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The following discussion was held on August 2.2, 1927, during the meeting of the Institute at Salt Lake City. It. IIIatch, Garfield, Utah.—The object of the meeting, I belicve, is to determine the proper chemical composition to insure long wear of a ball in a mill. This might also apply to rods. I feel that there is only one way of determining accurately the wearing qualitites of balls in mills, and that is by actually wearing out 400 or 500 tolls of different kinds of balls. Two things add to the wearing qualities of a ball: (1) the tenacity, with which the particular particles of iron or steel are cemented together; (2) the individual hardness of each partiele. My cxperience is that a ball that has a Brincll of 550 to 650 will give comparatively long life. There is considerable difference of opinion as to the best steel and iron alloys neressary to produce a satisfactory grinding ball. Some favor chrome, somr manganese and some nickel. Personally, I believe cast iron alloyed with chrome makes the best ball for small sizes; for large sizes (31/2 in. arid up) steel alloyed with mangancse is best. L. O. Howard, Pullman, Wash.—How would this method apply to hning? A. Kissock, New York, N. Y.—I do not subcrribe to that exactly. As I am connected with the Climax Molybdenum Co. you would hardly expeet me to. We have been much interested in trying to work out this grinding-ball problem and have spent a, great deal of thought and effort on it. As we are associated with the American Metal Co. and have a number of Proprrties of our own, we are in poaition to try our ideas on ourselves first. We have tried different compositions, but, have not done anything very remarkable with them yet,, except that we have been able to say that the combination of chrome and molybdenum has given the best, wearing ball. Mr. Hatch feels that iron is the best. medium for grinding, hut since toughtiess as well as hardness is a factor in wearability we feel that a well made steel is better for this purpose. Another difficulty with cast, or chilled, iron is lack of uniformity front day to day or from heat to heat, and the impossibility of protlucing balls free from blow or shrinkage holes which matcrially affect their life. If cast iron is made hard it becomes brittle and lacks strctc11 or toughness. This prevents its use in the larger sizes, aS break:lgc, is a sorious hantlic:~p to efficiency. We have trirtl hard and brittle balls and softer but very tough balls and have proved that maximum hardness, with sufficient toughuess to prevent hrcakagv, is the most important factor. in resistarnce of a steel to abrasion. It is well known that. chromium is one of the best hardening agencies for cither iron or. steel; and molybdenum is recognized as an clerment capable of introducing tonghness. In other words, the proper combination of chromium and molybdenum permits unusual hadness with still sufficient touglmess to stand up under severest impact. It is yet too early to give any actual mill results of this new Combination and though we are proving our ideas at our own properties we have to depend on others to help us make the data more general and more worth while and would like to get some testa 206

Jan 1, 1928

By T. Matthews

"One critical factor in mineral reserves reporting, as well as mine-reserves reconciliation, is the impact of dilution and ore loss in the mining process. This paper considers the implications of various factors on dilution and ore loss projections, by orebody geometry, mining method, and ore control systems. We also discuss the implications of resource estimation methodology on dilution for reserves. DEFINITIONS Dilution and ore loss are two critical concepts in mining, which address the differences encountered between modeled grade and tonnages and actual production. Dilution is volume increase and grade reduction caused by multiple factors, chief among which are mining of waste material along ore-waste contacts, mining of internal waste as ore, and misclassification of waste as ore in the ore control process. There are also geostatistical and estimation aspects sometimes lumped with dilution, including the volume-variance effect (the tendency for small volumes of material to include a less regular distribution of grade than large volumes of material). Ore loss is described as reductions of ore volumes in the mining process due to misclassification of ore as waste in the ore control process, exclusion of discontinuous mineralization from mining due to geometry or continuity, and mechanical losses in the mining process. Dilution is typically taken as an increase in tonnes of ore with no change in contained metal (and thus results in a reduction in grade.) (Some workers consider the likely grade of the diluting material as well, particularly in deposits with gradational grade boundaries—this will be addressed later in the text.) Ore loss is typically taken as a reduction in tonnes at average grade of the ore, and thus results in a reduction in both tonnes and contained metal. If model (resource) tonnes are Mt, grade is Mg, and contained metal is Mm, the resource with ore loss (L) and dilution (D) included (Rt, Rg, and Rm) will be:"

