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By F. Habashi

"A short account will be presented on the extraction of rare earths from monazite sand, bastnasite ore, and phosphate rock of igneous origin. This includes mineral beneficiation, leaching methods, fractional crystallization [of historical interest], ion exchange, solvent extraction, precipitation from solution, and reduction to metals. INTRODUCTIONOriginally, the term rare earths was only used for the oxides, R2O3, which are similar to one other in their chemical and physical properties and are therefore difficult to separate. Within the rare earth group, the elements scandium, yttrium, and lanthanum differ in their atomic structure from the elements cerium to lutetium (the lanthanides, Ln). Scandium occupies a special position with respect to this classification and its other properties, and therefore does not belong to either of these groups. The rare earth elements always occur in nature in association with each other. The isolation of groups of rare earth elements or of individual elements requires costly separation and fractionation processes owing to the great similarity of the chemical and physical properties of their compounds, which explains why the history of their discovery has extended over such a long period.The word “rare”, when used to describe this group of elements, originates from the fact it was thought that these elements could only be isolated from very rare minerals. Considering their abundance in the Earth’s crust, the term rare is now inappropriate. These elements are lithophilic and are therefore concentrated in oxidic compounds such as carbonates, silicates, titano-tantalo-niobates, and phosphates.The abundance of the rare earth elements taken together is quite considerable. Cerium, the most common rare earth, is more abundant than cobalt. Yttrium is more abundant than lead, whereas Lu and Tm are as abundant as Sb, Hg, Bi, and Ag. For all practical purposes promethium does not occur in nature. It forms only in nuclear reactors."

Jan 1, 2012

By C. H. Schack

Extractive metallurgy techniques currently employed to recover silver from primary ores and secondary scrap were reviewed and evaluated to identify and delineate metallurgical problems whose resolution would increase the supply of silver from domestic materials. The survey revealed that practically all primary silver is recovered by froth flotation concentration of various types of ores, followed by smelting and refining of the separate lead, copper, and zinc concentrates. Silver losses during the complex processing are, with rare exception, inconsequential. Furthermore, any silver production gain from base metal ores, which contribute about two-thirds of the total primary silver, is directly dependent in improvement in the market for the base metals. Statistical data on new and old silver scrap are wholly inadequate to make reliable conclusions about scrap processing problems and the possibility of increasing the recovery of silver from the many forms of secondary silver- bearing materials. The available information indicates (1) that efficient silver reclamation practices are employed by the larger users of silver, and (2) that recovery of additional secondary silver involves solution of problems of collection rather than of processing. Several possibilities exist for limited increases in silver production from primary ores by improvement in metallurgical practices. Specifically, research is needed to (1) solve the problem of recovering silver from the copper ores of the Copper Range district, Michigan; and (2) devise economically feasible methods for recovery of silver from presently marginal or submarginal ores that because of grade, location, and frequently complex nature cannot presently be exploited by conventional techniques.

Jan 1, 1965

By Abid Adekunte

"Whilst safety is considered to be of high priority in every aspect of engineering projects, it is equally important for designers and contractors to be continually aware of their obligations to the immediate environment and the society as a whole. These include responsibilities to minimise the amount of nonrenewable natural resources and energy used on projects, to reduce carbon foot prints on projects, to minimise the quantity of wastes produced on projects, to minimise the level of pollution on construction sites and to reuse materials and waste products whenever and wherever possible.In other words, professional engineering practice needs to be accompanied by an underlying fundamental objective to improve, restore and sustain the environment. However, achieving this objective requires continuous collaborative interaction and effective communication between the different specialists involved on every project from the early stages. In addition, developing a well-thought-out economical solution is key to achieving the sustainability aspect of the above objective.This paper focuses on the design, construction and management of a recently completed large multi-level basement scheme in Central London, with greater emphasis on collaborative approaches taken by the design engineers, commercial managers, construction managers and site operatives to deliver the most reasonably economical and sustainable solutions to the client. Solutions were based on combinations of general and specialist engineering knowledge, with due considerations for health & safety, sustainability, cost, practicality, time and community requirements.INTRODUCTIONUnderground structures have become vital components of urban life worldwide e.g. tunnels serve many water, wastewater, highway and railway schemes, basements have been incorporated into many urban commercial, institutional and residential developments, while many public underground car parks have been built to deal with the incessant problem of insufficient surface parking spaces in busy urban centres.The safe design, construction and maintenance of underground structures have been well-mastered by the deep foundation industry over the years. However, just like many other areas of engineering, aside the need to satisfy safety requirements, underground construction practice is now faced with a new set of requirements; the demand for more sustainable and cost-effective solutions, with reduced environmental and societal impacts. Designers and managers of underground construction schemes are now compelled to minimise the use of natural resources and energy, to minimise the amount of waste produced, to minimise the level of environmental pollution, noise and disruption to traffic and normal societal life at ground level around underground construction sites. In addition, the recycling of site wastes and reuse of materials have now become important aspects of underground space development. Considerable effort is being put into promoting sustainable development across the industry."

