Trans-Hudson Partnership (GTHP), a joint venture of WSP USA, Inc., AECOM USA, Inc, and STV Incorporated, is providing preliminary engineering services to Amtrak for the Hudson Tunnel project as well as supporting the NEPA process for getting the record of decision (ROD). This preliminary engineering design effort by GTHP includes geotechnical exploration and laboratory testing, design of structures, tunnel contract packaging and procurement planning.The Hudson Tunnel Project includes the construction of a new Hudson River Tunnel system and rehabilitation of the existing North River Tunnel. The new tunnel system will be constructed south of the existing North River Tunnel, from North Bergen under the Palisades to Hoboken in New Jersey, below the Hudson River, and connecting directly to Penn Station in New York (Fig. 1). The tunnel system is configured as two single-track tubes, intermediate ventilation shafts and cross passages in compliance with NFPA- 130 requirements. The adjacent surface alignment west of the Palisades will be constructed on viaducts, embankment and retained fills. The existing North River Tunnel (Fig. 2) consists of two single-track, electrified rail tunnels extending from tunnel portals in North Bergen, New Jersey to Penn Station in New York. Completed in 1910 by the Pennsylvania Railroad, the tunnel opened at the same time as Penn Station and the four, single-track, East River tunnels that connect Penn Station to Queens and onto Long Island and New England, respectively. Both tunnels in the existing North River Tunnel were inundated with brackish river water during Superstorm Sandy (Fig. 3), resulting in the cancellation of all Amtrak and NJ Transit service into New York City for five days. After the brackish water was removed from the tunnels, the residual chlorides and sulfates have had on-going detrimental impacts on the interior concrete and rail systems."

Sep 1, 2019

By F. L. Pirkle, W. C. Bagby

The International Mineral Valuation (IMVAL) Committee, founded in 2012, develops strategies for conducting mineral valuations. These strategies have been developed into a mineral asset valuation template called the International Mineral Property Valuation Standards Template and is part of IMVAL's work to establish consistent international standards for mineral property valuation and reporting. This template is a living document that is updated from time to time and is based on three core values or pillars (Fundamental Principles): Competence, Materiality, and Transparency. Objectivity, Independence, and Reasonableness may be applied as required by national codes or standards. The Template harmonizes international standards for valuation of mineral assets as real property and represents a consensus of current good practices. It is not a stand-alone reporting code and does not supersede existing national reporting standards. The Template deals with mineral-property valuation as distinct from mineral-project evaluation. INTRODUCTION In his 1989 book, “The New Realities”, Peter F. Drucker, Clark Professor of Social Science at Claremont Graduate School, California, stated: “Information is data endowed with relevance and purpose. Converting data into information thus requires knowledge. And knowledge, by definition, is specialized.” (p. 209) The discipline of mineral valuation is knowledge-based and requires a mineral valuer to collect, analyze, and interpret data that are material to a mineral valuation assignment. In so doing, the valuer turns the data into information (data come first, followed by information as determined by the mineral valuer) for use by the client (from whom the valuer obtained the mineral valuation assignment) and other intended users. The valuer uses his or her experience and education (each valuer’s knowledge base) supported by a foundation built upon competency, materiality, and transparency, the three pillars of mineral valuation (“minerals valuation”, “mineral-property valuation”). The International Mineral Valuation Standards Template (“IMVAL Template”, IMVAL”, “Template”), third edition dated May 2018, defines mineral valuation as: “The estimation of the Value of a Mineral Property in money or monetary equivalent. The word ‘valuation’ can be used to refer to the estimated value (the Valuation conclusion) or to refer to the preparation of the estimated Value (the act of valuing).” (p. 14) Furthermore, the IMVAL Template clearly separates valuation from evaluation: “The Template deals with Valuation, which is distinct from Evaluation. The distinction inherent in these defined terms is that Valuation addresses the estimation of value of a Mineral Property, whereas Evaluation addresses the broader assessment of a Mineral Property for an investment decision.” (p. 2)