Jan 1, 2015

By M. Stefanakis, M. Errington, A. Kontopoulos, J. M. Prevosteau, K. Adam

The Olympias arsenical pyrite concentrate assaying 25 g/t Au, 40% S, 40% Fe and 12% As is highly refractory in nature; an oxidation pretreatment step is required to liberate gold and render it amenable to cyanidation. In the present study mineralogical analysis techniques including Image Analysis, SEM, EPMA, SIMS, Mossbauer, ICP/MS, etc., have been employed in order to investigate the mode of gold occurrence within the Olympias pyrites. Bacterial oxidation was used as a case pretreatment route and bacterially leached products were examined under SEM. The mineralogical observations and the relevant metallurgical and cyanidation test data were combined to establish a correlation between the mineralogical characteristics of the raw and oxidised products and conditions prevailing over the oxidative pretreatment step and the gold liberation achieved.

Jan 1, 1990

By E. Ilgar

"Deposition studies were conducted in acid copper electrolyte to determine the influence of chloride ions on cathode morphology. A statistically designed screening test was carried out in the absence and presence of 20 ppm CI- using a three factor, two level factorial design, in an electrolyte containing 36 gl'! Cu2+ and 150 gl-! H2S04, The independent variables evaluated were agitation; current density and temperature and their influence on surface roughness was determined. The copper deposited at current densities where activation was the primary control mechanism appeared similar in morphology whether stirring was used or not. The addition of 20 ppm CI- to the electrolyte gave rougher deposits under the same conditions. In the mixed control regions, considerably rougher, dendritic deposits were obtained when CI- was present. Agitation was effective in reducing the copper surface roughness both in the apparent activation and mixed control regions in the presence ofCI-. The results of this study showed that 20 ppm Cl- polarized the copper deposition at low overpotentials but caused depolarization at higher overpotentials.IntroductionChloride ion is inherently present in copper electrolyte, either as an additive or from other sources such as make up water. The behavior of the chloride ion is well documented in electrorefining operations, but its role in copper winning is less obvious. However in both cases there is evidence that cathode growth and solution chemistry are strongly influenced by its presence. The mechanism and electrochemical action of the Cl"" have been shown to be very complex, therefore a better understanding of its influence on electrocrystallization is essential for improved cathode deposit growth control. It was proposed that Cl"" polarizes the copper deposition reaction at low concentrations due to CuCI formation but depolarization occurs at higher concentrations due to the formation of a soluble CuCI2"" complex [1,2]. Franklin [3] reviewed the mechanism of additives in the electrodeposition process and proposed that the Cl"" complexed with copper, adsorbed on the cathode as an induced anion leading to an increase in the reduction rate. At cathodic overpotentials less than 100 mY, lppm NaCl had a polarizing effect, i.e. an increase in impedance of the charge transfer step. At higher Cl"" concentrations up to 100 ppm, depolarization occurred as evidenced by a decrease in impedance, which was attributed to soluble cuprous complexes [4]."

Jan 1, 1997

By A. H. Jones

The Belmont mill at Tonopah, Nev., was designed and constructed by the Belmont staff. Ground was broken in August, 1911, and milling operation started July 25, 1912. The metallurgical flow sheet, and the machinery adapted 60 carrying out operations in accordance with this plan, were decided upon from experience gained in the treatment of Belmorlt mine ores at the old Belmont mill at Millers, Nev. The detail drawings were madc by the engineering staff of the Tonopah-Belmont Development Co., under the supervision of Otto Wartenweiler, who also had direct charge of the construction, consulting with the General Superintendent of the company, Frederick Bradshaw, and the writer.

