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By A. B. Samaddar

A prototype automated mapping and spatial information management system has been developed, and illustrates how a powerful map manipulation capability and a comprehensive display system can be combined using both raster and vector mapping: The concept of a mapbase and information retrieval mechanism, query language as well as text and graphical menus, is introduced. The Geographic Information System (GIS), which has been built around a system for storage and retrieval of spatial and textual data, allows interaction with geographic space represented on a displayed map. The prototype is demonstrated using maps and information of an open pit mine.

Jan 1, 1989

By Donald J. Olson, Thomas J. Lutzenberger, John Ramage

The North Shore Inline Interceptor, Phase IA tunnel is a 8,550-meter (28,000-ft) interceptor tunnel currently being constructed by Traylor Bros./Frontier-Kemper, Joint Venture, using a 9.8-meter (32-ft - 4-in) diameter Robbins tunnel boring machine (TBM). This tunnel is being driven in Silurian age dolomite approximately 91.5 m (300 ft) below ground surface. Significant water inflows were encountered when the tunnel drive penetrated the thinly-bedded Waubakee Formation. Flow increases approaching 0.75 cu m per min per 30 m of tunnel (200 gpm per 100 ft) have occurred in this formation. After driving approximately 2,285 m (7,500 ft) of tunnel (200 m full face in the Waubakee Formation), total flows exceeded 12 cu m per min (3,200 gpm) with about 5.7 cu m per min (1,500 gpm) entering the tun¬nel from the 200 m (600 ft) of exposed Waubakee Formation. Additional water control measures consisting of increased pumping capacity, increased water treatment capacity, surface grouting ahead of the tunnel, grouting ahead of the tunnel face and panning to improve the working environment for installation of tunnel support, were implemented to deal with the large water inflows. Currently (January 24, 1989), 3,400 m (11,000 ft) of tunnel has been driven, total water inflows are in the range of 11.7 cu m per min (3,100 gpm) with only 6.8 cu m per min (1,800 gpm) inflow from about 1,220 m (4,000 ft) of tunnel driven full face through the Waubakee Formation.

Jan 1, 1989

By K. K. Haramy, J. McDonnel

INTRODUCTION Primarily because of mining at greater depth, an increasing number of coal mines in the United States experience floor heave problems. In many instances, the floor heaves at a slow rate without causing health and safety related problems; only additional roadway maintenance and coal handling equipment are required. However, when rapid, massive heaving occurs, the safety of mine personnel in the vicinity is jeopardized. Extensive floor heave causes a redistribution of stress around the mine opening and can cause additional ground control problems. This paper presents an analysis of rapid floor heave in a deep western coal mine. The analysis is based on field measurements, laboratory data, and beam design theory. Factors affecting floor heave, such as mining-induced stress, mine opening size, entry orientation, mine geology, rock physical properties, and gas pressure, are considered. Examination of floor heave in the mine indicates that heaving is primarily caused by deformation of a soft floor member that is subjected to high mining-induced stress. Theoretical analysis of in situ floor stresses resulting from overburden loading indicates that floor failure will occur. The analysis is confirmed by visual observations of floor heave in the mine. Recommendations for mine layout and opening design to control rapid, massive floor heave under these conditions are also presented. MINE-FLOOR-FOUNDATION THEORY The floor stratum in a coal mine acts as a foundation to support coal pillars and artificial supports, thereby providing support to the mine roof. The overburden load, transferred through pillars and other supports, applies tremendous stress to the floor. Soil mechanics theories provide solutions for foundation design problems that apply to the mine floor. Based on foundation theory, vertical load on pillars causes high shear stress zones in the floor. If the floor is relatively weak, it may fail and dislocate upward into the mine opening. Strong roof strata that do not readily fail transmit most of the overburden load through pillars to the floor. Heaving may result, depending on the thickness and physical properties of the floor

Jan 1, 1986

By B. Denby, R. Hollands

Mine information is often multi-disciplinary, dynamic and spatially complex. Different departments use the same data in many different ways, information changes over time and mines change their shape continuously. Earthworks InTouch is a radical VR-based system developed by AIMS Solutions and marketed by Earthworks, which provides a rapid and intuitive interface to a wide range of mine information. VR is used to provide an interactive and visually accurate, dynamic 3D model of the mine workings and equipment operating in the mine. Individual objects in the mine can be linked to external applications that provide up-to-date and context sensitive information. Equipment movement can be simulated or tied in to real-time survey from GPS systems for example or excavator productivity data can be extracted from a production database. The paper will highlight the major advantages of using such a VR interface to access valuable and time sensitive information.

