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By Irwin Roman

NUMEROUS results and formulas have been published for analyzing seismic records, but most of them apply only to large-scale phenomena such as are encountered in studying earthquakes. In a few cases,1 formulas have been published for some of the simpler structures. In the present paper, an attempt will be made to analyze several types of struc-tures without using methods more advanced than those of a first course in calculus. In, tracing a disturbance through a medium, it is almost always possible to base the analysis on Fermat's Principle of Extreme Time, which states that waves of displacement travel between points in such a manner as to make the time of travel an extremum with respect to all neighboring paths. In the simpler cases, comprising most of those used in optics or geophysical prospecting, this time is a minimum and the principle is often referred to as the Principle of Least Time. Within a homogeneous medium, having a uniform speed of transmission of the disturbance in all directions and throughout the medium, the paths are straight and are refracted at the interfaces in accordance with the Snell law of refraction, which states that the ratio of the sine of the angle, made by the ray with the normal to the interface, to the speed of trans-mission is the same on both sides of the interface. Thus, in any medium composed of homogeneous sections, this same ratio has a constant value at all points. In particular, if all interfaces are horizontal, it is apparent that the angles of incidence are the angles made by the ray with the vertical direction. Furthermore, the incident ray, the refracted ray and the normal to the interface are all in the same plane at each refraction;

Jan 1, 1933

By Evert Hoek

An empirical criterion is presented for use in estimating the strength of heavily jointed or weathered rock masses. This criterion incorporates the intact strength of the rock material and introduces two dimensionless parameters m and s which characterize the behaviour of the interlocking particles in a jointed rock mass. The use of rock mass classification systems for estimating the values of these parameters is discussed. The application of this non-linear failure criterion to the analysis of slopes is illustrated by means of a worked example.

Jan 1, 1983

By Fun-Den Wang

An open pit rock structure usually contains geological planes of weakness. They are formed by joints, faults, bedding planes, fractures, and cleavages. Rock slope failures often occur in the form of sliding of rock blocks along a plane or several planes. Such a rock block has three- dimensional geometry, and consequently a vector method of analysis has been found useful in evaluating its stabi1ity.l-3 Rock blocks of a tetrahedral shape with one free surface have been analyzed by Londe.3 Rock blocks formed by sets of parallel joints have been analyzed by Wittke.1,2 The present chapter presents the analysis of rock blocks formed by planes of weakness of arbitrary orientation, and of three-dimensional geometry. A plane of weakness is represented by its dip and strike in vector form and is reduced to the form of a linear equation. The geometry of the rock block is defined by solving the linear equations. The geometric characteristics of a rock block are based on triangles and tetrahedrons. By this treatment, the three-dimensional geometry is simplified and the number of calculations of forces and moments is reduced. Methods of finding the geometric characteristics are presented, along with equations for calculating the resultant forces and moments and the factor of safety. BASIC ASSUMPTIONS The following assumptions are used : The solid part of the rock mass is much stronger than the rock mass at the plane of weakness and the rock mass will only fail along planes of weakness.

Jan 1, 1972

By Fun-Den, Wang

An open pit rock structure usually contains geological planes of weakness. They are formed by joints, faults, bedding planes, fractures, and cleavages. Rock slope failures often occur in the form of sliding of rock blocks along a plane or several planes. Such a rock block has three- dimensional geometry, and consequently a vector method of analysis has been found useful in evaluating its stability. Rock blocks of a tetrahedral shape with one free surface have been analyzed by Londe. Rock blocks formed by sets of parallel joints have been analyzed by Wittke. The present chapter presents the analysis of rock blocks formed by planes of weakness of arbitrary orientation, and of three-dimensional geometry.

Jan 1, 1972

By J. R. Sturgul

Two problems which are common to nearly every branch of applied physics, including geophysics, are the ‘Dirichlet Problem’ and the ‘Poisson Problem.’ A numerical method for their solution is derived and a problem of heat flow in a plate is solved using a high-speed digital computer. The solution to this problem is presented in a form which illustrates the versatility of computer output.

