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By Joseph Jensen

When the legal holders of Government permits in the Middle dome of Kettleman Hills entered into an agreement on May 27, 1929, to suspend all drilling activities on five permits, covering portions of the Kettleman Hills Middle dome, until Jan. 1, 1931, and the owners of fee lands contiguous thereto assured Secretary Ray Lyman Wilbur, of the Department of the Interior, that they too would respect a drilling suspension for a period of a little more than 19 months, none of these interested parties realized that this was the first step in a chain of events that would culminate, more than four years later, in the formation of the Middle Dome Corporation for the development of the Middle dome area in a unit plan that would be the first unit plan to be approved by the California Regional Producers Committee and recommended to the President as a satisfactory unit plan, under Section 7 of Article III of the Oil Code, approved Aug. 17, 1933. Neither did they realize that more than two million dollars would be spent before oil or gas would be successfully and continuously produced from wells drilled on that Middle dome area. On Oct. 1, 1933, under the terms of the Middle Dome Agreement, the Middle Dome Corporation assumes control of activities and is responsible for the division of all product's produced from the Middle dome area to members of the Middle Dome Corporation. This Middle dome plan is the second successful unit plan developed in California in the past three years, the first being the Kettleman North Dome Associationll formed under the agreement, of Jan. 31, 1931, for the unified operation and development of more than 12,000 acres of land on the North dome of the Kettleman Hills. All other unit plans discussed in the past four years in the state have not yet been completed, for one reason or another, but under Section 7 of Article 111 of the new Oil Code numerous plans of development, some of which may be unit plans, will be forthcoming within the next few months. There is much

Jan 1, 1934

THIS paper is the outcome of experiments carried on and experience gained. at the Waihi-Paeroa Gold Extraction Company's tailings plant at Waihi, New Zealand. The plant was erected to treat accumulated tailings which had been discharged into the Chinemuri River by the Waihi batteries.The Chinemuri River is a common sludge channel for all mining debris, tailings, and ashes from the power plants, the last being the cause of occasional high residues, which gave so much trouble to the management. The tailings were dredged from the bed of the river into barges by means of a Pohle air lift, the power being supplied: by a 13 b.h.p. Tangye oil engine driving an air compressor and a centrifugal pump. The sands were elevated from the barges by bucket-belt elevators over screens, to eliminate large particles and rubbish, into storage hoppers, and from there fed direct into four C. Judd Ltd. tube mills.The method of treatment was fine grinding in a weak cyanide solution, agitation in B. and M. tanks, filtration with turn-over vacuum filters, and precipitation with zinc shavings. The comparatively high values of the residues in gold gave a great deal of trouble, 'and it was not until repeated experiments were carried out that the cause of the trouble was located. While the value of silver residues remained stationary, the gold values...

Jan 1, 1912

At Namdeb, submerged beaches are earmarked for sampling and future mining and various sampling configurations are tested for optimality through the use of spatial simulations. For the creation of these virtual orebodies, basic statistics and variograms are needed, but in this specific instance no data exists from which the necessary parameters can be determined. The best that can be done is to use proxy data from onshore beaches, with adaptations where needed. The reworking of raised beaches during periods of rising and falling sea levels in some cases destroyed the internal beach structures, and it is very difficult to determine the variograms. A method is proposed whereby simulated annealing is used to adjust the sample locations to align the data pertaining to beach crests or cliff lines, thus improving the variogram structure along the shoreline in the direction of the highest geological continuity.

Jan 1, 2014

By B. Dimitriades

Data on smog-forming reactivities of exhaust aldehydes are scarce. Such data were obtained by irradiating in a smog chamber typical exhaust aldehydes, individually and in exhaustlike mixtures. Observed reactivity manifestations were rate of nitrogen dioxide formation (RNO2) and yields of oxidant, peroxyacetyl nitrate, and formaldehyde. Results showed that exhaust aldehydes vary widely in reactivity. Formaldehyde showed high RNO2 reactivity but low oxidant yield; benzaldehyde, [m]-, and [p]-tolualdehyde were totally unreactive when irradiated individually; [o]-tolualdehyde was reactive. In mixtures, benzaldehyde manifested reactivity in terms of peroxybenzoyl nitrate yield. Exhaust aldehydes as a group are judged to be as reactive as the exhaust olefin group. The importance of the aldehyde contribution to exhaust reactivity and methods for assessing such contribution are discussed.