Jan 1, 1916

By E. Almendras de Siegel

Pyrometallurgical processes have the thermodynamic capability of treating complex and dirty ores and concentrates to produce high purity metals and inert slags. Modem pyrometallurgical processes are environmentally sound and competitive with other processes. However, there is still a need for sensors and other practical tools that permit a rapid evaluation of the performance of these processes. In order to contribute to satisfying this fundamental requirement, the authors developed the IDENT.LA software that permits the automatic mineralogical analyses of inorganic materials, including the final and intermediate products of pyrometallurgical processes. The technique allows determining the grain size distribution of mineralized inclusions, the surface relations between metallic phases, and conducting modal analyses of the essential phases that are present in the samples. Three basic automatic operations are performed: creating a representative image of the sample; identifying the metallic and non-metallic phases; and measuring the features of the resulting image. The results are used to evaluate the performance of pyrometallurgical and other processes. In this paper, the authors discuss the application of the technique to a sample of slag from a slag cleaning process that uses a carbonaceous reductant. In this case, process performance impacts not only on the efficient reduction of the slag magnetite and on copper recovery but also on the quality of the process off-gas. The mineralogical analysis of the slag is a valuable tool in assessing process performance and in recommending changes of operating conditions.

Jan 1, 1999

Jan 1, 1920

By C. Desmeules

"Carbon addition in the oxide pelletizing process is a big concern at the Sidbec-Normines pelletizing plant since 1976.Laboratory pot-grate testing carried out before the initial start-up of the Port-Cartier plant indicated that the nominal pelletizing grate capacity could be increased by fifteen per cent with a suitable carbon addition. Also an improved induration cycle offered the possibility of a significant energy reduction within the process with no adverse effect on pellet quality. A one-month plant scale program duplicated the lab test results and confirmed the anticipated cost saving by using these techniques. Since March 1980, Sidbec-Normines used coke addition as a current operation.This paper reviews briefly earlier laboratory and in-plant test work carried out to investigate the effects of adding carbon materials to the Fire Lake hematite concentrate, and presents operation techniques and plant results of carbon addition in the Port -Cattier pellet plant.IntroductionThe Sidbec-Normines pelletizing plant at Port-Cartier, Quebec, is designed to produce six million ton s per year of oxide pellet s. It is a Dravo-built two-line plant; one line to produce three million s tons per year of blast furnace grade pellets averaging 5.5 per cent silica, and another line of three million ton s to produce direct reduction grade pellets of about 2.0 percent silica.The laboratory pot-grate test program was conducted in 1977 at the British Steel Corporation Research Laboratories in England, with the assistance of J .E. Appleby, consultant to British Steel Corporation (overseas services) Limited.The purpose of that test program was to determine the optimum energy saving cycle and to study the physical and metallurgical effects on blast furnace and direct reduction pellets."

Jan 1, 1983

By C. R. McEwen

The displacement equations of Buckley and Lever-ett' have been successfully applied to the prediction of oil recovery in frontal drives for a number of years. Commonly, the capillary pressure term is omitted from Leverett's fractional flow formula. The resulting satura-tion-vs-distance curves become multi-valued, however. Buckley and Leverett, recognizing that the neglect of capillarity was most likely the cause, proposed that this part of the solution he ignored. An ingenious method of propagating a discontinuity in place of the multi-valued portlon of the curve was devised by Cardwell using "non-capillary displacement theory". However, it would seem that a completc description of the displacement pracess would require the inclusion of capillary forces. Three publications on displacement theory have appeared in which capillary pressure was included. Ter-williger. et al', calculated saturation profiles which matched those which they observed when gas displaced water vertically downward. Based on their study, Jones-Parra and Calhoun5 roposed a method of computing saturation distributions sufficiently removed in time from the initial conditions so that all saturations in the flood front region were assumed to move with the same velocity. This latter assumption corresponds to the tangent construction on the flowing fraction-vs-satura-tion curve proposed by Welge." A numerical solution to the problem of water displacing oil from a water-wet porous medium was recently presented by Blair, ef at'. The initial conditions included a uniform saturation slightly above interstitial water saturation. that is, the permeability to water ahead of the front was not zero. This appeared to result in a region of slowly rising water saturation ahead of the front, at least for the particular set of relative permeability and capillary pressure data used to illustrate the computation. The authors also postulated an "end-effect" at the outflow face of the system, whereby no water could pass out of the system until the water saturation had built up to a high value. The saturation profiles computed under these assumptions show water accumulating at the downstream end of the system while the flood front proper is still traveling toward the outlet. The purpose of this paper is to present the results of a numerical solution to the one-dimensional water-flooding equation in which no outlet end-effect is considered and where there is no flow of water ahead of the flood front. It should be noted that the contemporary paper of Fayers and Sheldon8 deals with the problem under discussion. For a thorough treatment including both capillarity and gravity the reader is referred to their paper.