Jan 1, 2002

By Archie W. Fletcher, R. J. Wesely, Nathaniel Arbiter, A. D. Zunkel

In contrast to pyrometallurgy's six thousand year history in the production of metals, that of hydrometallurgy is of relatively recent origin. The earliest reference to it at all was in the 16th century, with the first applications to copper in the 17th and 18th. In the 19th century, increased demands for pure metal resulted in development of electrolytic refining, and early in this century electrowinning. The rapid growth in wpper production in the present century, paricularly in the United States and Chile, stimulated the development of new technology for leaching, and for the recovery of copper from leach solutions. Solvent extraction has become a major factor during the past quarter century by permitting novel leaching technology which produces dilute or complex solutions. In addition, solvents other than sulphuric acid, and chemical methods for precipitating copper metal are now of increasing interest. These are trends which should grow in importance in the future with the need to process lower grade and more complex materials. The evolution of copper hydrometallurgy is reviewed briefly and key factors in recent major developments are presented with details of specific operations and with trends for the future indicated. The relative importance of copper hydrometallurgy is compared to that of pyrometallurgy in the light of probable changes in ore supplies and character.

Jan 1, 1993

By Thomas Oberndorfer

Recent publications indicate that there is a rising interest in the field of mining method selection, and increasing efforts are being undertaken to develop satisfying solutions. Yet, computer assistance for mining method selection (MMS), or in other, terms assistance in the (pre-)feasibility state of a project, still lags behind the computer application in other mining activities. This is true for research as well as for application. This paper is intended as a contribution to the development in computer-assisted mining method selection, and focuses especially on underground hard-rock mining. It is structured in four main parts. The first deals with general aspects of mining method. selection within the process of mine planning, and with problems and requirements which derive from this specific situation. In the second part some numerical MMS-approaches hitherto published are briefly introduced, and investigations on these approaches are discussed. Based on .these experiences, in the third part an analysis of the complex system MMS is presented. It focuses on heuristics, influencing factors, objectives, assessment-routines and mining methods, and emphasizes the essential necessity of a profound mining method description (MMD) specially developed for the requirements of MMS and numerical processing. Accordingly the fourth part of this paper presents a mining method description model developed at the Department of Mining Engineering, Montan-University Leoben (MUL), Austria. It describes the consequences of the investigation, in particular the new mining method description model, on 'the design of a MMS-system. The paper closes with a outlook on the possibilities of an successful MMS-system being realised.

Jan 1, 1992

By K. E. Robinson, G. Re, L. Skoski

Introduction A new technology is evolving as a result of growing industry and government concerns over the potential impacts of possible airborne emissions from uranium tailings piles. A major component of the technology is the use of earth covers to stabilize the tailings after mill operations have ceased. While various analytical models have been used to predict the thickness of required covers, experimental validation of the models has been necessary. This paper presents the results of a field program to select and test cover material to determine its suitability for eventual reclamation of a currently active tailings pile. The two main criteria guiding the study were the U.S. Nuclear Regulatory Commission radon flux requirements (reduction to less than twice background pre-1979, and to 2 pCi/m2 -sec above background post-1979) and the desire to employ locally available material. The methodology chosen for this study consisted of three main elements: o Determination of the background radon flux. o Determination of the radon flux from the tailings pile. o Experimental determination of the cover material diffusion coefficient and and calculation of cover thickness. The first two elements of the study are relatively straightforward, the last phase is discussed in detail. Background Radon Flux Measurements of radon-222 emanation rates from the surface of the ground were taken at three sampling locations. Samples were collected by means of the accumulator can method described by Wilkening, 1977. Both morning and afternoon samples were collected at each site to obtain an average. The measured fluxes were fairly uniform and did not differ greatly among sites. The overall average flux for all sites was 0.63[+]0.28(o) pCi/m2 -sec. This value is equal to the average radium-226 concentration determined in the soil, thus yielding a one to one ratio of radon-222 emitted (in pCi/m2 -sec) to soil radium content (in pCi/g). Tailings Pile Radon Flux Two sites on the tailing pile

