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By F. Dai

Granitic rocks usually exhibit strongly anisotropy due to pre-existing microcracks induced by geologic loadings. The understanding of the rock anisotropy in mechanical properties such as tensile strength is critical to quarrying and stabilization of underground structures. In this paper, Brazilian tests are conducted in combination with MTS material testing machine and split Hopkinson pressure bar (SHPB) system to measure both static and dynamic tensile strength of anisotropic Barre granite. Samples are cored and labeled using the three principle anisotropic directions of Barre granite (BG). These directions are also chosen as the loading directions for the Brazilian discs. For dynamic tests, pulse shaping technique is used to achieve dynamic equilibrium in the samples during the test. Finite Element Method is implemented to formulate equations that relate the failure load to the material tensile strength employing a orthotropic model for Barre granite. For samples in the same orientation group, the tensile strength shows clear loading rate sensitivity. The tensile strengths exhibit clear anisotropy under static loading; while less anisotropy under dynamic loading. The tensile strength anisotropy of Barre granite is interpreted as interactions of the pre-existing microcracks.

May 1, 2009

By Chris Bennett, Glen Kosick

"Process modeling and equipment sizing procedures for SAG circuits has advanced significantly over the past two decades. However, no matter how exact the hardness tests, models and scale-up calculations, if the ore samples being used for design do not accurately represent the orebody then major design errors can be encountered. This paper will describe a hardness testing method for identiQing the power requirement profile of an orebody, to an extent that design errors due to poor sampling can be greatly reduced or avoided altogether. It will provide some insight into the magnitude of hardness variability that can be encountered in an orebody. Finally, the paper will preview how detailed hardness distribution data can be incorporated into mine block models, to optimize SAG circuit design for an orebody, both fi-om a capital investment and throughput point of view.INTRODUCTIONIt has long been known that many SAG/AG' circuits experience wide swings in throughput. These throughput variations are almost always of a magnitude not anticipated in the plant design; consequently, they are detrimental to the expected return on investment for the mining companies. It is clear that the throughput swings are mainly caused by changes in ore hardness. In 1993, in an attempt to address this problem, MinnovEX began investigating the possibility of using a small scale SAG test (2 kg charge) to predict SAG power requirements from drill core samples. The objectives of the small scale test were to enable mining companies to do many more SAG hardness tests than currently undertaken for a particular orebody. To make this possible, the SAG tests had to use a minimal amount of sample, be cost effective, and give acceptable accuracy in the prediction of SAG power. If this small scale SAG test proved accurate, then the high sampling frequency would yield results that approach the true hardness distribution of an orebody. This hardness distribution could then be used to derive the distribution and variability of specific energy required throughout the complete orebody. This specific energy (kWh/t) can be thought of as the power required to grind one tonne of ore per hour (kW/tph) to a specified size. Once the true distribution of power requirement throughout the whole orebody is understood, the grinding circuit design team can make an informed decision regarding the hardness value that is most appropriate for sizing the SAG equipment. Throughput losses due to hardness variation could be deliberately planned for or avoided altogether (a capital cost decision)."

Jan 1, 1999

Ground support audits are sometimes necessary in ageing underground mines. Usually, the purpose of such audits is to assess the state of the ground support in various parts of the mine, identify areas that require attention and establish rehabilitation requirements. In 2005, Brunswick Mine, located in Bathurst, New Brunswick, Canada, completed a comprehensive mine-wide ground support audit. The areas examined included excavations in several mining blocks, as well as ramps, shaft stations, garages, shops, etc., throughout the mine. A vast amount of data was collected over a period of two weeks by multiple auditing teams. The audit was followed by a data digitisation exercise, and the creation of a data management system to store audit results and keep track of subsequent rehabilitation activities as they occur. One aspect of the data management system was the incorporation of a function for reporting on ground rehabilitation progress, along with the capability of updating mine level plans for easy visual presentation of this progress. This article describes the approach implemented at the mine to carry-out the audit, as well as the database constructed to manage the results.

May 1, 2009

By Peter A. Eshun

This paper studies two methods that account for risks associated with gold mining projects such as mineral risks and country risks. The first method is sensitivity analysis, which investigates the effects of a change in any economic parameter such as operating cost, capital investment, gold price or taxes on the viability of the project. The second method is Monte Carlo Simulation technique, which takes into consideration the simultaneous random variation of the economic parameters on the project's viability. An automated simulation cash flow model has been developed as part of this paper. Sensitivity analysis and the simulation model have been used to investigate the economic viability of the Dokrupe Gold Project (DGP) serving as a test case. It is concluded that, the Monte Carlo Simulation technique gives a more realistic judgement of the economic viability of gold mining projects.