By A. J. Phillips, A. A. Smith, J. S. Smart

THE preparation of a sufficient quantity of high-purity copper for extensive laboratory use in the study of impurity effects has been an integral part of a research program in progress at the Central Research Laboratory of the American Smelting and Refining Co. for the past several years. Initially the degree of purity desired was that necessary to meet two essential requirements for experimental accuracy: (I) no impurity was to be present in the copper in an amount capable of producing a detectable effect on the properties to be studied, (2) even the minor changes in properties caused by the addition of extremely small amounts of individual elements were to be measured without significant interference from contaminants. In the course of the investigation, evidence has accumulated to justify the conclusion that this copper is of exceptional purity; in fact, no impurity can be detected by any chemical method or spectrographic technique known to the authors. The present paper describes the method of production of the copper and presents some of its properties. PREPARATION OF HIGH-PURITY COPPER The elimination of impurities from commercial electrolytic copper is accomplished by a three-step purification process. The first operation consists of an electrolysis through a purified CuS04-H2SO4 electrolyte using bagged anodes, low current .density (5 amp. per sq. ft.) and low temperature (25°C. max.). The electrolyte is prepared from commercial Cu2SO4 and is purified by heating the solution and adding I gram Fe as Fe 2(S04)3 to each 100 grams dissolved copper; sufficient hydrated oxide of copper, prepared from Cu2SO4 and NaOH, is supplied to precipitate Fe(OH)3, which carries down arsenic, antimony, tin, selenium, tellurium and other minor constituents. Silver and remaining traces of lead are removed by addition of Na2S to the acidified filtrate, which is then refiltered after standing hot overnight. The cold solution is made up to 30 grams per liter Cu and 150 grams per liter H2S04 and introduced without addition agents into the electrolytic system, which consists of a double row of hard-rubber battery boxes with the inside webbing and partitions removed, arranged in seven steps of ascending height. Electrolyte is uniformly supplied to the two highest cells by glass siphons operating from a constant-level reservoir, and flows by gravity through the bank of seven cells, entering each at the bottom and leaving at the top. Glass air lifts continuously supply the returning liquid to the constant-level reservoir for recirculation. Each cell contains three 434 by 43a by I-in anodes cast from high-quality electrolytic wire bar copper, various lots of which have been used with equal success. The anodes are pinned to sheet copper hangars shaped to prevent crawl of the electrolyte to the multiple-wired bus bars-which would result in fouling of the contacts and hang inside wool flannel bags stretched over open wood frames. The deposit

Jan 1, 1941

By D A. Kepert, D Clark

During early 2004, Fortescue Metals Group (FMG) began an aggressive exploration and drilling program in the Chichester Range, targeting iron enrichment developed in the Nammuldi Member at the base of the Marra Mamba Iron Formation. The timely recognition by FMG of distinct zones of (hypogene) microplaty hematite (mplH) enrichment overprinted by extensive supergene mineralisation led to an early reappraisal of the geological history of the area and characterisation of the possible structural and stratigraphic controls on mineralisation. Regionally, the Chichester Range dips gently at less than 5¦ to the south, however, detailed mapping shows that this regional limb is overprinted by low amplitude, long wavelength, north/south to northeast/southwest trending folds. The locations of major structures in the Marra Mamba Iron Formation, combined with spectral analysis of known mineralisation, allowed extrapolation and prioritisation of exploration target areas. The delineation under cover and understanding of these structures was enhanced by detailed airborne magnetic data. Recognition that supergene mineralisation was associated with a palaeotopography that continued significantly under cover to the south under sediments of the Fortescue River valley led to the discovery of extensive supergene mineralisation together with additional mplH mineralisation. A model for the landscape evolution and preservation of enriched Nammuldi Member was generated in order to help communicate both the complexities involved with targeting drill holes beneath cover and the potential limits to the lateral extents of mineralisation.