Jan 1, 1969

By Francis Foley

WITH the possible exception of high-speed tool steel, the service demanded of rock-drill steel is probably more precarious than that of any other tool steel. Unaided by the helpful influence of alloys and dependent solely on the efficiency of the heat treatment applied for its ability to stand up under the abuse to which it is necessarily subjected, rock-drill steel is worthy of intensive study. For its heat treatment the smith has his fire, an oil fire perhaps, and a quenching bath; he judges' the temperature by his eye. There are shops where excellent drills are produced by this method, but there are more where the product varies between very good and very bad. Pyrometers with specially designed equipment are used in but few cases. But the responsibility for rock-drill failures does not rest entirely on the smith. Little has been published concerning the efficiency of drill steel, though the Canadian Mining Journal' published the breakage record of a large number of hollow drill steels. This record indicates that most of the breaks occur during the early life of the steel and that as a given batch of steel is used, its percentage of breakage decreases. This fact, the article points out, is at variance with the much-talked-f theory concerning failure from crystallization and fatigue. It seems to point to the fact that the greater part of drill-steel failure from breakage is traceable to faulty manufacture, resulting in defects in the bore of the hollow steel from inclusions of slag or oxides, etc. As this defective material meets with early failure, it is weeded out. In addition, some breakage may be caused by a lack of proper condition with respect to heat treatment of the steel as furnished by the manufacturer. In the article mentioned, the breakage of 1 ¼ -in. (3.17 cm.) hollow steel is given as 4.62 per cent. for the early period of use, with a decrease to 3.35 per cent. and 2.67 per cent. With time in use. For 1-in. (2.5 cm.) hexagonal hollow steel, the figures for breakage are 0.18 per cent. and 0.06 per cent.; attention is called to the "enormous decrease in breakage by the use of smaller diameter drills." The figures are given as so many "drills sharpened," but there is no way of determining the percentage of

Jan 6, 1921

By L. W. Saperstein, W. B. Wells, L. B. Phelps

Several strip mine spoils are being examined to better understand their physical nature. The spoils were core drilled and each hole was logged using a nuclear geophysical tool to obtain bulk density data. Bulk density is an important property which provides insights into spoil porosity as well as other characteristics. The holes were drilled in spoils representing a variety of overburden removal methods, spoil ages, spoil depths, and area lithology. The relationship between bulk spoil density and mining method, spoil age, spoil depth, particle size, and lithotype is presented.

Jan 1, 1984

By T. P. Harrington, P. G. Doctor, K. A. Prisbrey

Crushing and grinding ore consumes so much energy that it represents a major component of total processing costs. While it has been estimated that only about 0.6% of the total energy expended in grinding is actually used to create new surfaces, accurate measurement of this quantity is difficult. If energy expended in crushing and grinding could be more directly measured, alternatives for increasing efficiency of the processes could be evaluated more effectively. Since the energy intensity associated with rock fracture is related to fracture sonority, it should be possible to use this sound (acoustic emission) to measure the actual energy expended. However, it is difficult to apply this approach because the mill environment is so noisy. To make the approach practical, a method for differentiating acoustic emissions caused by rock fracture from those caused by extraneous noises must be found. Pattern recognition analysis may provide such a method. This paper presents the results of pattern recognition analysis to make two types of differentiations: acoustic emissions caused by crushing two types of minerals (quartz and chrysocolla) and those caused by two extraneous noise sources, and acoustic emissions produced by each mineral.

Jan 1, 1982

By Charles S. Barrett

NUMEROUS determinations1-7 of the tex-ture of cold-rolled polycrystalline iron, steel, and ferritic alloys have been made with good agreement among the various observers as to the principal features of the texture common to all, but there has been no adequate explanation of the texture in terms of the behavior of individual grains. This study presents an explanation of the texture based on the observed rotation of single crystals when deformed in a manner similar to a grain in the aggregate, a method we have found useful in leading to a better understanding of compression and tension textures;8,9,10 in particular, the aim has been to determine experimentally the end orientations of rolled single crystals of iron. These are discussed in connection with the point of view of Wever1 and of Boas and Schmid2 that the rolling texture is a simple compression texture (compression normal to the rolling plane) superimposed on a simple tension texture (tension in the roll-ing direction), and the point of view of Kurdjumow and Sachs3 that three ideal end orientations exist.

