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By P. C. Upadhyay, J. G. Singh

Reissner's thick plate bending theory has been recast for rocks which exhibit the property of double elasticity: different Young's modulus and Poisson's ratio in compression and tension. The governing differential equation and other relevent expressions have been presented in a form compatible to the applied mechanics results so that they can readily be used. Effect of the ratio of Young's modulii in compression and tension, (Ec/Et), on the maximum plate deflection and the maximum bending moments has been evaluated over a wide range. It has been found that the inclusion of bi-modulus property through a parameter (ß = Ec/Et), changes the sheer deformation of the plate to such an extent that the bi-modular effect of rock cannot be overlooked in the thick plate analysis, especially when ß is expected to be greater than 2.

Jan 1, 1982

Established as a Division September 27, 1949 LeRoy Scharon, Chairman C. M. Cooley, Secretary 29 West 39th Street New York 18, N Y

Jan 1, 1952

By David B. Brooks

Identified potential resources of lead and zinc are lower, relative to reserves, than the same ratio for other metals, Either there is little material below present grades or, if it exists, there are no data on it. The author examines both these factors in detail, and also introduces a third possibility. In their 1961 monograph, The Future Supply of the Major Metals, Bruce Netschert and Hans Landsberg noted that identified potential resources (that is, known but submarginal resources) of lead and zinc were much lower relative to reserves (that is, known and supermarginal resources) than was the same ratio for other metals.' Put another way, it seemed that for such metals as iron, manganese, copper, and aluminum, slightly more favorable economic conditions or modest advances in technology would greatly increase reserves by permitting the exploitation of vast quantities of leaner or deeper or otherwise less valuable mineral deposits. But for lead and zinc, Netschert and Landsberg concluded that either: "(1) there is relatively little material below present cutoff grades; [or] (2) such material exists, but for some reason there are no data.'12 This situation, which they called "the lead-zinc anomaly'' has been subsequently discussed by other authors. The purpose of this paper is to carry the discussion further by examining the evidence in favor of (1) and (2) and by advancing a third alternative. There are at least two reasons for devoting time to the lead-zinc anomaly. First, while it is unlikely that we shall have to turn to alternative lead or zinc resources in the near or middle-term future, the longer run resource picture for the two metals is not so certain.3 Both within the United States and for the world as a whole, new discoveries will have to come at a fair pace to keep up with growing rates of consumption. Thus, it is important to see whether there exist lower grade or nonconventional potential sources of two such useful metals that we could turn to at some time in the future. The second reason for studying the lead-zinc anomaly is also related to resource adequacy, but is of more general significance. Depending upon whether the anomaly is technologic, geochemical, spatial, or temporal in origin, we shall be able to draw some conclusions about the resource picture for other metals. Can we expect the apparent pattern of lead-zinc resources to be repeated? If so, will technologic advances in either exploration methods or mineral processing be able to alter the pattern? Or is the pattern unalterably set by geochemical distribution? Most important, are metals characterized by what seems to be an anomaly, different in any way from metals for which low-grade or nonconventional sources already have come to be exploited, as the porphyry deposits have for copper. In sum, investigation of the lead-zinc anomaly represents a case study combining both physical and economic aspects that may open up a neglected area in evaluating mineral resource adequacy. WHAT IS THE LEALLZINC ANOMALY? There are two dimensions to evaluations of the potential of any mineral resource? The first involves the degree of certainty that we ascribe to the estimate: how much do we know about the size of the resource as a result of geological mapping, exploration, and mine development? This dimension is expressed by the terms measured, indicated, and inferred reserves (and, if you wish, 'undiscovered reserves'), all of which terms carry with them the implication of exploitability under current cost-price conditions. The other dimension to evaluations of a mineral resource involves the economic limits of the estimate: how will the size of the resource vary with different (usually more favorable) cost-price conditions? (This economic dimension should be understood broadly to include all factors bearing on the cost-price relationship. In this sense it subsumes technology because any resource is exploitable at some cost; the role of technology is to bring cost down.) The latter dimension is expressed in the terms potential or sub-marginal 'ore,' and is logically quite independent of the former. For example, we have relatively good measurements of the tonnage of manganese in low-grade deposits in this country, though they are too lean to be considered reserves; on the other hand, we are much less certain of our measurements of new lead and zinc deposits in Missouri, though there is no question but that there is a sizable reserve. Thus, it may be uncommon but is not a contradiction to talk of measured submarginal ore or inferred potential ore.