Jan 1, 2005

By Thomas P. Meloy

As the importance of particle shape in mineral processing is increasingly recognized as an major variable in predicting the behavior of both individual particles and particle systems, whether it be in dense media, froth flotation, comminution or the flow of particles, new method of shape characterization are being developed, particularly for use on image analyzers. These shape characterization methods may be broadly classified into the analytical, empirical and physical formation methods. Discussed are approaches and the strengths and weakness of each of these methods. Moreover old and new shape measuring techniques are reviewed, particularly the new image analysis methods techniques such as Fourier, Haar, Fractal, Walsh and Delta as well as a variety of other techniques such as tabling, the Cascadograph, settling and L/D ratios. Also discussed are the problems of doing shape research, current progress and the future of the field.

Jan 1, 1990

By Douglas Bunting

The first presentation of this paper was before the Pennsylvania Anthracite Section of the Institute in May, 1914, after which a committee was selected to verify and add to the data contained in the original paper. The author is indebted to G. W. Engel, H. W. Montz, R. V. Norris, and H. H. Otto, of this committee, for additional information. I also wish to acknowledge the courtesies extended me by a number of the mining companies for information relative to accidents, systems of proving, and mining practice. The paper should bring forth additional criticism and recommendations, which will be of value in establishing future practice relative to this subject. Throughout the northern anthracite field of Pennsylvania glacial and alluvial deposits of sand, gravel, and clay exist in varying quantities. The extent and character of these deposits are described by N. H. Darton in Bulletin 45 of the U. S. Bureau of Mines, entitled, Sand Available for Filling Mine Workings in the Northern Anthracite Basin. It is estimated that the northern field contains 10,000,000,000 tons of these deposits, or a sufficient quantity to cover the 176 square miles of coal area to a depth of about 25 ft. These deposits of sand, etc., overlying the coal measures attain a maximum depth of more than 300 ft., and are usually saturated to such an extent as to render them semi-fluid. It is this condition of fluidity that limits the mining of coal seams cropping in or in close proximity to these deposits, and it is in the interest of safer and more efficient mining methods under these conditions that the study of this subject is here presented. The dangers incident to mining under deep deposits of sand have long been realized by operators in the northern anthracite field, and much has been done to prove the contour of the rock and vein croppings underlying these water-bearing deposits of sand and gravel. Although, as far as we know, the accidents of the past have not resulted in the loss of life, except in two instances, yet nearly all were attended with more or less miraculous escapes of men working in the vicinity of the breaks, so that the probable existence of pot holes, etc.,

Jan 1, 1915

By R. E. Zane

[The Northwest Experiment Station of the Bureau of lines, in cooperation with the College of Mines, University of Washington, has completed a detailed investigation of the physical and chemical properties of western cokes made or used in the Pacific Northwest, as evaluated by standard methods. 4/ One of the chemical properties determined, to which more or less importance has been attached, was reactivity or combustibility. As no standardized procedure is available, it was necessary to develop a workable method for evaluating this property. The combustibility of coke is usually measured by the formation of carbon dioxide with time at a particular temperature or by the reduction of carbon dioxide to carbon monoxide. Analysis of the resulting gases commonly is required to evaluate the result. The method described in this paper is simple and direct in that the sample of coke or other carbonaceous material is weighed as it burns; the loss in weight and time is indicated by a balance and clock arrangement. Gas analyses are not rewired. Methods similar in principle have been used by Tu, Davis, and Hottel6/ and by Oshima and Fukuda7/ for determining the combustion rate of carbon and for studying the effect of ash on combustion characteristics. Both methods: are more elaborate in procedure and apparatus required than teat described here. Brief the method comprises burning a sample of coarsely grained. coke or]

Jan 1, 1940

By Robert Agar

This paper reviews the mineral exploration applications of satellite and airborne multi- and hyperspectral data and field spectrometers, and attempts to provide a setting in which each might be best applied.