Jan 1, 1971

By William P. Jones

THE consumption of sulphuric acid, one of the most important commodities in our modern industrial world, is often used as a barometer for industrial activity. The economics of acid manufacture are largely dependent upon the location of the place of consumption and the availability of raw materials in that locality. Sulphuric acid is made from SO2 oxygen from the air and water. Therefore the sulphur dioxide is the only raw material to be considered in an economic study. SO2 can be obtained from almost any material containing inorganic sulphur, such as elemental sulphur, pyrites, coal, sour gas and oil, metallurgical gases, waste gases, or gypsum and anhydrite. Many tons of acid can also be reclaimed by the recovery and concentration of spent acids. The aim of this paper is to present a guide to the economic aspects to be considered when the installation of an acid plant is contemplated. It must be remembered that 1 ton of elemental sulphur produces 3 tons of sulphuric acid and that the shipping of sulphuric acid by tank car is very costly. The size of the plant must also be given careful consideration. For instance, operation of a plant producing 5 tons of acid per day might be warranted in Brazil or Pakistan, whereas economics usually favor buying quantities up to 50 tons per day for use within the United States. Elemental sulphur, when available at the low price of 1 ½ ¢ per lb delivered at an acid plant, has always been the raw material most frequently used for sulphuric acid. All conditions favor its use at this price. The so-called sulphur shortage has been the subject of so many technical papers, magazine articles, and newspaper items during the past year that it hardly seems necessary to mention it again, but a very brief review of the matter will serve as a foundation for the discussion that follows. There is no shortage of sulphur. Only a shortage of low-cost Frasch-mined brimstone exists today. Other more expensive sulphur-bearing materials are plentiful, both in the United States and abroad. The low cost of Frasch-mined brimstone has discouraged the development of higher cost sources. However, the approaching depletion of Gulf Coast dome deposits and the greatly increased demand for sulphur here and abroad have made it necessary for industry to prepare for conversion to utilize sulphur in other forms. For future planning this situation must be considered permanent and not temporary. This conclusion is based on the fact that although sulphur demand will continue to rise, the production of Frasch-mined sulphur probably will not increase greatly beyond its present level of about 5,000,000 long tons per year. The International Materials Conference in Washington estimates 1952 requirements of the free world at nearly 7 ½ million long tons; and the Defense Production Administration has recently set a new goal for 8,400,000 long tons annual domestic production by 1955. The total sulphur equivalent produced in this country in 1950 was 6 million tons. What, then, are the alternatives for the manufacture of the vital chemical, sulphuric acid? Today about 85 pct of this country's sulphur, and nearly 50 pct of the world supply, comes from our Gulf Coast salt domes and is extracted from the earth by Frasch's hot water process. The Gulf Coast salt dome deposits have been the most important known natural deposits in the world, producing 90 million tons of sulphur during the past 50 years. However, at the present rate of extraction these deposits cannot be expected to last indefinitely. Pyrites Pyrites are, and have been for many years, the source of more than 50 pct of the world's sulphur requirements. The principal use, of course, is in the manufacture of sulphuric acid. The use of pyrites in the United States has diminished greatly because of the availability of low cost native sulphur, but pyrites have continued a major source of sulphur in many other countries. The most available pyrites for use in this country are in the form of lump pyritic ore and in mill tailings from flotation of other minerals such as lead, zinc, copper, gold, and silver. An important factor, when the use of pyrites for acid manufacture is being considered, is the disposal of calcine. A ton of sulphuric acid requires approximately ¾ ton of high-grade pyrite and results in ½ ton of calcine. If the calcine is a fairly pure oxide, free of harmful impurities, it can be used, after sintering, in an iron blast furnace burden. Its value might be as high as 15¢ per unit of Fe at the blast furnace; or possibly $10.00 per ton of sinter, if it assays 65 pct Fe. This might result in a credit of $4.00 per ton of acid if the sintering plant and blast furnace are both located adjacent to the acid plant. On the other hand, several factors must be considered before this credit can be realized, i.e., freight to blast furnace, availability of sintering facilities, methods of eliminating impurities, and the removal of valuable metal values. In some locations it would be most economical to dump the calcines.