Jan 1, 1980

By [Miroslaw] M. Hajdasinsk

The identification of the real internal rates of return (IRR's) of a project is essential for its economic evaluation. The existing methods for the calculation of IRR's are both cumbersome and unreliable, mainly because of their inability to effectively isolate the real IRR's and incapability of discovering multiple IRR's of even multiplicity. In this paper, a concept of the 'cash flow pattern tree used for isolation of the real IRR's of a project is presented. This concept, combined with the Sturm procedure for counting the real distinct zeros of a polynomial within a specified interval, leads to the development of a method and computer program for isolation and calculation of the real IRR's of a project. The method examines whether or not real IRR's exist, and if they do, isolates them within bounded and narrow intervals in a mathematically founded way. The isolated IRR's, whether simple or multiple, are subsequently calculated either directly or by means of an appropriate approximation procedure. Numerical examples assist the development of the method and the corresponding computer algorithm. Because any Net Present Value treated as a function of interest rate can easily be transformed into a polynomial, the method presented also constitutes a method for finding the real zeros of a polynomial.

Jan 1, 1986

By Alan G. Mayton, Jon C. Volkwein

The U.S. Department of the Interior, Bureau of Mines, in cooperation with an American firm, has been contributing toward the creation of a new highwall mining system for extracting coal in active, unreclaimed contour strip mines in the United States. The prototype system features the computer-based, remote control, video operation of a thin-seam continuous miner. Haulage is accomplished remotely also with a 76-m (250-ft) long multiple-unit continuous haulage (MUCH) conveyor system on rubber-tire vehicles. One aspect of this multi-faceted effort has been to design a ventilation system for removing dust generated at the face during the extraction process. The remote mining system eliminates the need for personnel in the mined workings. Ventilation is required to remove visible dust from the area inby two video cameras. These cameras are located approximately 6 m (20 ft) from the face, one on either side of a modified Jeffrey 102HP continuous miner. Removing the dust from this area provides the remote operator with constant visual monitoring of coal extraction at the face and thus, insures the effective operation of the mining system. A ventilation system was designed for use in a mine opening with a maximum cross-sectional area of roughly 4 sq m (44 sq ft) excluding the mining machinery. This paper describes the ventilation system and discusses how it was developed in view of the constraints imposed by the mining equipment, mining conditions, and the extraction process.

Jan 1, 1989

By Walter E. Jaworski, William R. Beloff, John Dunnicliff

As a step in the endeavor to reduce future tunneling costs in New York City, the Environmental Protection Administration, Dept. of Water Resources, instituted a program in 1972 to monitor the performance of the lining of one of its tunnels. A monitoring program was included as part of the contract specifications for the East Branch Interceptor Sewer tunnel for the Port Richmond Water Pollution Control Project in the hope that measured data would indicate possible future cost effective design or construction improvements. The monitoring program involved measuring ground deformations, circumferential liner stresses, longitudinal liner stresses, and jacking pressures. This paper presents some of the findings from these measurements, with emphasis on liner stresses. PROJECT DESCRIPTION The 3.05m (10 ft) diameter steel lined tunnel was constructed under two separate contracts. The easterly portion, Contract 3A, was approximately 3109m (10,200 ft) in length and constructed by Peter Kiewit Sons Co.1 The westerly portion, Contract 3B, was approximately 2160m (7100 ft) in length, and constructed by Richmond Constructors, a joint venture of Grow Tunneling Corp., MacLean Grove & Company, Inc., Grove, Shepherd. Wilson & Kruge, Inc., Morrison-Knudsen Company, Inc., and Andrew Catapano Co., Inc. Each contract included three test stations, hence a total of six along the tunnel route. Excavated material along the tunnel route consisted primarily of dense fine to coarse sand with varying percentages of gravel and silt with occasional boulders. Pockets of organic silt were encountered on Contract 3B and a large portion of Contract 3A ran through slightly weathered serpentine and schist. Overlying material and the groundwater level varied considerably along the route as did the height of overburden. Figures 1 and 2 show the generalized soil profiles for Contracts 3A (PK stations) and 3B (RC stations) respectively.