May 1, 2004

By Arthur L. Holloway, James C. Mugford

"The Underground Research Laboratory (URL) is located in southeastern Manitoba, in the Lac du Bonnet granite batholith of the Canadian Shield. It was constructed by Atomic Energy of Canada Limited (AECL) to conduct geotechnical research for the Canadian Nuclear Fuel Waste Management Program, assessing the concept of permanent disposal of nuclear fuel waste deep in plutonic rock.One of the primary objectives of the research program at the URL is to develop a nondestructive rock mass characterization method that can be used during siting, design and construction of a used fu el waste disposal vault. An experimental program was established to assess radar reflection profiling as a technique for fracture characterization in granite. The highly resistive, homogeneous nature of the Lac du Bonnet granite is ideal for the propagation of electromagnetic energy at the radar range of frequencies and water-filled fracture zones act as excellent reflectors because of their contrasting electrical properties.Radar reflection profiling was undertaken to characterize a major fracture zone located between 5 m and 10 m below Room 211 on the 240 m level of the URL. The profiling was done at a frequency of 120 MHz, on a 1m grid laid out on the bare rock floor of the room. Reflectors identified in the analog data were correlated between the profile lines, digitized, and a three-dimensional surf ace for each recognizable reflector was constructed. These surf aces were then compared with data obtained from the examination of numerous cores from adjacent boreholes intersecting the fracture zone. A very good correlation was found between the major radar reflectors and the most intensely fractured regions of the zone. Modelling studies also showed that a series of prominent shallow radar reflectors were caused by a borehole drilled close to Room 211."

Jan 1, 1990

By Michel Aubertin

Les haldes à stériles contenant des minéraux sulfureux réactifs constituent un milieu favorable à la production du drainage minier acide (DMA). Au sein de ces haldes, les processus physiques, géochimiques et biologiques qui mènent à la production du DMA sont nombreux et complexes. Un des aspects critiques qui affecte la génération de DMA est la distribution et le mouvement de l?eau dans les roches stériles. La modélisation numérique est un outil qui permet de comprendre, pour éventuellement contrôler, les mouvements de l?eau (et donc réduire la production du DMA) dans les haldes pendant la période d?exploitation de la mine et à sa fermeture. Plusieurs simulations numériques des écoulements non saturés dans des haldes ont été effectuées. Pour ces simulations, on a considéré divers types de matériaux, diverses conditions atmosphériques et diverses configurations géométriques. Les simulations réalisées montrent que l?on peut contrôler les mouvements de l?eau en introduisant des couches de matériaux fins intercalées dans les haldes formées de matériaux grossiers. Des couches horizontales ne sont cependant pas appropriées puisqu?elles peuvent, dans certains cas, favoriser la création de zones humides susceptibles d?amplifier les effets du DMA. Une faible inclinaison des couches de matériaux fins vers l?extérieur permet de palier à ce problème. Les couches inclinées favorisent un drainage des haldes vers la périphérie. Ceci a pour effet de garder sèche une grande partie des stériles et de réduire, par le fait même, la production du DMA.

Nov 1, 2002

By A. Vien, B. C. Flintoff, R. P. Edwards

"This paper provides a critical review of the development and application of advanced controls in mineral processing at the industrial level. These algorithms can be sub-divided into four broad categories: Kalman filter, self-tuning, extended horizon, and knowledge based or expert systems. Applications from each category are described outlining the benefits derived, the relative advantages of that particular controller, and potential limitations of the controller which may inhibit their more widespread application. The paper will conclude with a description of control algorithms which are currently in the rudimentary design stage, but may hold tremendous potential for mineral processing control systems in the next decade. INTRODUCTIONThe Canadian mining industry has a large installed milling base and many plants are run with manual or low level automatic process control. The competitive pressures imposed by the market will not allow these operations to ignore the significant increase in efficiency that can be achieved through the effective application of advanced process control. These improvements will come in the form of better quality, higher productivity and reduced costs.There have been quite a number of reports of successful applications of advanced control in mineral processing applications. As this trend continues, and more of the work is documented, the technology will be more effectively transferred to process and control engineers. It is the authors' opinion that the most difficult problems facing process control are not really technical in nature. Rather, they lie more in process control education. This extends from management, through engineering to the operators.The purpose of this paper is to provide a tutorial type overview of some of the more frequently encountered advanced control algorithms. The assumption is that the reader has a superficial knowledge of this technology. In the discussions which follow, several techniques are explored within the framework of simple process examples. Industrial examples are cited for each and an evaluation of the expected longer term potential is given."