Jan 1, 1952

By G. L. C. Young

The first full-scale Reichert cone concentrating plant to be erected at a large South African gold mine was at President Steyn Gold Mining Company, Welkom. ThiR plant was installed as a part of the runof-mine mill extension of 150000 t per month that was commissioned in 1976-1977.

Jan 1, 1982

By Dieter Neuschiitz, Pengfu Tan

"In order to understand the sintering phenomena during iron ore sintering process, a CFD model of iron ore sintering has been developed, combining with the kinetics of 15 relevant chemical reactions with the aim of describing the temperature fields and the gas flow patterns in the sintering bed. This CFD model can be used to simulate the concentrations of the gaseous and solid species, temperatures of the gas and solid, melting and molten fractions of the mixture, gas velocities, temperature zones and residence times of the gas in each temperature zone. IntroductionThe off-gas analyses clearly revealed that the off-gas of a sinter strand does not have a composition corresponding to thermodynamic equilibrium, for example, the CO, CO2 and O2 concentrations are not the mutually consistent equilibrium values. Apparently the chemical reactions in the sinter bed are controlled kinetically. Therefore kinetic modeling of sintering reactions combined with CFD modeling is necessary to understand the sintering phenomena during iron ore sintering process.Several models of iron ore sintering have been developed since 1970 [l-l 4l, each being more refined than its predecessor. The models were formulated as a series of differential equations to describe chemical and physical changes occurring at a point in the bed. These equations were solved numerically in a vertical plane along the strand. The present CFD model, based on the Nath's model [14], has been published in the reference [15]. In this work, some new chemical kinetic models of gas-solid reactions are incorporated in the present CFD model. The concentrations of gaseous and solid species, temperatures of gas and solid, melting and molten fractions of solid, velocity of gas, and residence time of gas in each combustion zone can be calculated by this model."

Jan 1, 2004

By Chris C. Sundberg, Ronald E. Heuer, Stanley L. Paul, Peter M. Douglass

Use of prestressed concrete cylinder pipe (PCCP) for pressure tunnel liners is gaining popularity with contractors, engineers, and owners. This paper presents loading considerations and a beam-spring computer model approach to tunnel liner analysis, together with ultimate strength (US) and service load (SL) procedures for liner design. The US procedure is best suited to check for adequate liner strength under extreme loading conditions. The SL procedure, based on conventional pipeline design practice, is considered more appropriate when addressing crack control and serviceability under normal working load conditions. Other design and construction considerations are discussed and a design example is presented.

Jan 1, 1987

Throughout the 1970s, the US Bureau of Mines rode an ebb tide in Washington political circles. In rapid fire succession, the agency lost its mine health and safety enforcement responsibility (1973), a large portion of its energy research responsibility (1975), and then its fuel statistics functions plus a sizable portion of its coal R&D (1977). By 1978, johnny-come-latelies in the Energy, Labor, and Interior Departments had siphoned away from the Bureau some $125 million in program responsibilities as well as 900 of its employees. The bruising decade came to a close with a Department of Natural Resources proposal that, in its original form, would have scattered the Bureau’s responsibilities to the winds. There is no doubt in my wind,” said Lindsay Norman, acting director of the Bureau of Mines (see box), “that were the Bureau to continue down the path it was on, the next step was closing the doors and going out of business.” The doors are still open, but erosion of responsibilities had a devastating effect on the resources available to fulfill the Bureau’s mission. Devastating,too, in terms of internal morale, considering the Bureau had six directors in a 10-year span. “When the troops are in the trenches and are being shot at,” Norman said, “they need a leader—hopefully, a permanent one— that can get them advancing. This is something the Bureau did not consistently have in the 1970s.” In September 1978, Roger Markle climbed aboard as director of the Bureau to rejuvenate the 70-year-old agency. He resigned only six months later* but the program Markle set in motion is being carried through by Lindsay Norman. Since Norman’s appointment as acting director, he has spent considerable time on the road explaining his agency’s redefined goals. At one such stop in Duluth, Norman and his two deputy directors, Charles Kenahan and Mike Kaas, answered the following questions.

Jan 6, 1980

By M. Soranzo

This paper presents a restoration operation of the load-bearing capacities of a deep foundation which did not satisfy the original design conditions. The operation was preceded by a series of tests carried out after construction of the pile foundation. In order to verify the efficacy of the method, both load tests on piles before and after intervention and tests on the material used in underpinning the piles were carried out.