Jan 1, 2017

By L. H. Adami, E. G. King

The heats of formation of four sulfides --MnS ( alabandite ) , FeS ( hexagonal pyrrhotite ) , ZnS ( wurtzite ) , and CdS ( greenockite ) -- were determined by hydrochloric acid solution calorimetry . The heats of formation from the metals and rhombic sulfur at 298.15 ° K are , respectively , -51.01 ± 0.19 , -23.81 ± 0.24 , -45.86 ± 0.20 , and -35.70 ± 0.30 kcal /mole . The corresponding free energies of formation were calculated from the heats of formation and the pertinent entropy values .

Jan 1, 1964

By Chi Zhang, Junyi Wu

"The use of permanent stainless steel cathodes for electrorefining and electrowinning of cathode copper had been introduced to the market long time ago and now is a well-accepted technology worldwide. During the last decades, the Chinese copper refinery industry had been growing rapidly and many large scaled production plants had been built. In the modern refineries, permanent stainless steel cathodes are introduced and used instead of traditional starter sheets. The most common steel grade used is austenitic stainless steel S31603 (316L/1.4404), while both S30403 (304L/1.4404) and N08904 (904L/1.4539) have been used depending on the actual working conditions, especially with regarding corrosion environment. While 316L permanent cathode functions well in many plants, different kind of problems, such corrosion and deformation, have been reported. There is therefore an increased need for more suitable material. New stainless steels, such as duplex stainless steels, with better properties have been tried and introduced into the application of permanent stainless steel cathode with satisfied results. The article introduces first the Chinese copper refinery industry and properties of duplex stainless steel in general, and then describes the development of using permanent duplex stainless steel cathode, including the actual working conditions, production of cathode sheets as well as the experiences of application in details. After more than one year’s usage, the advantages of permanent duplex stainless steel cathodes are clear seen.INTRODUCTIONChina has become a major player in the international copper market, accounting for around 40 percent of global refined copper demand. Despite the slowdown of the Chinese economy, the consumption of copper products will still increase, but with a medium and/or low growth which will be the new situation for the coming years. The average growth rate is expected to be around 5 percent per annual. In the coming Five-Year plan for National Economic and Social Development a number of initiatives will be finalized which will require massive amounts of copper. In 2015, the expected consumption of copper products will be over 9 million metric tons. The main driver of the consumption is the electric power industry which accounts nearly the half of the total consumption; followed by cooling application with 15% and transportation with nearly 10%, see figure 1."