Jan 1, 1992

By P. Oyanader

"In 2001, the Catholic University of Chile undertook a maintenance benchmarking study of six open pit copper mines having mill capacities varying between 18,000 t/d and 156,000 t/d, and collectively responsible for 58% of Chilean copper production. This paper describes the methodology used to conduct the study, as well as the overall results. Key performance indices were selected to measure the effectiveness, efficiency, and development of the maintenance process. Using a balanced scorecard philosophy, these indicators were divided into client satisfaction, financial, internal process, and learning and growth indices.Maintenance was found, on average, to be responsible for 44% of mine production costs. Percentage planned maintenance of equipment fleets was found to be low by world standards, averaging 35%, 56%, and 44%, respectively, for blasthole drill, shovel, and haul truck fleets. Fleet availabilities were found to be significantly influenced by the percentage of planned maintenance achieved, while maintenance cost per equipment was found to decrease non-linearly with increases in percentage planned maintenance. Investment in technical training (including planned maintenance practice) was found to be low by global standards. The paper concludes that fleet availability and maintenance costs in Chilean open pit operations could be considerably improved by improving and/or developing maintenance planning standards, and investing in training personnel in planned maintenance techniques"

Jan 1, 2005

By Sibabrata Patnayak

A major problem during shovel excavation in oil sand mining is the variability of material diggability resulting in varying mechanical energy input, cycle time, energy consumption, wear, and stress loading of shovel dipper-andtooth assembly. This variability greatly influences the mining equipment performance. Different approaches such as empirical ground classification systems, analytical methods, and performance monitoring that are used to determine diggability of groundmass are reviewed. It is concluded that the existing empirical diggability classification systems are site specific and mostly based on rock and therefore, cannot be used for shovel excavation in oil sands. The O&K wedge test is a simple and useful index test for establishing correlations between cutting resistance and geotechnical properties of coal and other soft rock overburden material. But this test, when performed on small size unconfined oil sand samples, may not give reliable indication of diggability because of the boundary conditions on the specimens. Digging predictions made using analytical and laboratory digging models need to be verified with performance monitoring data to better understand the digging effort in oil sands.

Apr 1, 2005

By Rick Collins

Presentation Agenda 1.Sudbury Basin 2.Diamond Drilling 3.Planned Production 4.Safety 5.Timeline 6.Sustainable Development 7.Scope Elements 8.Progress 9.Delivery Approach 10.Owners and EPCM Roles 11.Contract Styles 12.Mine Systems & Technologies 13.Q & A

May 1, 2009

By M. Kalin

"Ecological Engineering and Biological Polishing technology is a decommissioning approach for inactive coal, uranium and base metal operations. To improve acid mine drainage water some fundamental aspects of wetland ecology and sediment microbiology are combined, to provide conditions to allow for biomineralization of the contaminants.This paper summarizes the first records of microbial alkalinity generation in acid mine drainage through the utilisation of the ARUM process. The process requires that the seepage is at pH 4.5 where sulphate reducers utilize sulphate to produce hydrogen sulphide, which in turn precipitates with metals. The pH increase is brought about by alkalinity generating microbes.The ARUM process has been successful in increasing the pH from 2.5 to 7.0. Flow through reactors operated in the laboratory continuously for more than 60 days have removed Ni from 13 mg/L to < 0.01 mg/L. Design parameters are being developed for low flow rates of 5 L/min in a test system receiving seepage from a tailings.1.0 INTRODUCTIONAcid mine drainage associated with mining wastes poses a significant environmental problem. Conventional means to treat acid mine drainage (AMD) use chemical treatment system. Ecological Engineering technology uses natural biological means to curtail and ameliorate AMD during mine operations and at the time of decommissioning. The premise underlying Ecological Engineering technology is that AMD is the result of a natural process enhanced by mining activities. Therefore, in nature, a process providing a natural balance to AMD has to exist, which, when assisted through appropriate means, can counteract the detrimental effects of AMD on the environment. This process is microbial alkalinity generation which is known to occur in wetlands, lake and ocean sediments (Baas Becling et al, 1960)."