Jan 1, 1968

HOWARD N. EAVENSON, Chairman C. T. HAYDEN, Vice-chairman, Bituminous Coal Production CHARLES DORRANC~ Vice-chairman, Anthracite Coal Production HOWARD P. ZELLW, Vice-chairman, Evaluation of Coal for Coke Making W. H. F'LTLWEILER, Vice- Chairman Gas and Its Manufacture 3. B. MORROW, Vice chairman, Coal Preparation

Jan 1, 1928

By H. Matlock

Beam-columns with continuous or discontinuous transverse and angular loads and elastic restraints are represented mathematically in a manner corresponding to finite-element mechanical models. Solutions for linearly elastic cases are accomplished by direct recursion-equation elimination of unknowns, and for cases involving nonlinear loads and supports, by repeated trial-and-adjustment of complete elastic-type solutions. Five practical applications are presented by which various capabilities of the general method are illustrated. The examples include simulation of a pipeline launching and the bending and collapse of a conductor pipe in deep-water drilling operations. INTRODUCTION The diversified and complex operations being conducted in support of the production of offshore oil have produced a wide variety of new problems in structural mechanics. Many of these problems cannot be solved by conventional analytical or experimental approaches and have therefore stimulated inquiry into new methods of solution. It is the purpose of this paper to give a brief description of an analytical method for solving nonlinear beam-column problems and to illustrate the generality of the method by applying it to several problems related to offshore operations. Although the data for all of the examples are artificial, the cases discussed will be recognized as being based on actual situations. DESCRIPTION OF METHOD The analytical approach which is to be described stems from research on offshore foundations, in particular, the study of lateral-load behavior of foundation piles. The method represents a generalization of a technique which was suggested by Gleser' and extended by Focht and McClelland2 and Reese and Matlock." To maintain generality and therefore versatility in the method, a considerable variety of input data is considered. Fig. 1 illustrates the various types of loads and restraints which might be applied to a short segment of a beam. Each of the terms illustrated in the figure is shown acting in a positive sense. Capital letters are used to designate concentrated quantities whereas the corresponding lower-case symbols indicate effects which are distributed in some way along the length of the beam. The transverse loads and the elastic restraints may be divided into two classes: (1) loads Q and q and springs S and s, which act normal to the axis of the beam, and (2) couples T and t and rotational springs R and r, which act in an angular sense. In addition, there is an axial force P which may be constant or may vary along the length of the beam. The bending stiffness of the beam (the product EI of the modulus of elasticity and the moment of inertia) is designated by the symbol F. The assumptions of conventional elementary beam theory provide the basis for the present method. Among these are the neglect of shearing and axial deformations and the limiting of consideration to straight beams of symmetrical cross-section. Lateral deflections are considered to be small compared to original dimensions. A deformed element of such a beam is shown in Fig. 2a. The curvature of the beam is approximated by the second derivative of the deflection y with respect to distance x along the beam. It is assumed that the material of the beam is linearly elastic and therefore the relation of Eq. 1 between curvature and bending moment M is the ordinary expression from elementary beam theory. A generalized beam element is shown in Fig. 2b. The element has been deflected in a positive direction by an amount y and tilted through a small positive angle dy/dx. The various loads and elastic restraint reactions are detailed in the figure. Temporarily, only distributed effects are considered; provision for concentrated loads and restraints will be made subsequently. Eq. 2 in Fig. 2b is obtained by summing the forces and moments acting on