Jan 1, 1940

By J. S. Fulton

THOSE who live in steel-mill towns are so accustomed to the sight of flames spouting from the mouth of a Bessemer vessel that they seldom pause to think of the amazing process behind it. Actually cold air is being blown through a hot liquid and, instead of cooling it, raises the temperature of the liquid. When coffee is too hot to drink, we know that blowing on it will cool it, so it was no wonder that when Henry Bessemer (or William Kelly, as your patriotism chooses) first proposed this cycle of steel production, he was considered mad. When Bessemer and Kelly started their investigations around 1852, there was not much practical knowledge of metallurgy and, in consequence, there was wide variation in the product made by their process. It was appreciated that the silicon, carbon and iron were all potential fuels, but not until Mushet discovered the beneficial effects of having manganese in the pig iron did the process really become commercial. Bessemer's patent of 1855 covered a crucibleful of liquid iron into which a refractory tuyere was lowered and the blow started. Since that time virtually every conceivable form of vessel, bottom arrangement, tuyere size and location have been suggested or tried. There have been stationary vessels with fixed bottoms, that were side, top or bottom blown; tilting vessels with two sets of side tuyeres at different elevations; vessels like a three-compartment septic tank; vessels of a cylindrical form supported on the long axis with tuyeres along the side submerged by a partial rotation of the vessel (this type continues in copper refineries) ; portable vessels to make the blow in a ladle over a mold in a foundry; a combination of a cupola and converter in one shell, and various other arrangements. But in all these experiments, compressed air for the blast was presupposed and there was little discussion of the quantity or quality of the air delivered to the tuyeres. At one time or another various practices that now are forgotten have been tried or suggested: for instance, the use of inert gas at the end of the blow; the addition of fuel to the blast; the use of hot-blast stoves; the drying of the air to a minimum moisture in the blast. Except in the last-named method little attention was paid to the quality or quantity of the air blown. PHASES Of the many papers published on various phases of the Bessemer process, nearly 170 according to one bibliography, over go per cent were concerned with the metallurgical phase and less than 10 per cent discussed various sections of the pneumatic phase. Since the two phases are coincidental, apparently nine times as much thought has been given to the result as has been given to one of the causes of the Bessemer process. Is it not possible that if more attention had been paid to the pneumatics so many papers would not have had to be written on the troubles in the metallurgical phase? A study of published papers and conversation

Jan 1, 1941

By R. J. Batterham, P. W. Roller

Granulated sinter mixes of three iron ore types were prepared with a range of water contents in a laboratory investigation. The mean diameter of the granulated mixes and the void fraction of beds of the mixes were determined experimentally. Pressure drop measurements over a range of flow rates were made in a laboratory permeameter with pressure tappings at several depths in the bed. The Ergun equation was applied to the results to determine the shape factor of the granulated mixes. Pressure readings down the bed were used to estimate the local void fraction in the bed using the Ergun equation and the calculated granule shape factors. It was found that there was a decrease in void fraction with depth in the bed. The significance of this and the variation of shape factor values with the amount of water used for granulation is examined in relation to the strength of granules of the sinter mixes. The experimental and mathematical techniques presented may be useful in interpreting the behavior of the permeability of sinter beds after ignition.

Jan 1, 1986

By J. V. Calara, J. D. Miller

The sign of the surface potential for complex non-reactive ionic solids cannot be predicted solely from consideration of the hydration energy of gaseous ions which constitute the ionic lattice. Accurate analysis of these systems must involve the hydration energy of surface ions, which requires knowledge of the crystal structure, the identification of cleavage planes, and the calculation of binding energies of surface ions. Surface binding energies for ionic solids can be determined if the Surface Madelung Constant is known. A computational technique was developed for the calculation of Madelung Constants for infinite lattices which gives excellent agreement with the values calculated by other more complicated methods reported in the literature. Extension of this technique permits the calculation of Surface Madelung Constants and binding energies of surface ions, [Aus], for semi-infinite solids. The hydration free energy of gaseous ions, [AFh], together with the calculated binding energy of surface ions, [Aus], allows calculation of the hydration energy of surface ions,[AGh], as for the case of the ionic solid, MX: [ ]

Jan 1, 1976

By J. D. Dixon

Procedures are given for calculating stresses in underground tunnel supports which accounts both for the structural behavior of the support and that of the adjacent rock mass. Stresses in the support are caused by service loads and rock reactions. Service loads are due to rock pressures, hydrostatic and hydraulic pressures, selfweight of the support, or other utilitarian-type loads. Rock reactions, equal and opposite those in the support, are due to the deformational interaction that results as service loads deform the tunnel support against the adjacent rock mass. The procedures developed for solving this problem are an application of matrix structural analysis. The principles involved in this method allow for the consideration of the deformable characteristics of most tunnel support systems and an iterative solution procedure is applied to determine the areas of support-rock interaction. Numerical results of example problems are given.