Jan 1, 2016

By H. Majima

In spite of the importance of the presence of pyrite in the flotation of sulphide ores, not many studies have been made from the electrochemical point of view. It is generally recognized that the oxidation of sulphide minerals is one of the most Important factors among those which affect the floatability of sulphide minerals. The concept that the presence of oxygen is essential to the flotation of sulphide minerals is supported by numerous experimental results (1). The presence of oxygen in sulphide minerals- aqueous solution systems would affect the electrochemical behaviour of sulphide minerals and subsequently lead to more complicated reactions on the surface of sulphides. Actually some of the phenomena observed in sulphide flotation are deemed to be more appropriately explained from the electrochemical point of view. The author and co-workers have studied extensively the electrode reactions of pyrite and its significance in sulphide flotation. The results have been partly published elsewhere (2-7). In this paper, the author discusses the electrochemical nature of pyrite, and the three different phenomena observed in pyrite flotation: (1) Xanthate¬dixanthogen system on pyrite, (2) Flotation of complex sulphide ores containing pyrite and (3) Depressive mechanisms of pyrite with cyanide. The phenomenon which has been known as an iron contamination effect due to steel grinding media on sulphide flotation is also explained from the electrochemical aspect. However, this problem is not directly concerned with pyrite, and it will be discussed elsewhere (8).

Jan 1, 1971

By Edward P. Barrett

SPONGE IRON has been defined as the metallic product formed by the reduction (removal of combined oxygen) of iron ore or other iron oxides at temperatures below the fusion point of iron. This product probably derived the name "sponge iron" from its porous nature. When the reduction proceeds at slightly higher temperatures and the particles of metal weld together or finally even melt to yield pellets or balls that lack the porosity and low-density characteristic of sponge iron, the product might more correctly be called "direct iron."

Jan 1, 1954

Datun Concentrator currently processes complex sulfide ores in Gejiu Municipality, Yunnan Province, China. The ore contains much higher arsenic than other ores. The run of mine ore is fed to the concentrator to recover copper and tin by bulk flotation and gravity concentration, and then the other sulphides, such as pyrite, arsenopyrite, etc. didn?t get utilized and are discarded as tailings due to the high arsenic content. In order to utilize the pyrites in the tailings, a series of tests have been conducted for finding the solution of arsenic removal from high arsenic-bearing pyrite concentrates through simple flotation process. By means of orthogonal experimental design, the optimized levels and main factors have been found out for the roughing stage. Through selection of the effective in-organic depressants for the arsenic-bearing minerals, the arsenic in the pyrite concentrate can be removed to meet the requirement of sulfuric acid plant (As%=0.5%) by the open flotation process, i.e., one-time roughing and two-time cleaning.

Jan 1, 2014

By M. H. Rinkenbach, C. A. Taylor

The detonating compound cyanuric triazide was discovered*** and patented**** by Erwin Ott, and on account of his claims, the Bureau of Ordnance, U. S. Navy, desired more complete data, so an investigation was made. The results obtained were such that the Bureau of Crdnance recommended publication thereof for the benefit of the explosives industry. Some of the patent claims regarding cyanuric triazide are as follows: 1. It is not poisonous in contradistinction to fulminating mercury and lead azide. 2. In contradistinction to the hitherto employed priming agents it is fusible, and its fusion point (94°C) is so low that the product melted by a single heating in water or steam bath, can be poured without danger in the capsule shell. It solidifies therein after cooling, and shows the density of 1.5. 3. It has been determined that the cyanuric triazide, in spite of its very much higher priming actions, is much less brisent then ful- minating mercury and lead nitride. 4. The chemically pure cyanuric triazide (C3M2) constitutes colorless crystals melting at 94°0., and is not volatile. It is not affected by cold water, and only slowly saponified by hot water. It is relatively insensitive to friction and not too strong concussion, but explodes by impact or when hea ted to 170°C., or when heated suddenly. It is not more sensitive to friction and shocks then fulminating mercury. 5. The preparation of the triazide is preferably carried out by acting with an excess of sodium azide in an aqueous solution; in the cold, on cyamric chloride gradually suspended in the said solution.