Jan 1, 2010

By S Lehane, S Pearce

The characterisation and assessment of waste rock has been the subject of considerable research, and many guidance documents have been published both internationally and within Australia. While these documents provide detailed information on how to characterise waste rock, there is not a great amount of detail on how to determine the optimal waste management options from an operational viewpoint. For example, typical questions that a mine operator would seek answers to include: What placement method should be used (eg end tipping versus paddock dumping)? What is an optimal tip head height for waste placement in a storage facility? How should sulfide grade control be carried out?Defining the contributing factors to waste management and waste material placement and assessing the contribution of each variable directs these assessments towards a semi-qualitative and quantitative methodology. Quantitative methodologies show an increase in the confidence of these assessments by providing logical, measureable assessments.As part of a strategic assessment for waste management at an active mine site, a detailed risk-based investigation of the influence of variables common to waste placement was completed. These variables included placement method, placement height, sulfur grade and material conditioning (eg compaction) on the associated risks of waste material storage. The assessed risks include temperature assessments (potential for thermal take-off as a result of spontaneous combustion), toxic gas production and flow and acid production potential. Applying a numerical modelling approach to the assessment of the different waste material placement strategies allows for the variation in risk to be graphically presented and communicated through risk matrices and histograms.CITATION:Pearce, S and Lehane, S, 2015. Quantitative risk assessment tools to assist with waste management and placement guidelines, in Proceedings Tailings and Mine Waste Management for the 21st Century, pp 353–364 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 27, 2015

By N Jamson, T K. Rohde

The Mine is an underground zinc (Zn), lead (Pb) and silver (Ag) operation in central New South Wales (NSW). Broadly speaking the Mine has two domains that require rehabilitation, the mine industrial area (MIA) and the tailings storage facility (TSF). The MIA has been used for the handling and processing of ore and contains elevated sulfate, sulfide and metals (Pb, Zn). The TSF receives the by-products of processing, that is, potentially acid forming (PAF) tailings which also contain elevate sulfate, sulfide and metals. Typically, the rehabilitation of a TSF involves two controls. Firstly, controlling the potential for PAF tailings to form acid rock drainage (ARD) by limiting interaction with oxygen. Secondly, once the tailings are unsaturated, limiting interaction with water (usually as rainfall) to reduce the potential for ARD to be transported to the receiving environment. These two controls are often employed in the form of a cover.In semi-arid environments there are many Australian examples of covers that have been built to limit interactions of mine by-products with oxygen and water. Typically, the covers contain one or more layers and are built from soil and rock which may include run-of-mine rock. The Mine however has limited supplies of stockpiled soil; and run-of-mine rock is not generated in large volumes because it is used as backfill underground. A cover design strategy was developed to cater for these limiting factors. The strategy identified soil, ore and rock accretion (the accretion) below the MIA could be a potential source of borrow material for the cover. The purpose of this paper is to describe the cover design process, the method and results of large (2 m tall) column trials that were used as a cost-effective way to trial three cover options and finally, the paper describes the water balance that was developed from the column trial results and subsequent modelling using SVFlux.CITATION:Rohde, T K and Jamson, N, 2018. Making use of potentially contaminating mine waste in cover design, in Proceedings Mine Waste and Tailings Stewardship Conference 2018, pp 285–298 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 23, 2018

By Italo Oñederra

A review of breakage and fragmentation literature has shown that only a few models have been specifically developed for applications in underground production blasting. These approaches, however, have applied empirical relations that do not adequately consider ring blasting geometries, have failed to appropriately respond to changes in basic design input parameters, and have complex input and calibration requirements. This justified the development of an alternative modelling framework to specifically address the prediction of fragmentation in underground production blasting. In this sense, the new model, designated as “FRAGMENTO”, is introduced in this paper. The basis of FRAGMENTO is a “single ring” deterministic model which can be extended into a stochastic model to simulate the impact of external operational factors on fragmentation. The single-ring component mechanistically models the extent of both near field and mid to far field fracture zones to predict the distribution of rock fragments expected to report to drawpoints. In this paper the response of this key component is evaluated and its practical application demonstrated with the introduction of a methodology to infer critical burden conditions.