By C. R. McEwen

This paper presents a technique for calculating the original amount of hydrocarbon in place in a petroleum reservoir, and for determining the constants characterizing the aquifer performance, based on pressure-production data. A method for doing this based on a least-squares line-fitting computationwus proposed by vanEverdingen,Timmerman andMcMahon in 1953. We found that their method would not work when there is error in the reservoir pressure data — even moderate error. The technique presented here appears to give reasonable answers when pressure data are uncertain to the degree expected in reservoir pressure determinations. The major change introduced in the present analysis is to limit the least-squares line-fitting to yield only one constant— the amount of hydrocarbon in place. The water-influx constant is then taken as proportional to the oil (or gas) in place. The constant of proportionality can be computed from estimates of effective compressibility and reservoir water saturation. It is also pointed out that the commonly used least-squares analysis assumes all of the uncertainty to be in the dependent variable. The material balance should be arranged so that this condition is fulfilled if correct inferences are to be made from statistical calculations. Examples are shown of the application of the new technique to gas reservoirs—both hypothetical and real—and to the oil-reservoir example of van Ever-dingen, Timmerman and McMahon. INTRODUCTION The amount of hydrocarbon originally in place in a petroleum resenroir can be estimated by means of the material-balance calculation. Simultaneous observations of pressure and amounts of produced fluids are required, together with the PVT data applicable to the reservoir fluids. If water encroachment is occurring, it is desirable to try to infer the behavior of the aquifer, as well as the original hydrocarbon in place, from the pressure-production data. This imposes additional demands on the method of calculation, and uncertainty in the data can result in large uncertainty in the answer. In addition, if the size of a gas cap is to be established, the whole problem becomes indeterminate, as pointed out by Woods and Muskat.1 Brownscombe and Collins2 simulated a gas reservoir and its aquifer on a reservoir analyzer and derived quantitative information on the effect of uncertainty in pressure and aquifer permeability on computed gas in place. Among the various techniques of estimating the performance of an aquifer, the method of van Ever-dingen and Hurst? based on compressible flow theory, seems to have been the most generally successful (see Ref. 4, for example). In this paper we shall confine ourselves to their representation of the aquifer. In 1953,' van Everdingen, Timmerman and McMahon5 introduced a statistical technique for deriving the amount of oil originally in place and the parameters which describe the aquifer. (We shall refer to this technique as the "VTM method'', as suggested by Mueller.6) Their example reservoir had no gas cap. It has been our experience that the VTM method gives a reasonable answer when the data are very accurate, but that inaccuracy (particularly in pressure) can cause the method to break down. The effect was first observed in gas reservoirs, but has since been seen in oil reservoirs also. In this paper we present another statistical method which has been successful in achieving a reasonable answer where the VTM method has failed. In the new method, one less parameter is derived from material-balance computations. It is assumed that values can be established for effective compressibility in the aquifer and reservoir water saturation independently of the material-balance calculation. The water-influx constant can then be obtained from these data and the quantity of hydrocarbon in place.

By Ken-ichi Hirano, B. L. Averbach, Morris Cohen, N. Ujiiye

The influence of plastic deformation in compression on the self-diffisivity of a iron has been measured in the temperature range of 742º to 885°C. The diffusivity is enhanced in proportion to the strain rate, but this dependence decreases with increasing temperature. The magnitude of the strain is relatively unimportant in this connection. Strain rates from 0 to -2 x 10-3 sec-1 were investigated, with a corresponding increase in diffusivity up to 3 x 103 times. The results are analyzed in terms of vacancy diffusion and the excess vacancies introduced during dejornzntion. It is concluded that grain boundaries are the main vacancy sinks in polycrystalline iron and that the vacancy lifetime is therefore dependent on the grain size. A typical vacancy lifetime at 800°C with a nzean grain-boundary intercept of 0.3 cm is of the order of 1 sec. LATTICE imperfections are considered to be the dominant mechanism of diffusion in close-packed crystals. Vacant lattice sites are usually the most important defect, but the enhancement of diffusion along grain boundaries and other short-circuiting paths has been well documented. Inasmuch as plastic straining produces a variety of defects, it would be expected that the application of stresses sufficient to cause plastic flow during a diffusion run might result in an increase in the self-diffusivity. Enhanced self-diffusion in a iron under compressive creep has been observed by Buffington and Cohen' and subsequent coworkers.2 Lee and Maddin3,4 have also found an enhancement in the self-diffusivity of silver single crystals undergoing torsional deformation. On the other hand, Darby, Tomizuka, and Balluffi5 have not observed any significant diffusion increase in single crystals of silver deformed either in tension or in compression, although the results in this case may have been affected by the occurrence of recrystallization. With poly crystalline silver, however, Forestieri and Girifalco6 have found en- hanced diffusion during compressive creep. A small decrease in the self-diffusivity of zinc single crystals under compressive loading has been reported,7 but the applied stresses in these experiments were too low to cause appreciable plastic deformation. For the cases in which enhanced diffusion has been found, a number of common effects have been noted. Usually, the ratio of the diffusivity during straining, Ds, to the diffusivity in the unstrained condition, D,, varies linearly with the strain rate, and does not seem to be a function of the plastic strain, at least up to ? = 0.2. Values of Ds/Du of the order of 100 have been reported'-4 but the enhancement decreases with increasing diffusion temperature. The activation energy for diffusion decreases markedly with increasing strain rate and approaches a level of roughly one-half the unstrained value. Most of the current explanations of these observations assume that excess vacancies are generated by the deformation, but rather large concentrations of excess vacancies and/or long lifetimes are required by these theories.',',',' Since the original work on iron, there has been an important improvement in the compressive-loading technique.2 The early data were also analyzed without taking into account the motion of the coordinate system in the specimens undergoing plastic deformation. This problem has now been solved by a number of investigators (see Refs. 11, 12, and the appendix of the present paper). Consequently, the strain-diffusion runs on iron for the Ds measurements were repeated and extended over wider ranges of temperature and strain rate. In addition, the original diffusivity data9 on the unstrained iron have been corrected for the divergence of the beam in the counting system and new data points have been added, resulting in somewhat different values for the self-diffusi-vities in a iron.10 The new values for Du are used in this paper. A comparison of Ds and Du confirms the large enhancement in the self-diffusivity of iron during compressive creep, as previously reported.',2