Aug 1, 1923

By J. D. Rice, H. H. Rachford, G. H. Bruce, D. W. Peaceman

The problem of unsteady-state gas flow through porous media leads to a second-order non-linear partial differential equation for which no analytical solution has been found. In this paper a stable numerical procedure is developed for solving the equation for production of gas at constant rate from linear and radial systems. An electronic digital computer is used to perform the numerical integration using an implicit form of an approximating difference equation. Solutions are presented in graphical form for various values of dimension-less parameters. The solutions are compared with the laboratory study of gas depletion in a linear system. INTRODUCTION Production of fluids from porous rock reservoirs is essentially a transient process. Transient gradients develop as soon as production begins, and further withdrawals continue to cause disturbances which propagate throughout the reservoir, each adding in some way to the prior ones. A correct mathematical analysis of this behavior is complicated by the fact that the transient or unsteady-state flow of compressible fluids must be described by difficult second-order partial differential equations. As a practical matter, three distinctly different cases arise: 1. Flow of single-phase liquid 2. Flow of gases 3. Multiphase flow The first of these has been found to give a linear second-order equation similar to the well-known heat flow equation. where 7 is fluid density, 8 is time, and a a constant for the system, provided d 7 = r cdp, where the compressibility, c, is constant over the range of pressure, p, considered. Solutions of Equation (1) for both linear and radial flow are available in several forms.2'3' On the other hand. the second case, which is the flow of gas, gives a non-linear second-order equation, the solution of which is not known. Although a number of approximate solutions have been proposed, each is limited in value by the associated simplifying assumptions. Inasmuch as the analysis of transient flow is limited to liquid systems, a solution of the second case is necessary if further progress is to be made in studying underground fluid movement. For this reason a solution of Equation (2) was undertaken by means of numerical integration of approximating difference equations. BASIC DIFFERENTIAL EQUATION Equation (2; is derived by combining the equation of continuity, the perfect gas law, and Darcy's law to give the basic differential equation Strictly speaking, the fluids present in a gas reservoir are not perfect gases. Furthermore, there are indications that over certain velocity ranges, Darcy's law is not applicable. It would not be practicable. however, to attempt to obtain numerical solutions which would take into account all the possible variations from these laws which could occur in actual systems. The

Jan 1, 1953

By M. B. Daza, B. Lattimer

"Even with modern detection and firefighting techniques, mine fires continue to be a safety concern. However, some underground mine fires can be addressed with the remote application of high expansion foam, reducing firefighter exposure to hazards. The flow of this foam can be numerically or computationally simulated in order to gain a better understanding of its behavior, but rheology parameters are needed as inputs to produce accurate simulations. For this reason, this work studies the rheology of firefighting high expansion foam using a foam generator and Poiseuille –Flow Rheometer. Rheological parameters for foams with expansion ratios between 250-1280 are represented by the consistency index (k) and the power law index (n) due to the results show a strong agreement with the Power Law model for non-Newtonian fluid viscosity. Furthermore, experimental results show that high expansion foam behaves as a shear thinning fluid with a power law index around 0.4 and viscosities in the range of s 0.1 Pa-s and 0.042 Pa-s under shear rates between 44 ??-1 and 187.3 ??-1. INTRODUCTION High expansion foams are called to foams with expansion ratio greater than 200. Expansion ratio (??) is defined as the ratio between the volume of foam produced (i.e. volume of foam solution and volume of gas) and the volume of foam solution used (NFPA 2014). Because of its high expansion ratio, one of the most important application of high expansion foams is to fill or flood large spaces such as hangars, storage facilities and underground mines for fire suppression. The foam can fill large structures using small quantities of foam solution within a short time (Sthamer 2012) (Martin 2012). Although the specific high expansion fire suppression mechanism has not been understood on a quantitative basis, a possible mechanism is fuel isolation when the foam act as a physical barrier between oxygen and the flame. Furthermore, as a consequence of this contact water is evaporated, causing cooling of fuel and surrounding air. Besides, water vapor as product of water evaporation causes a dilution of oxygen concentration available to the fire (Fleming and Sheinson 2012). High expansion foam can be applied remotely by means of conduit pipes or in situ close to the fire. In most of the underground mines scenarios, fires have to be addressed remotely to reduce miner and firefighter exposure to the hazards (Smith et al. 2005). Although high expansion foams should not be blasted and must be deposited directly on the area of application because of their low density (Harding et al. 2016) sometimes it is complicated to apply it directly to the fire due to complex access areas at underground mines. In these cases, foam has to be applied far away from the fire. Despite of this fact there is a lack of knowledge in terms of rheological behavior of high expansion foam under high shear rates (Gardiner, Dlugogorski, and Jameson 1998). Furthermore, there are a few attempts to simulate numerically the high expansion foam flow due to the ignorance of its rheological parameters and its complex behavior. (Weaire 2008)."