Jan 1, 1991

By Nick D. Rose

Outline ?Background ?History of inverse-velocity for failure prediction ?Methodolog ?Case Histories ?Three case examples of predicted slopefailure to actual date of occurrence ?One case example of mitigated slope failure using inverse-velocity to forecast failure time and schedule remedial measures ?Conclusions

May 1, 2006

By Bernard Dallaire, Jean Cayouette, Sylvain Duchesne

"Louvicourt Mine's concentrator, located near Val d'Or, Quebec, treats an average of 4,300 tonnes of ore per day composed mainly of copper, zinc, gold and silver. An analysis of concentrator revenues and metallurgical losses shows a potential for additional gain, particularly in regards to precious metals (kustelite) where recovery is usually around 67 -70 %. The planning, installation and trial operational period of two Outokumpu SK-240 flash cells at the underflow of the primary cyclones took two years. The use of (( flash flotation )) technology has made it possible to exploit the favourable conditions at the underflow of the primary cyclones such as precious metal concentration and the presence of liberated coarse chalcopyrite. These conditions permit early flotation (fresh surfaces) of the kustelite and the liberated copper. Since the start-up of the flash cells, the metallurgical gains have turned out to be very positive with increases in metal recovery reflected in appreciable NSR gains. Also, significant savings in reagent consumption and a coarser copper concentrate have made it possible to reduce the drying cycle of the Larox filter presses since the cells were put into operation.BACKGROUNDLouvicourt Mine is operated by Aur Resources Inc. (30% ownership) on behalf of its partners Novicourt Inc. (45%, subsidiary of Noranda Inc.) and Teck Corp. (25%). The mine is located in northwestern Quebec about 600 km north of Montreal and about 25 km east of the mining town of Val d'Or. The mine commenced commercial production in July 1994.The massive sulphide ore deposit lies at depths varying between 450 m and 900 m. Mining reserves (2% Cu equi. cut-off) as of Jan. Is', 2000 are estimated at 7.5 million tonnes of ore averaging 3.4% Cu, 1.8% Zn, 28.0 g/t Ag and 0.9 g/t Au. Delineated ore reserves permit the use of a mechanized transverse blasthole mining method. The extraction order is a typical 1.3.5 mining sequence. Primary and secondary stopes are 15 m wide, 15 to 70 m long (25 m long average) and 30 m high. Backfilling for pillar recovery and regional stability is required."

Jan 1, 2001

By R. E. McElvain

"Hydraulic transportation of solids in suspension with water or other carriers, such as oil is becoming more practical as economic situations develop with respect to the railroads and other carriers. Of significant importance, is also the increased size of the major operations and the total impact of larg- er tonnages and more critical sources of supply.There are several means of imparting energy into the solids and directing the material down a pipeline, but the centrifugal pump is emerging as the most practical piece of equipment when considering relatively large flows and recent development. We can now handle relatively high densities without interruptions. This provides the mining and transportation fields a more economical means of lifting and transporting coal and other mineral products.Equipment & MethodsWarman International has developed several methods of alternate PDP against high heads. We have, at least for the present time, shelved our pump which uses clear water to slurry method and have placed our major emphasis on the full development of the centrifugal pump. I personally see several similarities on the alternate reciprocating devices as compared with the steam piston type engine versus steam turbines. The centrifugal pump comes into its most advantageous position at about 2000 GPM and can also show advantages by means of increased mobility, when driving tunnels and in other difficult operations when considering the total economic results. We now have some interesting d<:ta on one 5 mile raw silica sand line designed for pumping at 200-400 tons per h:mr. This is a separate subject on a ""simplified approach to slurry transport"" and paper has been prepared for the Hydrotransport 5 proceedings in Germany this Spring. Reference 1 may be of interest to those who want to delve into the subject further, and I also have some advance copies of this paper."

Jan 1, 1978

By J. R. Goode

Rare earth elements (REE) and their compounds are critical ingredients in numerous necessities of modern life including: the permanent magnets used in electric motors, generators, speaker and hard drives; high performance automobile tires; catalysts; phosphors; optical glass; etc. World production of REE in 2014 was about 110,000 t with about 98,000 t/a being “Light” (LREE) and the balance “Heavy” (HREE). Unlike other mined commodities, the majority of the LREE produced in the world is a by-product and that from a single iron ore mine in China. The balance of the LREE production comes from four REE-only mines, two in China, one in Australia and one in the USA (now on Care and Maintenance basis). The LREE operations comprise very unusual flotation processes and complex hydrometallurgical plants. In contrast, most of the HREE come from a multitude of small in-situ leach operations exploiting a single, dispersed deposit in China using hydrometallurgy alone. All of the current REE operations produce an intermediate mixed REE product that must be separated to yield the high purity, individual, REE required by the market. This paper describes the processes being used to produce LREE and HREE intermediate products and the separation plants used to make the high purity REE compounds that are key ingredients in the magnets in earbuds, turbines, and automobiles; catalysts used in the production of gasoline, and so on.