Jan 1, 1963

By Richard H. Siller, Rex B. McLellan

A model for interstitial solid solutions has been considered in which a repulsive Potential exists between interstitial atoms in the solvent lattice. It has been shown that this model is consistent with the thermodynamic Properties of certain interstitial solid solutions. The model is then applied to the calculation of the variation of the diffusivity of carbon in au-tenite with composition. Although the energy levels at the saddle point, and thus the absolute values of dif-fusivity, cannot be calculated, it is shown that by taking the repulsive interactions between the diffusing atoms into account the functional form of the dependence of diffusivity on solute concentration can be derived. ThE composition dependence of the diffusivity, D, of carbon in austenite at a given temperature is well-known.'-3 smith3 tried to reconcile the observed composition dependence of D at 1000°C with the previously observed4 composition dependence of carbon activity using equations for D derived by arken5 and Fisher, Hollomon, and Turnbull,6 but was unsuccessful. In this paper we shall modify the approach of Fisher et al. by considering the "blocking" model7 for interstitial solid solutions, based on concept due to Speiser and Spretnak,' in which a repulsive potential exists between interstitial solute atoms in the solvent lattice, causing a certain number of interstitial sites to be "blocked" from occupancy by further solute atoms. We shall thus be able to describe the intimate relationship between the composition dependence of carbon diffusivity, a kinetic phenomenon, and the composition dependence of carbon activity in austenite. THEORY Consider for convenience one-dimensional interstitial diffusion in an fcc lattice in the [loo] direction. Fig. 1. Assume that solute atoms occupy octahedral sites only.7,9'10 These octahedral sites are located on {lOO} planes a/2Å apart. A solute atom, A, occupying an octahedral site on a {100 } plane denoted by 2, has twelve nearest-neighbor octahedral sites: four on plane 1, four on plane 2, and four on plane 3. Diffusion occurs when there is a net flux of solute atoms, through an imaginary plane shown with dashed lines, from plane 2 to plane 3. Fisher et al6. use the concept of activated complexes, as given in the theory of absolute reaction rates." They show that the number of solute atoms per cubic centimeter per second which pc — Fig. 1-Diagram showing the arrangement of octahedral sites (x) in the fcc lattice. pass in the direction of diffusion from activated to new interstitial position is: ?where C is the concentration of the solute in atoms per cubic centimeter, l/m + is the fraction of new interstitial positions corresponding to motion in the forward diffusion direction (transmission coefficient), ?F* is the free-energy difference between the activated complex and the reactants when each is in its standard state at the temperature of the reaction (independent of temperature and composition in the case of carbon in austenite), y is the activity coefficient of the solute species, and, finally, ym is the activity coefficient of the activated complex (assumed constant). The flux of atoms moving in the forward direction through an area of 1 sq cm perpendicular to the direction of diffusion is therefore: m+ Ym l ' atoms per second where is the distance between planes. The blocking model states that a nearest-neighbor octahedral site of a given solute atom has a probability, f, of being inaccessible to other solute atoms. The number of available sites for diffusion on a given plane will, therefore, depend on f, which is constant, and Nu, the number of solute atoms on that plane. The effect is to have more available sites in the diffusion direction, thereby increasing the net flux of solute atoms. This is reflected in the transmission coefficient, l/m. To calculate the transmission coefficient for solute