Sep 12, 2005

By Z. T. Bieniawski, Benjamín Celada

After emphasizing the importance of quantitative rock mass classifications in mining, originally directed to selection of rock support measures, but subsequently to estimates of rock mass properties such as rock mass strength and rock mass modulus of deformation, current attention calls for a classification specifically for rock mass excavability by tunnel boring machines (TBMs), which are used extensively in tunneling as well as in the mining industry. This paper introduces the Rock Mass Excavability (RME) index for predicting excavability of rock masses by TBMs using a quantification of machine performance and rock mass conditions. The RME index is based on five input parameters aimed at relating rock mass behavior and machine characteristics: (1) uniaxial compressive strength of the rock material, (2) drillability/abrasivity, (3) rock mass jointing at mine drift face, (4) standup time of the excavation, and (5) groundwater inflow. Development of the RME index entailed the collection of extensive data from more than 28 km of tunnels and some 400 case records from projects in Spain involving double-shield TBMs. In the process, a number of statistical correlations have been established between RME and such output parameters as degree of machine utilization, advance and penetration rates, thrust and torque of the cutterhead, and the specific energy of excavation. It was found that the RME index provides a particularly significant correlation for predicting the average rate of advance (m/day). In essence, the RME index is a classification system that features interaction of rock mass conditions with boring machine characteristics for use in the early stages of a project. It should be noted that the RME index does not replace the Rock Mass Rating (RMR) or Q-systems as used in mining and tunneling; indeed, one of the RME input parameters, standup time, is determined from the RMR. However, the approach presented introduces a specialized tool relevant to excavating tunnels and drifts. Possible applications to hard-rock mining are explored.

Jan 5, 2007

By Olice C. Carter, B. J. Scheiner

The Bureau of Mines investigated the removal of two toxic/heavy metals (cadmium (Cd) and lead (Pb)) from brass foundry wastewater. Polymers, copolymers, guars, and gums were used in conjunction with calcium hydroxide (Ca(OH)2) and magnesium oxide (MgO) to remove the metals from solution. Several polymers were successful in removing Cd and Pb from the wastewater. The concentrations of Cd and Pb were lowered from 19 to 0.01 ppm and from 20 to less than 0.01 ppm, respectively. The methods investigated could easily be adapted to many existing wastewater treatment facilities and/or be used independently.

Jan 1, 1991

By Scott D. Thayer, George H. Milly

INTRODUCTION Ambient concentrations of radon and its daughter products have been measured and analyzed by a number of investigators for a variety of purposes. Principal among these purposes have been: (1) descriptive, to characterize the distribution and changes in concentrations under various conditions; (2) research in the use of radon as a tracer gas in the study of atmospheric characteristics and motions, such as eddy mass transfer, diffusivity profiles, large scale circulations, and the like; and (3) the use of radon as an atmospheric tracer in exploration for uranium deposits.* This information forms the basic data for this paper and for its placing the ambient natural, or non-anthropogenic, radon concentrations into the perspective of ambient radon health standards and lung cancer risk calculations. To enable better understanding of some aspects of the ambient radon data, review and analysis is also performed on selected measurements of radon emanation or flux from the surface of the earth into the atmosphere. These measurements have generally been made for purposes similar to those for ambient radon, i.e., (1) description of radon emanation characteristics; or (2) to support and justify the use of ambient concentration measurements in atmospheric research; or (3) in exploration for uranium. Interest is also developing in the use of such measurements for earthquake prediction. In addition, to complete the perspective, brief examination is given to anthropogenic ambient and flux radon measurements related to the mining and milling of uranium, so that comparison can he made with the values from natural sources. As a frame of reference we cite here previous summaries of studies which have presented representative values and ranges of ambient concentrations and emanation rates. H. Israel, in the Compendium of Meterorology (1951), cites eight studies of ambient radon concentrations which we have selected as representative of non-anomalous continental values. Their means generally range from [0.06 to 0.15 pCi lit-1 with the smallest reported minimum of zero and the largest maximum 0.53 pCi lit-1. The overall mean is 0.10 with a standard deviation of 0.03 pCi lit-1. Means over oceans are much smaller, and the data scarcer, with only three values ranging from 0.0004 to 0.003 pCi lit-1 and a mean of 0.0016 pCi lit-1.] Thirteen studies from Israel's list were selected as representative of mountainous terrain. These data, except for the cases of higher elevations, frequently show significantly higher values than the average cases in non-mountainous terrain described-above. The averages range from 0.10 to 0.59 pCi lit-l; the smallest minimum is zero and the largest maximum is 9.2 pCi lit-1. The overall mean is 0.30 with a standard deviation of 0.17 pCi lit-1. Israel also cites five studies of radon emanation (flux) from the earth's surface. These show a mean of 0.40 pCi-2m-2 sec-1 and a range of from 0.21 to 0.74 pCi m-2 sec-1. Data on flux are naturally scarcer in the literature than data on ambient concentrations, because of the greater interest in and utility of the ambient information. In this paper we also give special consideration to observations of the variability in time and space of radon flux rates, and to the impact of these phenomena on the use of such data for a variety of purposes. NATURAL(NON-ANTHROPOGENIC)AMBIENT RADON CONCENTRATIONS We have examined the following reports for the data selected for this category; these studies were generally intended to describe radon characteristics in the atmosphere. Jonassen and Wilkening (1970); Bradley and Pearson (1970); Wilkening (1970); Lambert, et al (1970); Pearson and Moses (1966); and DickPeddie, et al (1974). Another set of studies which was reviewed was selected because the investigators made ambient radon measurements in the course of examining the use of radon as a tracer in atmospheric research. This set consists of: Israel and Horbert (1970); Carlson and Prospero (1972); Subramanian, et al (1977); Larson (1978); Cohen, et al (1972); Hosler (1966); and Shaffer and Cohen (1972). Finally, unpublished data from uranium exploration activities (Milly and Thayer, 1976) was analyzed. [Treating the ocean cases first, the mean values are generally consistent with those quoted earlier from Israel (0.0004 to 0.003 pCi lit-1); they range from 0.001 to 0.011 pCi lit-1, with 0.003 the most frequently reported value. Continental values, from eight studies, range in means from 0.07 to 0.41 pCi lit-1 (not including mineralized areas, or "uranium country", discussed later), with maxima as high as 2.4 pCi lit -l. For comparison, the means from Israel are 0.06 to 0.15 pCi lit-1, with a maximum of 0.53 pCi lit-1. Some of these studies also present the typical decrease of-1 concentration with height to 0.01 to 0.04 pCi lit at 5 to 7 km. The vast numbers of uranium prospecting radon data of]