Jan 1, 2016

By R. Ramírez, N. Aslin, G. Ríos, T. Bravo, A. R. Almansa

Lacy copper has been an on-going concern at Atlantic Copper for at least 10 years and was first reported to Glencore Technology in mid-2010. Over the past 12 years, many of the plates were replaced due to age and general deterioration however; plate passivation and lacy copper issues have persisted. After analyzing all the possible causes of this phenomena, it was found that the problem is caused by a degradation of stainless steel as a consequence of the deposition of Sb oxides. These deposits act as passivating agents of stainless steel, which reduces the density of copper nuclei, causing defective copper deposit, with low thickness and ductility. After doing several tests for reducing/removing the phenomena, the over-riding factor was found to be the anode-cathode overlap. An adequate overlap eliminates the problem of "lacy copper". This was verified during an eight month trial with anodes extended 2.5cm in length. Longer anode not only avoids the appearance of lacy copper, but also recovers cathodes that already have lacy copper. On the other hand polishing of plates only gives rise to a temporary solution that requires on-going polishing, to avoid the re-appearance of lacy copper. INTRODUCTION The electrolytic copper refinery of Atlantic Copper in Huelva (Spain) was commissioned in 1970 with an initial capacity of 40,000 t of cathodes per year. In 1975 the copper refinery was expanded to 108,000 t/year. From 1994 to 1996, a new expansion together with the implementation of ISA permanent cathode technology led to a capacity of 215,000 t/y. Since 1995, a progressive increase in the current density up to 350 A/m2 has been accomplished, which together with an increase in the number of cells from 1,120 to 1,204, has led to the present cathode production capacity of 290,000 t/y A lack of copper deposition in the lower part of the steel permanent cathodes was first reported in 2010. This phenomenon is known as “Lacy copper” because of the appearance of the copper deposit as it can be seen in Figure 1. The occurrence of this phenomena was relatively low and was assumed to be originated by an excessive anode scrapping. Nevertheless, in December 2015 Lacy Copper was observed in a significant amount of copper cathodes giving rise to the following issues: Increased tramp copper – housekeeping and maintenance problems Poor appearance of cathode deposit and untidy looking bundles

Jan 1, 2019

By J. A. McLennan, J. M. Ortiz

Nickel laterite deposits are typically formed from tropically weathered mafic-to-ultramafic complexes. The resulting nickel concentration is found within soil horizons and is mineable with regular dozer units. At the time of mining, digging elevations are needed at selective mining units (SMUs) or representative dozer regions (RDRs). Moreover, for mine planning, the costs due to dilution and lost ore require mining elevations to be specified. A conditional simulation approach is used to calculate “optimum” RDR mining elevations. Multiple realizations of the ore base surface are simulated. For a single bottom surface realization, dilution and lost ore costs are calculated over the entire vertical extent of each RDR. The optimum mining elevation is the elevation where the lowest summed cost of “accepting dilution” and “wasting ore” occurs. The reported RDR dilution is the cost of mining the volume of waste located below the bottom surface and above the optimum mining elevation. The reported RDR lost ore is the cost of not mining the volume of ore above the bottom surface and below the optimum mining elevation. For all ore bottom surface realizations, optimum RDR mining elevations and their associated dilution and lost ore costs are calculated and compiled to represent production uncertainty.