Jan 1, 2019

By R. L. Grayson, S. S. Eslambolchi

"In making strategic economic decisions, it is important for a mining company to gain insights on the impact of significant political, social and economic issues when planning for present and future mines. The size of any mine, measured by the average number of employees working in the mine, will likely vary according to the pressures generated by the significant issues from one year to another. The objective of this study is to develop a model that represents U.S. underground coal mine size transitions during the period 2002-2012 using data derived from the MSHA databases. Coupled with information on significant issues over the past ten years, this model is used to gain insight on the impact of the issues on mine sizes. Results indicate that the structural impact of the combined driving pressures can be discerned by examining the year-to-year stability of mine-size categories. The effects of The MINER Act, the Obama Administration environmental policies on coal, and the coal market are evident. The lessons learned from these analyses give good insights on what the industry and market responses have been on the structure of the underground coal industry over the period of study. INTRODUCTION It is apparent that key driving issues affect the structure and viability of the coal industry. The driving issues may be political, social, and/or economic in the final analysis, but are generally rooted in reaction to dramatic and publicized events or movements. Mine disasters, an increase in miners’ disease prevalence, strife in the coal fields, and negative environmental impacts on air, land or water can capture the attention of the media and the public. Some of the issues occur over a long period of time, like the current global climate change movement. The coal industry veteran can sense the changes in political and social sentiment, and attempt to react to the economic repercussions; however, the insights from the media and from unique combinations of driving pressures are difficult to fathom. Thus decisions made on inadequate information related to the driving pressures and their likely impacts could lead to missteps in corporate and market restructuring. One way to gain some more insight on the potential impacts is to examine the complicated restructuring of mine operations in reaction to the driving pressures of the recent past. This paper examines an 11-year history of the changes in the underground coal industry structure, as reflected by changes in the numbers of mines in various statuses by mine-size categories. Superimposed on the results of mine-size changes is a mapping of the key driving pressures that occurred over the same period, 2002-2012. It is assumed that using this methodology, some important insights can be gained on the immediate and delayed responses to the driving pressures during that period."

Jan 1, 2015

The molecular form of aliphatic amines precipitates in alkaline solutions when the amine solubility limit is exceeded and forms a typical colloidal system. The zones of mines precipitation and micellization are defined and it is shown that the appearance of a colloidal system in a certain pH range is a unique feature that makes weak electrolyte type surfactants differ from strong electrolytes. The formation of iono-molecular complexes reported in the literature is shown to be a pre-precipitation phenomenon. The zeta potential - pH curves for minerals and bubbles in the presence of amines in the pH range where the amine forms a colloidal precipitate are entirely determined by the precipitate. The pH dependence of the flotation of certain minerals using amines is discussed in the light of these findings.

Jan 1, 1989

"Tell us how you got involved in mining?I was first exposed to mining at a young age, as a consequence of my dad and his passion for the industry and rock collecting. Even though he graduated with a degree in mining engineering from Washington State University, my dad spent most of his career working as a structural engineer for the Boeing Company. At the time, Boeing supported a range of employee activities and clubs, including one devoted to mineral prospecting, small-scale dredging and rock hounding. My dad was extremely active in the Prospectors Club, where as a family, we spent a good part of my youth tramping around the Pacific Northwest digging for mineral specimens and panning for gemstones and gold. On my mother’s side of the family, I had relatives that mined in Dawson City and Fairbanks, AK which left a family legacy of sorts. I loved the stories that my dad and a close buddy of his, who was a geologist, would tell about various operations and towns, as well as the wild times at the annual Northwest Mining Association (NWMA) meeting in Spokane, WA. My first recollection of ever being at a commercial operation was during a tour of the Bunker Hill Mine with my dad when I was 7 or 8 years old; this had to have been shortly before the May 1972 fire at Sunshine. That visit of the mine and processing facilities made a permanent impression on me. While I always knew there was something special about the Silver Valley, I began to understand why. To this day, I still get the same feeling when I visit historic mining districts like Leadville, Morenci, Virginia City, Butte, Silverton and Barkerville. During our summer excursions to Helena, MT to dig sapphires, we would usually make visits to Butte and watch mine operations inside the Berkley Pit and surface activities at the Kelly and Mountain Con. In high school, I did well in math and science and began entertaining thoughts of pursuing a degree in engineering. Above all, I wanted to go to a college in the West that had a good academic reputation, where I could also play football. As a 6-ft, 190-lb nose guard, my options for a Division I scholarship were pretty slim, and there weren’t that many technical schools in the Northwest that were Division II that offered athletic scholarships. As fate would have it, I was unexpectedly contacted by Marv Kay, a legendary coach at the Colorado School of Mines (CSM), and was recruited to play ball. Fortunately, I had a couple of high school friends who were already attending CSM, and I had just secured a summer internship with Asamera Minerals in Wenatchee, WA. It was as if all the stars had aligned, and, with the support of my parents, I made the decision to attend Mines. Despite the stress of getting through CSM during a period when the mining industry was in freefall, it was a great decision to attend Mines, and I’m thankful for all the opportunities, friendships, and faculty mentoring I received as a student"