Jan 1, 2018

By George W. Bain

Summary During the last three years the discovery of gold in the belt of volcanic and sedimentary rocks extending eastward from the Porcupine and Kirkland Lake gold-fields has caused a great deal of excitement in mining circles. The area is heavily drift covered, and every aid to the location of veins is eagerly grasped. A knowledge of the physiographic history of the area is of the utmost importance in the application of many of these aids. Evidence is presented to show that glacial erosion has lowered the general elevation very little below the pre-glacial level, and that many glacial erratics have been carried less than three miles southward. Probably a knowledge of the general geology of a: region was never more necessary to the understanding of the distribution and continuation in depth of the mineral veins than in this area. Four distinct granites occur in the region, and gold-bearing veins are genetically associated with only one of these. Two types of quartz-feldspar porphyries have been found, only one of which has any bearing on the locus of the mineral veins. Many other examples of this complexity of associations might be cited, but everyone goes to show that in most cases the economic importance of the deposits can be realized only after the regional geology is understood. A series of sandstone, limestone and shale intruded by granite lies unconformably below the Keewatin lavas. The latter are intruded by a gneissoid granite and are overlain unconformably by the thick series of Timiskaming greywackes and silts. These are intruded by carbonated syenites and syenite porphyries which have since been rendered somewhat schistose.

Jan 1, 1927

By Hirsch H. H.

The paper, presented at the North of England Institute of Mining Engineers' general meeting held in Newcastle-upon-Tyne on 12th February 1916, gives a short description of the Hirsch lamp, which, though largely used in the United States of America, has not yet been adopted in Great Britain. The lamps, which consist of (1) the watchman's lamp and (2) the miner's lamp, are portable, and have been designed to provide a safe and reliable light for use by watchmen, and in mines, rescue-work, powder-works, oil-refineries, and other places where special precautions become necessary on account of the presence of explosive materials or gases. The lamps are in each in­stance operated by a storage-battery contained within a casing, and this supplies the current necessary for a miniature incandescent lamp. Each safety-lamp forms a complete unit and can be carried from place to place or held in any position. Appendices give details of battery cleaning, test results and safety reports

Dec 1, 1916

By J. P. Gu, C. Beckermann

"Melt convection and macrosegregation in casting of a large steel ingot is numerically simulated. The simulation is based on a previously developed model for multicomponent steel solidification with melt convection, and involves the solution of fully coupled conservation equations for the transport phenomena in the liquid, mush, and solid. Heat transfer in the mold and insulation materials, as well as the formation of a shrinkage cavity at the top are taken into account. The numerical results show the evolution of the temperature, melt velocity, and species concentration fields during solidification. The predicted variation of the macrosegregation of carbon and sulfur along the vertical centerline is compared with measurements from an industrial steel ingot that was sectioned and analyzed. Although generally good agreement is obtained, the neglect of sedimentation of free equiaxed grains prevents the prediction of the zone of negative macrosegregation observed in the lower part of the ingot. It is also shown that the inclusion of the shrinkage cavity at the top is important in obtaining good agreement between the predictions and measurements.IntroductionMacrosegregation in large steel ingots is one of the most well-known and now classical problems in the field of solidification and casting [1]. Commonly found macrosegregation patterns in steel ingots are a positively segregated zone at the top, negative segregation near the bottom in the equiaxed zone, inverse segregation near the ingot surface, V-segregates along the centerline, and A-segregates in the columnar zone [2, 3]. It is well established that the macroscopic transport of species leading to macrosegregation can occur by a variety of mechanisms, including thermally and solutally driven natural convection of the melt in the mushy zone, flow due to solidification contraction, and the sedimentation of free equiaxed crystals. Fredriksson and coworkers [ 4,5] provide recent overviews of the solidification transport phenomena and macrosegregation in ingot casting."