Jan 1, 2006

By H. A. Steane

"This presentation will cover some crushing and grinding considerations in plant design and operation. There is nothing basically new in the subject matter presented here; however, the viewpoint and interpretation may be novel and some of it controversial.The presentation is based on experience gained in the metallurgical design of plants for Placer Development Limited from 1960 to the present. The plants are listed on SLIDE No. 1.These plants have conventional crushing, followed by rod mill and ball mill grinding. I would like to think that autogenous grinding plants are the answer for eliminating secondary crushing plants and reducing the capital and operating costs; however, the autogenous plants seem to have some problems of their own and I have had no experience with them.Fineness of Grinding RequiredFirst let us consider the fineness of grinding required.The fineness of grind will affect the recovery obtained, and the relationship must be determined. If the grinding is too coarse, some of the valuable mineral, either free or locked in middling grains, will not be floated. However, as grinding is probably the greatest single operating cost, we do not want to grind any finer than is justified economically.Finer grinding should not be carried beyond the point where the net smelter return for the increment saved becomes less than the added operating cost. Even this fineness will be beyond the economic limit because of the additional capital cost for the equipment needed to achieve it. These factors will be discussed in more detail later.The Bond work index is the commonest method of expressing a measure of the effort that has to be expended in grinding. It is the kilowatt-hours required to reduce a ton of rock from an infinite size to 80% passing 100 microns. The formula allows a calculation to be made for other size ranges."

Jan 1, 1976

By R. Siy, O. Neiman, B. Hilscher

"A full-scale prototype of “Jameson Downcomer” technology has been installed and tested on a Tailings Oil Recovery (TOR) vessel in Syncrude’s Mildred Lake extraction plant. Jameson Downcomers are a type of mineral flotation equipment used in the coal industry that Syncrude has extended to the recovery of secondary bitumen in the oil sand extraction process. The TOR vessels are currently being operated as single-gravity separation vessels, in series with the Primary Separation Vessels (PSV’s). We have developed a model to differentiate between “floating” and “non-floating” bitumen in the PSV’s, and then applied it to verify that the current TOR performance only captures the “floating” bitumen by simple separation. The existence of “non-floating” bitumen provides an opportunity for recovery enhancement by means of the Jameson Downcomers. To achieve bitumen recovery enhancement, middlings slurry is withdrawn from the TOR vessel, and passed through a number of parallel Jameson downcomers, within which the slurry is accelerated to a high-velocity free jet, and impinged upon the slurry surface inside the downcomer, in the presence of air. The aerated slurry is returned to the middlings zone inside the TOR, resulting in an incremental recovery improvement of bitumen in the TOR. The operation of the downcomers is thought to produce suitably small air bubbles for the flotation of bitumen, either by fluid shearing during the slurry jet impingement, and/or by micro-bubble nucleation. This full-scale prototype design has met or exceeded the recovery expectations of the original Research piloting, recovering at least 40% of the non-floating bitumen. In Syncrude Extraction, this provides high business value by a separation efficiency gain achieved with modest expenditure. As well, the system has demonstrated excellent operability and maintainability.INTRODUCTION Syncrude Overview Syncrude Canada Ltd. is one of the largest producers of crude oil from oil sands. Our crude oil production facility has the capacity to produce over 15% of Canada's total oil requirements. To do this, we surface mine oil sand, extract the raw oil known as bitumen from the sand using water-based processes, and upgrade that bitumen into sweet light crude oil by fluid coking, hydro processing, hydro treating and reblending. Our final product, Syncrude Crude Oil (SCO), is sent by pipeline to three Edmonton area refineries and to pipeline terminals which ship it to other refineries in Canada and the United States. The Syncrude operation is comprised of four major technology areas: Mining, Extraction, Upgrading and Utilities. As well, Syncrude invests more than $40 million annually in science and technology, and is among the top 50 companies in Canada for Research and Development (R&D) investment. Syncrude holds 21 active Canadian and U.S. patents."

Jan 1, 2012

"In mineral exploration and mining applications, it is sometimes necessary to reduce sampling error in order to improve representivity of individual sample assays. Historic efforts to reduce sampling error have relied on the belief that larger samples exhibit less sampling error. Justifications for this belief traditionally have coupled the binomial theorem with an ideal geological material consisting of ore and gangue particles of equal size and shape (an equant grain model) and empirical tests of geological materials, to illustrate an inverse relationship between sample size and sampling variance. To date, no proof exists of this sample size-sampling variance relationship in real geological materials exhibiting variations in grain size, shape, composition, and degree of liberation.Using first principles calculus and the formula for the mean, sample mass and sampling variance are proven to be inversely proportional in all geological materials. Distribution assumptions and physically ideal geological models are not used in this proof. Furthermore, algebraic manipulations of expressions describing the variances of equant grain models consistent with binomial, hypergeometric, and Poisson distributions reveal that these models also exhibit an inverse sample size-sampling variance relationship. Thus, the sampling behaviors of these models are numerically consistent with the sampling behaviors of real geological materials, and these models can be used to estimate sampling errors in real geological materials using simple sampling parameters."

Jan 1, 2007