Jan 1, 1972

By B. H. Bergstrom, Will Mitchell, T. G. Kirkland, C. L. Sollenberger

SEVERAL constructive and fundamental studies have been made in the analysis of data obtained from experiments carried on with batch ball and rod mills. The operating characteristics of ball milling in small continuous circuits have also been appraised. It is from these analyses that some of the theories of comminution have been developed. Relatively few studies of continuous rod milling have added significantly to the fundamental concepts, because seldom have they yielded sufficiently consistent results. Perhaps they have been too limited in their scope. Careful control of the variables in batch grinding is simple compared with that encountered in a continuous operation. This factor alone has discouraged many investigators. Occasionally results of systematic changes made in industrial rod mill circuits have been published, but usually the data are sketchy and are restricted because -of the unwieldiness of the equipment used. The work, in general, has not been comprehensive; nevertheless it has provided empirical relationships that have bridged the gap between postulate and practice so that by proper manipulation of formulae, a mill designer can anticipate mill size and power requirements.1-3 Although operating variables of a small continuous mill are not so easy to control as with the batch mill, with present day devices, and with careful experimental work, consistent results can be obtained.

Jan 10, 1954

By B. H. Bergstrom, Will Mitchell, T. G. Kirkland, C. L. Sollenberger

In a previous article' the authors outlined a study I of the variables in rod milling and also reported data from a series of open circuit grinding tests on a massive limestone in a 30-in. x 4-ft end peripheral discharge rod mill. As a second part of the experimental program, an analysis is now presented for the 30-in. x 4-ft overflow rod mill grinding under identical conditions, except that discharge ports on the periphery of the mill shell have been sealed so that the products from the present series overflowed through a 9-in. diam opening in the center of the end plate. A variance analysis has been made of the combined data for the two experiments, and performances of the two mills are compared here. Included in the first report were descriptions of feed preparation, rod mill circuit, instrumentation and controls, and techniques used to evaluate data. Dependent and independent variables were defined, and variance analyses were made to test the relative significance of variables and to establish magnitude of error for the experiment. Significant data were plotted in various combinations, and conclusions were drawn from the graphs. The procedure and analysis in this series of tests follows the first tests and is not repeated.

Oct 1, 1955

By S. K. Kawatra, R. A. Seitz

The use of inferential particle sizing for closed wet grinding circuit control has been practiced for several years. This paper presents a review of some inferential sizing equations developed for pilot and industrial plants using regression analysis. An analytical development is then presented showing how the general inferential sizing model arises from the nature of the classifier model. The relation between the general sizing model and the individual equations is then discussed.

Jan 1, 1984

By Stanley M. Miller

For rock or soil materials assumed to be generally isotropic and homogeneous, seepage theory and analytic geometry can be used to develop a mathematical technique for estimating the steady state, pie-zometric drawdown to a slope face. The resulting parabolic drawdown curve is a function of slope angle and the height of the original water table above the slope toe. When the slope is cut at a rate faster than that which allows a steady state to be attained, a non- steady state analysis approximates the transient drawdown. Monte Carlo simulation provides realizations of possible drawdown curves that can be included in slope stability risk analyses.

Jan 1, 1983

By G. J. Cardwell

The rock and mineral analyst will be called upon to determine both the major and minor constituents in materials as varied as rocks, soil, sediments, concentrates and various liquids. These analyses will have interactions requiring extraction, matrix modification, and background correction. Analytical methodologies include classical gravimetric methods, such as fire assay, emission spectroscopy, X-ray fluorescence, atomic absorption, inductively coupled plasma, and neutron activation. With these capabilities the analyst can be called on to determine three-fourths of the elements in the periodic table. How can the earth scientist pick the method best suited for his particular sample?

Jan 1, 1984

By W. J. Kennedy, J. D. Gardner

A systematic method is presented for analyzing and improving energy costs in surface mines. Each mine is divided into drilling and blasting, overburden haulage, ore haulage, crushing and grinding, and lighting system. Specific methods of improving the energy costs of each system are discussed. Contributions of simulation and queueing to energy cost reduction are also discussed.

Jan 1, 1985

By Rajaraman V. Ramani, K. Sinha Atmesh, Robert Stefanko

Use of electrical power in the bituminous mining industry has increased many fold during the last few decades. Rapid changes have also occurred in mine electrical power systems in order to meet the demands from highly mechanized mines. Fires, explosions, and deaths due to electrocutions are the primary hazards due to the underground use of electricity, although there has been a marked decrease in the fatality rate from electrical accidents. However, efforts to eliminate electrical hazards and to insure trained manpower for better distribution, utilization, and protection of the electrical systems cannot be relaxed. In this article, 200 fatal accidents that occurred during the period from 1955 to 1970 have been analyzed. Accident frequency has been correlated with the size of the mine and of the work force, and with age and work and task experience. A strong negative correlation has been established between task experience and accident frequency. Though the available data permitted only a limited analysis, need for improvements in electrical power technology and for better education and training has been identified and discussed. Missing information in accident statistics is outlined and suggestions for better hazard analysis are presented.

Jan 1, 1975