Apr 24, 2001

By D. L. Ward

This paper is the result of a study, in 1919, to determine how much surplus power could be produced through the proper utilization of the entire gas flow from the two furnace stacks at the Federal Furnace Plant, South Chicago, Ill. Obviously, the problem was to measure the flow of gas through the main beyond the point where the amount necessary for stove operation was removed. In all probability, blast-furnace gas is the most difficult gas to measure, because of the high moisture and dust content, and the widely fluctuating flow from the furnaces. This wide fluctuation of flow forbids the acceptance of any one group of flow readings as indicative of normal operating conditions. A study of the conditions showed that a recording device on gas flow was necessary. As the gas at the point of measurement had passed through wet washers, and accordingly was saturated with water and contained considerable dust carried past the scrubbers in the form of sludge, no form of Pitot tube could be used, for this sludge would quickly plug the dynamic and static holes, spoiling the gage readings. An even more serious objection to the use of Pitot tubes was the impossibility of accurately measuring the cross-sectional area of the gas main on the plane of Pitot-tube installation. Given an absolutely clean gas and a perfectly circular pipe, it would be safe to assume, through measurements of the pipe diameter, that the gas main was of a certain cross-sectional area. But the continual depositing of sludge and the fact that the main was fabricated from riveted sheets led us to discard the idea of using Pitot tubes for this service. The Venturi tube was then considered, and had there been a sufficiently long straight run of gas main to accommodate a tube of the required size (72 by 28 in.) such an installation would very likely have been made.

Jan 2, 1921

FOR some time it has been recognised by the Metallurgical Staff that the presence of pyrite in the ore was adversely affecting the grades of the flotation concentrates.Following experimental work, it was decided to change over from the acid circuit in the mill to an alkaline circuit. The following description sets out the procedure adopted, -and the results obtained when such change-over was made.The Zinc Corporation ore consists mainly of galena, marmatite, calcite, and quartz, with smaller quantities of pyrite, fluorspar, and rhodonite.A clean specimen of marmatite picked from the ore assayed 53.4% zinc, and 10% iron, with no lead or insoluble. However, as zinc concentrates have been, at times, produced in the plant assaying over 53% zinc, and with only 8.7% iron, apparently the picked specimen of marmatite did not represent an average composition.The average would probltbly be between 8 and 9% of iron, and from 53.5 to 54.5% of zinc. It is obvious, therefore, that from this ore it is not possible to produce zinc concentrate of a higher grade than this average figure.In the Colorado School of Mines Quarterly for April, 1928, Vol. 23, No. 2, on page 47, we find the following statement:As the zinc in the ore exists as marmatite, which contains approximately 54.5% zinc and 10% iron, 49% zinc in the concentrate may be considered high.This statement refers to the ore treated in the Sullivan concentrator, owned by the Consolidated Mining and Smelting Company of Canada Limited.