Jan 1, 1981

Jan 1, 1904

By Russell C. Frith, David C. Oyler, Dolinar Dennis R., Christopher Mark

Unusual circumstances may require that a longwall retreat into or through a previously driven room. The operation can be completed successfully, but there have been a number of spectacular failures. To help determine what factors contribute to such failures, a comprehensive international database of 131 case histories has been compiled. The cases include six failures where major rock falls occurred in front of the shields, and seven even more serious failures involving major overburden weighting. The case studies suggest two types of room failure mechanism. The first is a roof fall type failure caused by loading of the immediate roof at the face as the fender or remnant longwall panel narrows. The second is an overburden weighting type failure caused by the inability of the roof to bridge the recovery room and face area, and affecting rockwell above the immediate roof. The data indicate that the roof fall type of failure is less likely when intensive roof reinforcement (bolts, cables and trusses) is employed together with higher-capacity shields. The overburden weighting failures, in contrast, occurred when the roof was weak and little standing support was used. Weighting failures were not greatly affected by the density of roof reinforcement. In one of the overburden weighting cases, in a Pittsburgh coal bed mine, stress cell, convergence, bolt load and extensometer data have been used to analyze the failure in detail. Key words: coal mining, ground control, longwall, recovery room.

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

By J. M. Barker

Formation of commodity agreements depends mainly on the economic instability and associated mitigation measures inherent in the economic conflict between more developed and less developed nations. Five types of possible agreements exist: futures market, buffer stock, restrictive agreement, multilateral contract, and compensatory finance. Lack of market separation between sulfur consumers and producers coupled with large world production and highly concentrated export production in theory suggest a restrictive agreement as most likely. In practice, stockpiling of sulfur, an informal buffer stock, as done in Canada and perhaps the Middle East, has been the main sulfur price-supporting mechanism in the past two decades. No commodity agreements involving sulfur now exist except for multilateral contracts. Sulfur agreements apparently have existed rarely, if at all, in the past. Law (1975) refers to sulfur as one of a group of commodities where "there have been additional control efforts of various types." Clearly, sulfur was a candidate, at least conceptually in the past, for some form of commodity agreement. The following discussion centers on the world sulfur market from 1976 to 1985 in this context.

Jan 1, 1987