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By K. Kim, T. M. Yegulalp

A new explanation of the scale dependency of rock strength is presented based on the theory of extremes. A brief review of past work on specimen size and strength relationship is followed by an introduction to the fundamentals of the underlying theory of extremes and its relationship to the scale effect. It is shown that the weakest link theory is directly related to extremal statistics and that parameters of strength distributions of rock can be derived as a function of the specimen size. Three sets of Brazilian test data are used to demonstrate the use of this approach.

Jan 1, 1994

By T. M. Yegulalp

A new explanation of the scale dependency of the strength properties of rock is presented based on the theory of extremes. A review of past work on specimen size strength relationship is followed by an introduction to the fundamentals of the underlying theory of extremes and its relationship to the scale effect on the statistical properties of the strength distribution. It is shown that the weakest link theory is directly related to extremal statistics and properties of strength distributions of rock can be derived as a function of the specimen size. Three sets of Brazilian test data are used to demonstrate the use of this approach.

Jan 1, 1992

By Alan D. Smith

[A standardized checklist in a questionnaire format, was established to investigate selected factors associated with coal nips roof falls, as derived from an intensive review of the literature. A plot study was undertaken to aspect and explore possible statistical relationships that may exist with these parameters. the Purposes of toe study were to: 1. Study in a systematic and empirical fashion selected parameters that may be capable of differentiating characteristics of roof falls; 2. Obtain some predictive indices cased on selected physical and management related variables so that predictions of future problems associated with mine roof falls can be completed, prior to its actual occurrence. Accomplishment of these goals should result in valuable guides to the mining engineer in scheduling exploration work and 4 determining economic feasibility of certain ground control and .lining pro and practices. The parameters associated with mine roof failure that where included in the questionnaire are: working section, county, spar., orientation degrees), pillar dimensions width, length), seam thickness, roof fall dimensions (length, width, surface area, volume), shape of fall (arch, dome, laminar), thickness of thinnest immediate layer, lithology of the first four i.e.-diate roof layers, thickness of h e first four immediate roof layers, type of initial support systems before failure, type of resupport system after failure, length and spacing of bolts in use before failure, length and spacing of bolts planned after allure, presence of .cater, time failure after It coal excavation, distance t3rest ace, physical operation during, time of coo failure, location of the roof fall entry failure occurred ence of sloughing of ribs before failure, and presence of floor heave condition before failure. The typical roof fall had an average roof spar of 20.3 feet, -06 feet depth o coal seam, occurred 136 feet from nearest face, coal seam thickness of inches, p--ar :width off 45 feet surface area D' roof fall 1151 ft2, mainly lamin- shaped, previously rat fore fall between good to very good, little floor heave presence, usually cracks before the fall about 40 percent of reported cases, shales in most of the immediate layers, and usually located in an entry or intersection. in addition, multiple linear regression techniques were employed in the testing process of 18 major research hypotheses in a search for relationships among the various parameters studied of which were found to be significant, once corrected for multiple comparisons.]

Jan 1, 1984

By Nick Warren

The problem considered is that of predicting rock physical properties from observations of the structure of the rock. The approach here departs from previous studies in that both the physical properties and structural features are taken as statistical data and the relations between them are cast as statistical functions. This approach I have termed a "quantitative petrostructure analysis". This Paper deals with two aspects of making such a study; parameterizing patterns of topographic features of rock, and characterizing variables to allow correlation studies to be carried out. The principle of a quantitative petrostructure analysis is outlined and illustrated using maps from two samples of Conway granite.