Mar 1, 2019

By Emily Sarver

"Across all sectors and commodities, a common theme is driving progress in raw resource supply: sustainable development (SD). Over the past few decades, the mining and minerals industries for their part have undertaken significant and intentional changes at every level to become more responsible — no longer to just their shareholders, but also to the environment, to the communities in which they operate and to society at-large. Led by some of the global majors, these industries have indeed helped to define and operationalize the basic principles of sustainable development. Now in the midst of a full-on cultural shift, they are also key players in the continual effort to re-examine and calibrate practices to meet dynamic and increasingly complex objectives.SME’s technical position statementAs a home for so many technical experts and practitioners, SME has long recognized the importance of a commitment to sustainable development by the mining and minerals industries. In April 2016, the Society formally adopted a technical position on the topic following years of participation in, and support for, related activities. The full position statement appears below. It was drafted, revised and presented for approval to the board of directors by SME’s Sustainable Development Committee.Statement of Technical Position on The Mining Industry and Sustainable Development:• The National Environmental Policy Act of 1969 (NEPA) and the Surface Mining Control and Reclamation Act of 1977 (SMCRA) imposed considerable environmental restrictions on the mining industry; SME has always reinforced strict adherence to the laws.• In 2002, SME established a Sustainable Development Committee to lead its efforts in this area and to propel the organization into global prominence.• SME is a signatory to the Milos Statement of 2003 on Sustainable Development, so it is committed to providing scientific, technical, educational, and research skills in minerals, metals and fuels.• SME recognizes that SD programs adopted by the industry have a tangible return on investment through brand recognition and loyalty, facilitation of permitting, reduced occurrence of community protests and vandalism and diminished political risks.• SME actively promotes educational programs that encourage professional growth and interaction with the engineering professional community through books, articles, symposia, short courses and/or conferences on sustainable development in the mining and minerals industries.• SME has developed abundant expertise to provide balanced advice to government bodies, congressional staff and other interested organizations."

Jan 12, 2017

By The SME Sustainable Development Committee

The evolution of sustainable development in mining is recognized as a key contributor to sustainable development (SD), which is defined as the ability of current generations to meet their needs without compromising the ability of future generations to meet their own needs (Brundtland, 1987). This includes, in equal parts, social, economic and environmental impacts ? triple bottom line (Munashinge and Shearer, 1995). Alternately, sustainability has been defined in relation to social, natural, human, physical and financial capital. Our way of life relies significantly on the materials provided by mining, while mining activity affects the triple bottom-line or the five capitals. The mining community and its professionals have come to realize the importance of engaging all stakeholders in the discussion on sustainability. SME, as the leading professional mining organization, has been involved in these discussions. The society has various initiatives in sustainable development for members and stakeholders. The objective of this article is to: provide historical context for current trends in mining and SD and share SME sustainability initiatives ? their goals and rationales ? with the broader mining community. This article is timely because the past year saw two landmark forums on sustainable development: Rio+20 ? the 20th meeting of the United Nations Conference on Sustainable Development, and MMSD +10, the Mining, Minerals and Sustainable Development project 10 years on. Furthermore, this year marks the 10th anniversary of the Milos Declaration on the minerals professional?s responsibilities in achieving sustainable development, forums in which SME was involved.