Jan 1, 1970

By J. Boldy

Discovery of the Delbridge massive sulfide deposit in the Noranda district of Quebec resulted from an appreciation of the significance of a mercury leakage halo as a lithochemical pathfinder to blind ore. Its location, relative to a geologically inferred ore-bearing horizon within complex volcanic stratigraphy was also a factor. Systematic sampling of microfractures present in outcrops delineated a diagnostic anomaly, drawing attention to an area considered prospective for buried ore. The massive sulfide deposit was subsequently found to be blind and topped at the 110-m (360-ft) level.

Jan 1, 1985

By William R. Webster

The unusual interest taken in the papers on steel at the New York (1922) meeting showed that the time is ripe for the renewal of the general discussion of the physics of steel, on the same lines that wete used formerly and produced such good and lasting results. The curves shown in Figs. 1 to 4 and the appendix were added to my paper1 after the February meeting, but, unfortunately, Figs. 1 and 3 were transposed; the curves on page 252 are for bessemer steel and belong on page 254; while those on page 254 are for open-hearth steel and belong on page 252. These errors are evident at once on referring to the data in Tables 1 and 2, pages 227 and 228. The curves for each 0.05 per cent. of carbon and manganese in basic open-hearth steel are given in Figs. 1 and 2; these lines for the lower carbons and manganese are comparatively uniform. Figs. 3 and 4 give similar lines for carbon and manganese in bessemer steel. The large break in the carbon lines from 0.55 per cent. to 0.60 per cent. is caused by much higher silicon in the steels of 0.60 per cent, carbon and over that are used for springs, etc. The estimated ultimate strength of pure iron, and the increase in strength by carbon, phosphorus, and manganese, with the different views regarding the same, were given and diseussed. All of this can be considered as an introduction to the practical use that is now being made of such data in selecting the heats of steel best suited to give the required physical tests called for in the finished rolled material. The chemical composition of the steel, of course, tells only a part of the story, as many other factors that have an influence on the physical properties of the steel must be considered, and controlled as far as is possible. Some of these have already been referred to, but there are other important ones to be considered and discussed.

Jan 1, 1923

By William R. Webster

The unusual interest taken in the papers on steel at the New York (1922) meeting showed that the time is ripe for the renewal of the general discussion of the physics of steel, on the same lines that wete used formerly and produced such good and lasting results. The curves shown in Figs. 1 to 4 and the appendix were added to my paper1 after the February meeting, but, unfortunately, Figs. 1 and 3 were transposed; the curves on page 252 are for bessemer steel and belong on page 254; while those on page 254 are for open-hearth steel and belong on page 252. These errors are evident at once on referring to the data in Tables 1 and 2, pages 227 and 228. The curves for each 0.05 per cent. of carbon and manganese in basic open-hearth steel are given in Figs. 1 and 2; these lines for the lower carbons and manganese are comparatively uniform. Figs. 3 and 4 give similar lines for carbon and manganese in bessemer steel. The large break in the carbon lines from 0.55 per cent. to 0.60 per cent. is caused by much higher silicon in the steels of 0.60 per cent, carbon and over that are used for springs, etc. The estimated ultimate strength of pure iron, and the increase in strength by carbon, phosphorus, and manganese, with the different views regarding the same, were given and diseussed. All of this can be considered as an introduction to the practical use that is now being made of such data in selecting the heats of steel best suited to give the required physical tests called for in the finished rolled material. The chemical composition of the steel, of course, tells only a part of the story, as many other factors that have an influence on the physical properties of the steel must be considered, and controlled as far as is possible. Some of these have already been referred to, but there are other important ones to be considered and discussed.