Jan 1, 1982

The ten-year "supply-demand relationship" tables in this chapter for various mineral and metal commodities have been adapted from Minerals in the U.S. Economy, compiled by the Bureau of Mines, U.S. Department of the Interior, published in 1975. Acknowledgment is made to the Bureau of Mines for compilation of the tables. [ ]

Jan 1, 1976

The U.S. Bureau of Mines Information and Analysis Directorate collects worldwide data on virtually every commercially important nonfuel mineral commodity. These data form the base for tracking and assessing the health of the minerals sector of the U.S. economy. The Bureau's data collection activity was instituted by the 47th Congress in an appropriations act of August 7, 1882 (22 Stat. 329), which placed the collection of mineral statistics on an annual basis. The most recent authority for the U.S. Bureau of Mines survey activity is the National Materials and Minerals Policy, Research and Development Act of 1980 (Public Law 96-479, 96th Congress). This act strengthens protection for proprietary data provided to the U.S. Department of the Interior by persons or firms engaged in any phase of mineral or mineral-material production or consumption.

Jan 1, 1993

Statistics is essentially a study of variability, the use of some suitable mathematical model representative of such variability, and the application of this inferred pattern of behaviour to practical problems. Probability theory is the mathematical structure devised for providing models for chance happenings. Perhaps the simplest example of a chance happening is the result obtained in tossing a coin. Although the result of a single toss can never be predicted with certainty, there is no reason why in repeated tosses the expectancy of heads and tails should not be equal. In such a case the outcomes of the experiment are said to be equally likely, so that the probability of obtaining heads (or tails) is 1 in 2, that is, 0,5. This simple probability .model refers to a 'mathematical' or 'unbiased' coin. Whether such probabilities are meaningful for actual coins tossed in any particular way is a matter for experience to determine. Probability models have also provided the basis for representing observed variability in cases where the actual under- lying probabilities are only partly known or defy analysis. A typical example of the latter case is the variability observed in the values obtained from gold or other ore samples. The interacting natural forces which gave rise to this variability are obviously very complex and are unlikely ever to be unravelled completely. In spite of this, probability theory and the more recent geostatistical theories have provided us with models which can represent this variability on a reasonable basis. Applied statistics and geostatistics must therefore never be accepted as exact mathematical sciences. Furthermore, a basic and essential concept is that in the type of applications covered in these notes, no model must ever be accepted as necessarily the final and exact answer to the problem; thus, any model must prove and continue to prove its appropriateness in practice, preferably by follow-up comparisons.

Jan 1, 1981

By C. Widham

Introduction It is generally accepted as dogma that sampling contributes most of the error in gold fire assays. Differences in assay results on pulps from the same sample interval are frequently regarded as evidence of the presence of the so called "nugget effect" of relatively coarse gold particles. It is true that coarse gold particles can contribute to substantial sampling fluctuations. But, while the process of sampling is probably the major source of error, the analytical process cannot be completely ignored as a possible contributor to erratic assay results. To maintain a stable assay process, the analytic part of the system must also be kept in control. One method of monitoring the performance of the analytic system is to systematically assay standard materials, whose sampling characteristics are carefully controlled. Gold assay standards are not prepared, nor can they be prepared, to account for both sampling and analytical errors. It is not possible to send coarse material to a lab for both preparation (i.e., comminution and splitting) and fire assaying and then come to conclusions only about the fire-assay process. Because most gold ores are very heterogeneous, sampling errors would, in most cases, completely mask the contribution of the analytical errors. Assay-standard material is prepared only to assess the accuracy and variability in the fire assay process. Because the objective of the assay standard is to provide information about the fire assaying, it is necessary to control the sampling error of the standard material, so that it is only a minor constituent of the discrepancies observed in any assay results. To do this requires that the particle size of the standard material be reduced to a point where the relative standard deviation of the sampling error (i.e... the standard deviation of the errors divided by the average gold content of the material) is 2% or less. For all but very homogeneous mineralization, this means that the material must be reduced to 100% -150 mesh before the sampling errors are adequately controlled. However, even reducing the particle size can contribute to sampling problems. The liberation of gold may cause segregation that can cause large sampling fluctuations that are not easily controlled while maintaining the desired grade. Because, in most cases, the standard material would already be in the "pulp" state when it is submitted to a lab for assay, it is not possible to entirely conceal the nature of the sample from the lab. This is a problem inherent in using assay standard material. Because of the contribution of sampling to error generation in the assay process, the use of "coarse" material does not solve the problem of submitting a totally "blind" standard to the lab. In the sections that follow, the selection, preparation, testing and use of gold fire assay standard material is discussed. While some may dismiss the production of standard material as folly, it is possible to produce and utilize standard material to stabilize and improve the fire-assay process to produce more reliable assay results. Material selection It is desirable to use material that has as nearly the same metallurgical characteristics as the samples with which the standards will be included. However, this is usually difficult. For many reasons, including the particle size at which a significant amount of the gold mineral is liberated, the sampling characteristics of even -150-mesh material may preclude the use of geologically and metallurgically similar ore as a standard. It is usually easier to get material having desirable grade characteristics with the necessary sampling properties than it is to find geologically and metallurgically similar material with the required sampling characteristics. High-grade standards are especially difficult to find and prepare. This is because, as grade increases, the size of the gold particles usually increases. Larger gold particles are liberated and tend to segregate during comminution, and the homogeneity of the material cannot be maintained. For grades much above 3 g/t (0.088 oz/ton), it is very difficult to find material that has the proper sampling properties. Old mill tailings are likely candidates for assay standards. Some of these have sufficiently homogeneous mineral contents, so that the sampling errors can be effectively controlled. Where mill tailings are either not available or are not acceptable, mineralization that has exhibited homogeneous results in reassays of the pulp material is also a good candidate for the standard. Finally, the mineralized rock being sampled may (and should) be used if adequate homogeneity in the -150mesh material exists. "Adequate" ("acceptable") homogeneity is defined below.) It is important to use standards having a wide range of grades. This alone may preclude the material being