May 1, 2013

In its largest product launch in company history, Cummins Engines welcomed more than 200 customers, vendors and media to witness the unveiling of its new QSK95 engine at its Seymour Engine Plant in Seymour, IN on Nov. 1. It took the efforts of 150 engineers to design the QSK95 and more than $100 million in investments to establish a new production line and test facility at Cummins? Seymour Engine plant. The result of these efforts is a new platform of engines that Cummins says will provide as much as 2,983 kW (4,000 hp) and will be the most powerful, high-speed diesel engine ever built.

Jan 1, 2012

By William H. Eatock

The Saskatchewan ore zone strikes slightly south of East, from the Alberta border to Manitoba; and dips to the South. The conventional mines are located along a broad strike line from Saskatoon to Esterhazy-Rocanville. Nine conventional mines have developed ore bodies at a nominal depth of 915 metres (3000 ft.). One mine had developed an ore body at 1525 metres (5000 ft.) by solution mining. Mining reserves of 100 years are not unusual in this vast ore body. Most of the mines were brought on stream during the 1960s. All the conventional mines were influenced by practices developed at Carlsbad, N.M. By 1970, the industry was faced with serious over-capacity resulting in the cancellation of some projects and the introduction, by the provincial government, of the Potash Pro-rationing Regulations designed to share the available market amongst all the producers. This resulted in production rates as low as 40% of capacity. As a result, the 1970s were characterized by attempts to reduce cost, rather than improve production or processing techniques. In recent years, the plants have all been brought to full capacity, and are currently involved in a massive program of expansion, which promises a period of advancing technology.

Jan 1, 1980

By W. D. Hausel

Archean supracrustal rocks of the South Pass greenstone belt of western Wyoming have been the State's most prolific source of gold and iron ore. Actual gold production statistics are incomplete, but as much as 400 to 500 thousand ounces may have been mined with some silver and tungsten as a by-product. Iron ore was also mined from the greenstone belt for 22 years, and production totaled more than 90 million tons. Immediately south of the exposed greenstone belt in the Oregon Buttes area, Tertiary boulder conglomerate, which has been eroded from the granite-greenstone terrain, may contain a gold resource of 28.5 million ounces (Love and others, 1978). The amount of gold placered from stream alluvium derived from these Tertiary conglomerates is unknown.

Jan 1, 1986

By C. A. Young

Cyanide is a toxic species that is found predominantly in industrial effluents generated by metallurgical operations. Cyanide's strong affinity for metals makes it favorable as an agent for metal finishing and treatment and as a lixivant for metal leaching, particularly gold. These technologies are environmentally sound but require safeguards to prevent accidental spills. Various methods of cyanide remediation by separation and oxidation, including photolytic advanced-oxidation processes, are therefore reviewed. Reaction mechanisms are presented throughout the paper. The methods are compared in regards to their effectiveness in treating various cyanide species: free cyanide, thiocyanate, weak-acid dissociables, and strong-acid dissociables.

Jan 1, 1996

By Max Friedemann, Alexandros Bousdekis, Anna Gustafson, Helmut Mischo, Håkan Schunnesson

Many devices used in mining are not monitored by sensors or do not have their own intelligence. By retrofitting sensors and real-time data processing, machines can be integrated into an existing digital infrastructure. Within the project Mine.io funded by the European Union a Sandvik DE110 exploration drill rig is being digitized using various AI algorithms at research and education Mine “Forschungs- und Lehrbergwerk Reiche Zeche (FLB)” of TU Freiberg. The aim is to increase the productivity of drilling with real-time evaluation of the current rock to be drilled and the current maintenance status of the drill rig. The drill rig is equipped with a speed sensor, pressure sensors in the hydraulics, 3-axis vibration sensor, borehole length measurement and temperature sensor. The sensors are additionally attached to the drilling rig and no structural changes on the drill rig are necessary. All data are processed real-time at a server structure outside of the mine using AI algorithms to analyze which rock (ore or host rock) is being drilled and to perform predictive maintenance. Processed Data are visualized for the operator to optimize the workflow and the productivity.

Feb 1, 2025

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