Jan 1, 1979

By Kent S. Roessler

The Bureau of Mines is currently investigating the geophysical application of Tomography to monitor leachate during in-situ mining. Determining the location of the leachate is important for both economic and environmental reasons. By analyzing a sequence of tomographic images, we can determine where highly permeable/fractured regions are located and hence, major flow paths. Since BOMTOM (Bureau Of Mines TOMography - Tomographic Reconstruction Program), and BOMCRATR (Bureau Of Mines Curved RAy Tomography - Tomographic Reconstruction Program) are sensitive to user-selected ray path arrival times, we are also investigating the use of neural networks to automate the process of recognizing this feature. This paper presents a technique for detecting fracture zones and their orientations in a region between two boreholes, by using a motion analysis study of a sequence of tomographic images. It also addresses the need for an automated/unbiased method to pick crosshole seismic arrival times using a trained neural network. In exploration geophysics, the picking of first break arrivals represents a pattern recognition task. The neural net paradigm has proved to be a good method of solving this type of task. To pick the first arrival peak of a trace, the network is trained with a set of known (user selected) first arrival peaks by creating a binary image of a set of traces. Once trained, the neural net correctly picked first arrivals of the remaining traces in the set.

Jan 1, 1992

By Paul C. Miclea

Hanford Reservation, in the State of Washington, with its deep basalt formations, is one of the three sites recommended by the Department of Energy for detailed investigations in order to select the first nuclear waste repository in the United States. Information obtained from several deep bore-holes drilled at Hanford indicates that the underground facility can be developed in one of the major basalt flows belonging to the Grande Ronde Formation in the Columbia Plateau, at depths greater than 3200 ft. One of the main concerns in the underground repository design is the achievement of acceptable environmental conditions during the development and the operation of the repository. For this, ventilation and air-conditioning are of prime importance and should be fully addressed. Besides the factors that determine the airflow requirements to meet the personnel and equipment operation needs, there are two major concerns that impact on the ventilation system design: the temperature of the in situ virgin basalt rock and the influx of groundwater. These two factors are related by the fact that the groundwater has the same temperature as the rock itself and they both constitute main sources of heat underground. Current information indicates that the temperature of the virgin rock at a depth of around 990 m (3250 ft) is 52°C (12S°F). However, there are some indications that the rock temperature at the selected horizon might be higher. This paper addresses the impact of the virgin rock temperature on the ventilation system and air-cooling requirements. Graphs with heat loads and cooling required for different rock temperatures have been prepared for a given model and network, using computer techniques for simulating the climatic parameters.

Jan 1, 1987

By G. Pan

A geostatistical approach is proposed for the design of infill drilling programs. The method consists of the following four major steps: developing geological favorability models, delineating mineralization and ore envelopes, classifying resource potentials, and designing infill drilling patterns. Geological modeling develops the permissible geological zones in which infill drilling is designed. Modeling mineralization and ore envelopes establishes criteria on the potential blocks to be drilled. The blocks that are included within the ore envelopes are considered in the infill drilling. The following four types of resource potentials are used in this analysis: measured, indicated, possible and barren. Blocks in the indicated category are the top targets to be confirmed in infill drilling. Blocks of possible resources may be considered exploration targets. The algorithms involved in the analysis include indicator favorability analysis, indicator kriging and ordinary kriging. A case study on a gold deposit of the Carlin type is presented to demonstrate the methodology. The deposit was originally delineated by a sparse drilling program with about 230ft of average spacing. The infill drilling design, based on the new method, suggests a significant reduction on the number of holes from a regular-grid infill drilling pattern.

Jan 1, 1996

By W. Blake, J. K. Whyatt, B. G. White

In situ stress on the scale of a tunnel or mine may be distorted by geologic structures. The resulting variations in in situ stress have a direct bearing on the potential for mining-induced seismicity. New evidence collected from the Lucky Friday mine by US Bureau of Mines researchers, as well as a review of previous case studies, demonstrated that in situ stress variations affect the [spatial] distribution of mining-induced seismicity. Although overcore stress measurements have been useful in these studies. they are too expensive and, depending, on conditions, may be too difficult to collect. However, information on borehole and raise breakouts: deformation of mine openings: and patterns of seismicity, ground-control problems and rock-burst damage can be used to build a stress database. In conjunction with maps of mine structure and geology and models of rockmass behavior, this database can then be used to build a map of in situ stress variations. Such a map could provide a means of anticipating patterns of mining-induced seismicity and. Thus, could be the basis for planning appropriate measures to ameliorate rock-burst hazards.