Jan 1, 1997

By S. Davis

It has been accepted almost as dogma that sampling contributes most of the error to fluctuations in gold fire assays. Differences in assay results on pulp material from the same sample interval are frequently regarded as evidence of the presence of the so called "nugget effect" or relatively coarse gold particles. It is true that if coarse gold particles are present they contribute to substantial sampling fluctuations, but while the process of sampling is probably the major source, the analytical process cannot -be completely ignored as a possible contributor to erratic assay results. In order to maintain a stable assay process, the analytic part of the system must be kept in control as well as the sampling and preparation part. One way of monitoring the performance of the analytic system is to systematically assay standard material whose sampling characteristics are carefully controlled. Gold assay standards are not prepared nor can they be prepared to account for both sampling and analytical errors. It is not possible to send coarse material to a lab for preparation (which includes both the processes of comminution and splitting) followed by fire assay, to make inferences only about the fire assay process. Because most gold ores are very heterogeneous, sampling errors would in most cases completely mask the contribution of the analytical errors. Assay standard material is prepared only to assess the accuracy and variability in the fire assay process.

Jan 1, 1995

By Robert F. Shurtz

This paper discusses and compares methods of statistical analysis of the information relating to the evaluation of an asbestos deposit. From a study of 10-ft. lengths of drill core, the separate effects of visual evaluation errors were determined, as well as the deviations between evaluators and the deviations produced by a slight displacement in the center lines of the check drill holes. The importance of careful statistical analysis of such information is stressed.

Jan 1, 1966

By John A. Wolfe, James A. Niederjohn

Applications of mathematical statistics to the field of exploration are still relatively new. There are two primary reasons why little has been published in this field. First, if one discovers an effective technique for exploration, he does not like to disclose it. Second, the geologist needs to work closely with a mathematical statistician, and the communications barrier between the disciplines is formidable. The authors, one a geologist and the other a statistician, were interested in the economic benefit which appeared to be possible in the inter-disciplinary area they call "geostatistics."

Jan 11, 1962

By John A. Wolfe

Applications of mathematical statistics to the field of exploration are still relatively new. There are two primary reasons why little has been published in this field. First, if one discovers an effective technique for exploration, he does not like to disclose it. Second, the geologist needs to work closely with a mathematical statistician, and the communications barrier between the disciplines is formidable. The authors of this paper, one a geologist and the other a statistician, were interested in the economic benefit which appeared to be possible in the interdisciplinary area which they have called "geostatistics." An actual example has been selected to illustrate this benefit.