Jan 1, 1930

By B. M. Larsen, T. E. Brower

INTRODUCTION THIS discussion is based on statistical manipulation and evaluation of operating data from several commercial blast furnaces which include rather wide variations in practice. We are concerned here mainly with the effect of manganese on sulphur elimination under operating conditions in commercial blast furnaces, but this effect can be outlined more clearly by including certain other variables such as silicon in iron and slag basicity, which are all in part interrelated. Real progress in understanding all of the smelting-zone reactions in this process requires more laboratory studies of slagmetal melts similar to those in the blast furnace, with careful control of oxygen pressure. Such experimental work is very difficult, however, and in the meantime, with the present scarcity of more fundamental data, such statistical trends and correlations as can be obtained from commercial furnace operating records may help in choosing laboratory test conditions as well as adding to our knowledge of operating procedures. We do not know just why the furnace data are apparently so irregular that statistical treatment of large numbers is needed to obtain accurate trends. It is .partly caused, no doubt, by the many simultaneous variables present, but there are perhaps also such factors as: (I) the continual swings up and down so characteristic of the process; (2) difficulty of accurate sampling of co-existing phases, as well as (3) the presence of both equilibrium and rate factors as a result of the fast driving of the process, In desulphurization, for example, the flow of thin layers of slag and metal over solid coke surfaces, plus the contact between droplets of iron falling through the slag layer in the hearth, would lead one to expect a close approach to equilibrium, On the other hand, most of the critical part of sulphur removal may occur in a short time and distance below the tuyeres with perhaps an accompanying decrease in oxygen pressure and the concurrent reduction of much of the silicon and manganese, so its degree of approach to equilibrium may be quite variable. PROBABLE CHEMISTRY OF DESULPHURIZATION Since there is little evidence that sulphur atoms in the iron solution are associated to any appreciable extent in molecules such as MnS, the transfer from slag to metal and back again can be written:* [(FeS) -, [FeS],[I] hence the following reactions seem most probable in the slag phase, (FeS) + (CaO) = (CaS) + (FeO), [2] and, (FeS) + (MnO) ;:2 (MnS) + (FeO). [31]

Jan 1, 1948

Reverse sensitivity is a critical issue for all extractive activities. Extractive industries can only establish in the location of the particular resource sought to be extracted. Avoiding a location near sensitive activities (such as residential activities) may, therefore, be more difficult for extractive industries, than for other industry (such as dairy factories).   This paper focuses on the following matters: +        principles to be derived from case law, +       district and regional council approaches managing reverse sensitivity effects, and +        avoiding, remedying or mitigating reverse sensitivity effects in the future.

Jan 1, 2006

By L. Adler

Two basic cases involved in the design of an opening in bedded rock are: 1) where the beds deflect from each other so as to be separated; and 2) where the beds deflect onto their lower neighbor, loading the latter while reducing their own load. Analysis of case 1 is relatively simple, while the interference of the original deflection curves in case 2 complicates analysis of the latter. Figures and formulae are presented for determination of interference loading in this situation. The design of an opening in bedded rock involves two basic alternatives.1'2 In one case the beds deflect away from each other, so as to be separated from their neighbors; in the other case the beds deflect onto their lower neighbor, loading it, while reducing their own load. This is shown in Fig. 1. The first case lends itself to a simple analysis, since the upper and lower boundaries of each beam remain a free surface. In the latter case, however, due to the interference of original deflection curves, the analysis is more complex. Earlier investigators of this interference problem solved it by making the tacit assumption that this type of loading was uniformly distributed along the beam's length. While there is no intuitive justification for this assumption, its use does lead to an approximate solution. Still, a more exact solution does not require this apparently unrealistic restriction. To achieve initial simplicity, the analysis will at first be limited to a two-bedded sequence, as in Fig. 2. Since both beams have identical end conditions and spans, the original deflections of their center lines are members of the same family of curves, as shown in Fig. 3. Therefore, if interference occurs at one point along their center lines, it will occur at every point. For convenience, the midspan point is that usually examined. Deflection at midspan for a uniformly loaded beam regardless of end conditions is: where c is a constant depending on end conditions; w is the body load and equals yh, lb per ft; y is the specific weight of rock, lb per ft'; L is the span, ft; E is Young's Modulus, lb per ft2; I is moment of inertia (for a rectangular section), I = bh3/12 = h3/12, (ft4); b is the width of beam and equals one; and h is the thickness of beam, ft; or 3U > yB an Substituting the appropriate values into Eq. lb, interference between the two beds can be predicted. Should it occur, the additional loads along the lower boundary of the upper bed and the upper boundary of the lower bed must be determined. From the principle of action and reaction, these added loads are known to be equal and opposite, as indicated in Fig. 4. Since the final deflection curves for both beds are identical (Fig. 3), their successive derivatives of y with respect tox must also be identical. That is:

Jan 1, 1961