Jan 1, 1997

By J de Cuyper, S. R. Rao, J. Leja, K. S. Moon, W. Freyberger

A prolonged grinding of sulphide ores in steel mills appears harmful to flotation recovery and selectivity whenever xanthates are used as collectors. Particles finer than about 10um show a pronounced decrease in floatability. A supposition was made that the cause of the reduction in floatability of ground sulphides is the presence of metallic iron abraded during grinding and deposited on the ground particles. Electro- chemical measurements were made of mixed potentials developed by different sulphide-mineral electrodes (galena, chalcopyrite, pyrite, marmatite, pyrrhotite) in xanthate solutions, without a direct con- tact or in contact with a metallic iron electrode. These measurements showed that without a galvanic contact between the sulphide and the iron, the values of mixed potentials were in the vicinity of the xanthate/dixanthogen redax potential. When contact with iron was established, the mixed potentials shifted towards the more negative reducing or cathodic values, The shift was greater the higher was the ratio of the surface areas: iron electrode to sulphide electrode. Further, the shift in mixed potentials was greater the more reducing were the conditions on the sulphide electrode. Chemical analysis of reaction products produced on the surfaces of sulphides and in the bulk solution showed that less thiosulphate was formed in all of the sulphide-xanthate systems and that more elemental sulphur was detect-

Jan 1, 1976

By S. G. Hardcastle, Akbar Sheikh

In Canadian underground uranium mines, bacterial leaching is being increasingly applied to low-grade ore reserves. At Denison Mines Limited uranium operations, old stopes are used as leaching vessels; these contain a leaching muck pile brought down by drilling and blasting from the back which contained a low-grade reef. The bacteria used require atmospheric oxygen to oxidize the pyritic ore. A study was initiated to evaluate the ventilation, including oxygen supply, specifically, of flood leaching stopes during their rest period. The method of ventilation investigated was a single ended compressed air system which feeds airlines laid under the muckpile and carried through the inlet pressure bulkhead. The air delivery system was tested for post- blast integrity with a sulphur hexafluoride, SF6, tracer gas technique. This was injected into the intake compressed air line and collected at the stope's borehole exhaust in grab-sampling bags. The samples were analyzed with a laboratory gas chromatograph and results provided information on the stope's airflow, average residence time, overall clearance time, volume of the airpath and the airflow distribution. The borehole exhaust was monitored by anemometer and psychrometer and indicated that the psychrometric conditions in the stope were independent of the area's ambient climate. Evaluation of the exhaust's standard gaseous composition showed the oxygen consumption of the bacteria to be independent of the investigated flow range. Field derived results are compared with computer models, theoretical predictions and laboratory investigations.

Jan 1, 1987

By Paulo Roberto Pereira

This paper is motivated by the belief that increasing drilling and blasting costs will not necessarily bring about better digging or crushing productivity. As a matter of fact it can be counter productive as the ensuing discussion will show. In the two case studies presented herein when powder factor increased, productivity at a rope shovel and at a primary crusher decreased. Experience has shown that equipment (shovel and primary crusher) productivity increases as the powder factor increases and concurrently operating costs decrease. This is illustrated by Figure 1where the graph shows (assuming drilling costs constant) that for increases in powder factor initially operating costs might fall till a certain point and then they start to go up again. By the same token we need to understand what is the behavior of the operation’s productivity. It seems intuitive productivity goes up for increases in powder factor but when an operation reaches the point of minimum operating cost one could say that productivity reached its maximum. For continuing increases in powder factor can productivity still go up or does it go down? This paper presents two examples where the productivities of a surface coal mine and of a quarry are reduced for increases in powder factor. This indicates that these two operations could be operating to the right of their minimum operating costs and maximum productivity and therefore wasting precious drilling and blasting dollars and resources. Moreover, their productivity is following the red dotted line in Figure 1 and the question becomes can they follow the blue dotted line for increased drilling and blasting costs? The industry owes to itself to determine this minimum operating cost point and what can be done in case that the productivity goes down afterwards despite an increase in drilling and blasting costs. In other words, utilize your drilling and blasting resources correctly. In the two examples that follow single explosive loading strategies make powder factor a valid means of comparing the results of productivity as a function of powder factor. Also, external factors such as equipment operator influence are eliminated due to the long time span considered in the analysis