Jan 1, 1923

Powder Metallurgy Committee Local Sections DETROIT Robert Henderson, President, Victor Gallatin, Vice-President, Secretary, J I Farmer, Treasurer John Check, NEW YORK K H Roll, Chairman

Jan 1, 1957

PRESIDENT ROBERT E. TALLY, JEROME, ARIZ. PAST PRESIDENTS FREDERICK W. BRADLEY, SAN FRANCISCO, CAL. WILLIAM H. BASSETT, WATERBURY, CONN. TREASURER KARL EILERS, NEW YORK, N. Y.

Jan 1, 1923

By Robert Glass Cleland

[NEW YORK OFFICE James Douglas President Chairman of Board Walter Douglas Vice-president President Louis S. Cates President Cleveland H. Dodge Vice-President Chairman of Board]

Jan 1, 1952

By G. T. Horne, P. J. Wray, S. Kinoshita

CONSIDERABLE evidence exists for a strengthening mechanism operative at intermediate temperatures in bee metals containing interstitial solute atoms. The strengthening is indicated by a maximum in the ultimate tensile strength1 as well as the fatigue

Jan 1, 1965

1-Coal and Coal Products HOWARD N EAVENSON, Chairman C. T. HAYDEN, Vice-chairman, Bituminous Coal Production CHARLES DORRANCE, Vice-chairman, Anthracite Coal Production HOWARD P. ZELLER, Vice-chairman, Evaluation of Coal for Coke Making W H. FULWEILER, Vice-chairman, Gas and Its Manufacture J. B. MORROW, Vice-chairman, Coal Preparation Bituminous Coal Production C. T. HAYDEN, Chairman R L ADAMS EUGENE MCAULIFFE HAROLD J ROSE WILLIAM H BLAUVELT H E NOLD D. A RUSSELL GEORGE W EVANS JAMES W PAUL CECIL W. SMITH JOHN A GARCIA GEORGE S RICE SAMUEL A TAYLOR H. S GEISMER W F RITTMAN F G TRYON FRANK HAAS J D ROGERS FRANCIS R WADLEIGH CHESTER M LINGLE

Jan 1, 1923

By H. W. Peirce

Identified and utilized Arizona salt deposits are of two ages: 1) Permian in the Colorado Plateau, and 2) Tertiary in the Basin and Range country. Uses include: a) storage of energy fluids in man-made solution cavities in both Permian (Supai Formation) and Tertiary (Luke salt body) salt and b) production of marketable products by solution and evaporation of tertiary salt. The two liquid petroleum storage Projects have a combined storage capacity in excess of 380 million L (100 million gal). Current production of salt products approximates 32 kt/a (32,000 stpy). Increasing demand for both storage and salt products is anticipated.

Jan 1, 1983

ALL that I have been able to tell you concerning the ordinary practice of parting with aqua fords I have striven to demonstrate to you as briefly as possible. Now, before passing on to speak of other things, I wish to teach you the method that you must follow in order to recover whatever is good in those chalky precipitates of that acid and all the silver that you put in; it was for this reason that I told you to save them in a cucurbit by themselves. This is called "water of whites" by the master parters, and in reality is nothing other than the precipitates of thick phlegm of aqua fords, white as chalk. If these were not extracted from the acid, the spirits of the infused materials [69] would be almost without

Jan 1, 1942

Iron and steel lire subjects that will receive the attention clue them at the meeting in. St. Louis. Within the past 2 years the smelting of iron ore on a large scale has been started in the St. Louis area, and the blast furnaces are in full operation. Ore is being received. from the Lake Superior region, in large barges .brought clown the Mississippi River. Firebrick, for the lining of the furnaces, is made in the. St. Louis district to a greater extent than elsewhere in the country. At this meeting, there will probably be a discussion of the possibilities of the increase of manganese production in this country, and of improved methods of using it in steel manufacture.

Jan 10, 1917

By Gerald Sherman

Asbestos ore is hard, well intersected by free fissuring but not completely enough to avoid heavy secondary blasting, and is a more valuable ore than usual for caving. These factors have resulted in deviations from standard caving practice in details but not in principles.

Jan 4, 1950