Jan 1, 1999

By David J. Mack

A survey and critical appraisal of published information about Young's modulus was originally made by the writer because of a complete lack of information about this very important quantity in works on. mechanics, physical metallurgy, physics, and other sciences. It was felt that a comprehensive summary of such information about Young's modulus might be of general interest and may suggest new problems or lines of attack on other problems that involve E. Hence this paper has been prepared even though it is only a review, with no new ideas or experimental data. The references are only those used in assembling the paper. No attempt was made to compile a complete bibliography on the subject of Young's modulus. CalculatioX oP YouNg's Modulus from Theoretical or Empirical CoNsidera-tions Many attempts have been made to compute E from theoretical considerations. The earliest calculations were probably those of Tomlenson (1883) and Souther-land (1891), but Fess'enden4',~ made extensive calculations a few years later and arrived at the relationship: £ = 78.TOw(i)* where V is the atomic volume. In 1923, Peczalski, working from the same standpoint but with more information available on atomic structure, arrived at an identical relationship, which he expressed as: where B is a constant of value about 8 . 107, p is density and mis atomic weight; the atomic volume, of course, being ml p. Portevind4 immediately pointcd out that while the equations of Fessenden and Peczalski were true of the common metals, they gave low values for the refractory metals with high moduli (Fig. I). He showed (Fig. 2) that much better concordance was obtained by means of an empirical equation of the form: F- KT" where K is a constant; T the absolute melting point; V, atomic volume, and a and b constants of value approximately I and 2 respectively. This constant K in the Portevin equation is not necessarily the same for all elements, as shown by Thompson. Other equations for E based upon theoretical considerations have been derived by Honda and Yamada49 and Lasareff.50 The most recent calculations of elastic moduli based upon quantum mechanics are probably those of Fuchs He extended the method of Wigner and Seitz for calculating the lattice energy and compressibility of monovalent metals and computed the elastic constants of lithium, 18

Jan 1, 1946

By G. H. Khoe

Neutralisation of acid uranium mill tailings with lime or other alkaline materials is usually practised to reduce the dissolved concentration of heavy metals and radio nuclides. Computer modelling of this process was carried out using the geochemical equilibrium code MINTEQA2. Computed dissolved metal and sulfate concentrations were compared with laboratory-based experimental data. It was found necessary to include the modelling of adsorption of trace metals (such as uranium and lead) by the precipitated ferric hydroxide in order to obtain acceptable concentrations in the neutralised liquors. There were limitations of the modelling exercise due to important aspects which were not addressed or properly accounted for such as chemical reaction kinetics and the effect of high ionic strength. These are discussed in the paper.

Jan 1, 1991

By H. Feldheiser

Acid resistant brick linings are state of the art for anti-corrosion linings in tanks for high pressure acid leaching (HPAL) treatment. The design of these brick linings has to take into account the almost non-elastic behaviour of the brick lining inside a relatively highly elastic steel vessel. There must be tools and data available to determine for the steel vessels the thermal growth plus the pressure expansion and for the brick lining the linear thermal expansion and the chemical swell. Thermal shocks and pressure drops are not regular operating events but their negative influence on the lifetime of a brick lining has to be a part of the engineering study. Finite Element (FE) models as well as a lot of research and development on brick lining materials is the only way to find a path through the complex engineering work for pressure vessels.

Jan 1, 2004

By H. R. McCabe

"The study of a detailed series of structure and isopach maps of the Palaeozoic strata of southwestern Manitoba indicates that the principal Palaeozoic tectonic elements -the Williston Basin and Elk Point Basin -have been modified to a considerable extent by major tectonic features of the Precambrian basement. The principal basement feature is the break between the Churchill and Superior provinces, which coincides roughly with the Manitoba-Saskatchewan border. East-west-trending orogenic belts within the Superior crustal block may also be reflected to some extent in later Palaeozoic movements. In addition, the Superior crustal block, as a whole, appears to have had a slightly different response to the tectonic forces, giving rise to both basin subsidence and basin uplift. During periods of deposition, especially during Ordovician time, the Manitoba portion of the basin appears to have undergone a relatively higher rate of subsidence, whereas during periods of erosion relatively greater amounts of uplift and truncation have occurred. As a result, the depositional and erosional patterns for most of the Palaeozoic formations in southwestern Manitoba are somewhat anomalous relative to the regional basin framework.Some prominent Palaeozoic structures probably are the result of salt solution and differential compaction caused directly or indirectly by relatively minor tectonic movements related to Precambrian basement features. In particular, the prominent hinge line at the edge of the Devonian Prairie Evaporite salt basin may be due, in large part, to salt solution. Numerous other small structural lows, structural highs and isopach thicks, probably resulting from salt solution, occur along the salt edge and have been important in modifying and controlling Mississippian oil accumulation in the Daly-Virden producing area."