Jan 1, 2005

By James Warren Andrews, Philip C. Nyberg

The regulation of exposure of underground personnel to radon and its daughter products has significantly changed since the 1950's. The U.S. Bureau of Mines - Mining Enforcement and Safety Administration (MESA) - Mine Safety and Health Administration (MSHA) sequence of standards and regulations have lowered the maximum allowable occupational exposure and now the new Environmental Protection Agency (EPA) National Emission Standards for Hazardous Air Pollutants, effective in 1990, have further regulated uranium mine emissions. Under the authority of Section 112 of the Clean Air Act (42 U.S.C. 7401), the EPA has set regulations for the control of radon (Rn-222) emissions from underground uranium mines as well as other sources. Since the venting of radon from the mine atmosphere to the outside air is a major component of the miner's protection, and since this is the first quantitative effort to limit gaseous mine emissions to the environment, it was felt that it would be useful to examine the implementation of the EPA regulation at working mines. The concern was not only for determining compliance with the regulation but also for observing what effect the rule might have on mine air quality and thus on worker exposure. The regulation is stated in terms of the maximum permitted radiation dose to the closest potentially exposed individual, which is calculated from a computer program supplied by EPA and radon emission rates measured by the mine operator. Relative proximity to nearby populations determines the allowable magnitude of mine exhaust ventilation emissions. For some mines this is a serious operational constraint.

Jan 1, 1991

By Lawrence W. Teufel

Knowledge of in situ stress and natural fracture distribution at depth improves our ability to stimulate and produce low permeability reservoirs. The focus of this study is three closely spaced, 2.5 km deep vertical wells in the Piceance Basin of Colorado. The wells were completed through the tight lenticular and blanket gas sands of the Mesaverde Group. In situ stress directions and magnitudes were determined from hydraulic fracture tests and anelastic strain recovery measurements of oriented core. The distribution, orientation, and characteristics of natural fractures in the subsurface were determined from detailed observations of over 1300 m of core, of which 400 m was oriented. Stress measurements clearly show that horizontal stresses are strongly influenced by lithology. In a sandstone/shale sequence at a depth of about 2.0 km in situ stresses in sandstone formations are anisotropic, with the average ratios of the minimum and maximum horizontal stresses to the overburden stress being 0.82 and 0.96, respectively. In sharp contrast bounding shale formations are lithostatic. This stress contrast between sandstones and bounding shale formations could act as a barrier to hydraulic fracture propagation during stimulation and impede vertical fracture growth. Natural calcite-filled fractures are present in over 7 percent of the core, with several horizons having a much higher frequency of fractures. Fractures are found primarily in sandstone. The fractures have a strong preferred orientation of N 1060E[+]110, which is aligned with the maximum horizontal stress and direction of hydraulic fracture propagation. The interaction between a well developed fracture fabric and anisotropic stresses in sandstone formations produces a permeability anisotropy, with the maximum permeability aligned with the fracture fabric and maximum horizontal stress.

Jan 1, 1986

By J. W. Leonard, D. A. Newman

Discussion by N. Standish and P.N. Standish Leonard and Newman (1989) describe concepts and plans of their forthcoming project designed to increase the bulk density of broken coal at various stages of its production and handling. This is an excellent idea and something that will certainly be useful to the coal mining industry worldwide. The authors seek to achieve bulk density increase by "reducing oreliminating, through chemical additives and engineering design, particle voidage and enhance particle consolidation trickling between the point of breakage (at the face) and loading (in the shuttle car) to increase coal bulk density and productivity." In the paper, they present some supporting results of bulk density versus moisture, with or without oil addition, from the steel industry research. Unfortunately, the paper contains many misconceptions and half-truths that detract from an otherwise excellent objective of the project of increasing bulk density by reducing particle voidage-"the bottom line evaluator." Correct. Theory Definitions Coal bulk density is the ratio of the mass of a collection of discrete particles to the volume that it occupies (ASA, 1980). There can be no possible argument about this definition. Mass and volume are readily measured both in laboratory and large scale installations. So, to obtain the bulk density, one simply divides the measured mass by the measured volume. It is here that we come unstuck as everybody who has ever had to reconcile book values with the measured stock tonnages knows. Where does the problem originate? Almost invariably in a too casual a reading of the above definition and the words "a collection of discrete particles." The word collection means "a number of objects collected or gathered together, viewed as a whole" (The Oxford English Dictionary, 1989). If one knows the bulk density of a pile of coal viewed as a whole,

Jan 1, 1991