Jan 1, 1967

By Lindsay D. Norman

Computer models for simulating the construction and for calculating the properties of particulate solids in two- and three-dimensional systems (coverings of circles and packings of spheres, respectively) were developed. By simulating the physical process of constructing circle coverings and sphere packings, in which the circles or spheres were randomly selected from many different distributions of sizes, physically realizable loose random assemblies were simulated whose physical and geometrical properties were predictable with the computer. Many of these properties, such as the number of contacts, are extremely-difficult to measure accurately, or considerable ingenuity is required in their determination. All of these properties were easily and accurately calculated by the computer models for many different coverings and packings constructed from equal, discrete, uniform, and log-normal distributions of particles. In addition to the loose random assemblies, dense random covering and packing constructions were simulated whose properties are ideal upper limits for those of the loose random coverings and packings. The properties of the dense random coverings and packings, heretofore only obtainable by theoretical analysis, were also simply obtained. The statistical geometry of loose random coverings and packings was studied, and several new interpretations of the area-covering or space-filling requirements in these systems were made. In two dimensions, it was found that the properties of all loose random coverings are predictable by taking suitably weighted averages of the corresponding properties of just four kinds of polygons whose edges are defined by connecting the centers of mutually tangent circles in the covering. The distributions of these polygons that permit area-covering were determined, and empirical equations for predicting the density, average coordination number, and average pore area in loose and dense random coverings were formulated. The properties of loose packings were determined by performing a simplicial division of the computer-simulated assemblies to produce a unique set of minimum volume, space-filling tetrahedra whose edges connected the sphere centers in each packing. A simple empirical equation was formulated that permits the calculation of the average number of contacts in any sphere packing, random or regular. Some of the statistical geometrical properties of the simplicial tetrahedra in the computer-simulated packings were analyzed. The tetrahedron edge length distributions in all the loose random packings were nearly identical when the edges were presented in terms of sphere diameters, regardless of the sphere population in the packing. Moreover, the gap lengths in the loose packings were to an excellent approximation representable by a uniform distribution of sizes. The distributions of spheres in tetrahedra resulting from the simplicial division of the loose random packings also existed in the tetrahedra in dense random packings. These observations were employed in developing a unique method for predicting the geometrical properties of loose random packings without simulating the assembled packing. Instead, the space-filling simplicial graph could be predicted for any given density of packing of any sphere population. The cumulative packing properties of these tetrahedra were shown to be nearly identical to those calculated by all loose random packing simulations attempted in this investigation. The simplicial tetrahedra completely describe a packing and can therefore be used to predict all properties of interest.

Jan 1, 1971

By Herbert H. Einstein

Rock mass deformability is commonly predicted using correlations with RQD or other indices of rock mass quality, or by extrapolation from large in-situ tests. Based on the probabilistic description of rock masses empirically developed in Part I a new approach was attempted in modeling for predictions of deformability. This approach decomposes the rock mass into spatially variable joints described by probability distributions, and intact rock blocks. Stiffnesses and elastic parameters are associated with the joints and intact blocks respectively, and deformations built up by adding the contributions of each. This model allows relaxation of many of the simplistic geometric assumptions which constrain parallel attempts to model deformation in rock masses. The model has been applied to four standard cases in order to test its results against previously existing models, and to check whether it replicates empirical correlations. When joints are taken as parallel, common empirical correlations are closely approximated by the model output. However, the closeness to empirical correlation breaks down when variability of the jointing geometry is increased.

Jan 1, 1979