Jan 1, 1962

By A. L. Boerner

Off-highway tire costs represent a significant portion of the total mining costs in openpit, truck-shovel operations. To extend the lives of tires, the site-specific factors influencing tire life should be investigated Valuable data can be obtained by combining historical operational data captured by a mine dispatch system with detailed tire and maintenance histories. Assuming that failure counts satisfy a Poisson distribution, F-tests can be applied to determine significant deviations from desired or target counts. The methodology developed in this paper can be used to identify the haul routes and loading and dumping zones that have significantly higher incidences of tire failure. Corrective action can then be targeted at these zones by modifying the shovel or truck operator practices; changing the haul route maintenance and clean up practices; or altering the bench, ramp or waste dump design parameters. An example is given of the correlation of tire separation and tire impact failures with haul routes for a fleet of nine Caterpillar 793C trucks in operation at the Chuquicamata Mine in northern Chile. A high incidence of impact failures was observed for the ex pit ore crusher and for tires installed in the left outer rear position on the trucks. The latter was postulated to be due to a preference for drivers to execute right-hand turns prior to dumping. Recommendations were made to revise crusher and dump cleanup practices and investigate the feasibility of super-elevating the surface of dumping zones to reduce ground pressure on the left rear tires.

Jan 1, 2002

By G. Pouskouleli, T. A. Wheat

"The role and benefits of using statistical methodology in the development and optimization of materials and processes is examined. It is shown that considerable benefits accrue from the use of an appropriate design in which a number of factors (process parameters) are varied simultaneously while the system response such as percent recovery, degree of separation, purity, etc. is monitored and ultimately optimized.Compared with the commonly encountered one-factor-at-a time approach, this schema exploits reduced experimentation (thereby requiring reduced resources [staff, time, dollars, etc.]) yet yields quantitative information on the significance of each factor and their combinations on the measured response."

Jan 1, 1992

By Daniel Hodouin, Antoine Berton

Mineral processing plants are monitored and controlled using measurements that are usually processed by on-line material balance calculation techniques. However, gross errors, due to sensor biases or failures, may corrupt all the process variable estimates. On-line gross error detection methods are required to ensure efficient mass balance evaluation. In the proposed approach, material imbalances and raw measurement corrections are tested by statistical techniques designed to detect and isolate sensor problems.

Jan 1, 2000

By J. M. Mutmansky, T. K. Greer

This paper takes a look at the optimal velocity to be used in coal mine entries and determines a statistical relationship for optimal velocity that can be applied under current mining conditions. This relationship provides the optimal velocity for coal mine airways under variations in power cost, mining cost differential, airway friction factor, time value of money, airway lifespan, and quantity of air carried. This enables the ventilation engineer to make an easy, rapid determination of the optimal velocity for planning purposes.

Jan 1, 1985

By M. Bhattacharya, A. Dutta, P. Barat

"Pinning of dislocations at nanosized obstacles like precipitates, voids and bubbles, is a crucial mechanism in the context of phenomena like hardening and creep. The interaction between such an obstacle and a dislocation is often explored at fundamental level by means of analytical tools, atomistic simulations and finite element methods. Nevertheless, such studies fail to predict the effect on the overall plasticity on account of insufficient information about the underlying statistics of this process comprising a large number of dislocations and obstacles in a system. Here we propose a new statistical approach, where the statistics of pinning at idealized spherical obstacles is explored by taking into account the generalized size distribution of the obstacle along with the dislocation density within a three-dimensional framework. The application of this approach has been demonstrated for dislocation pinning at nanovoids in neutron irradiated type 316-stainless steel.IntroductionPresence of nanoscale obstacles like precipitates, voids and bubbles play a crucial role in determining the deformation behavior of a crystalline solid on account of the interactions between the line defects and such localized obstacles. In the context of the glide motion of dislocations, the obstacles can offer resistance to a moving dislocation, thereby causing a hardening effect [l-3]. In some other cases, inclusions like voids and bubbles can affect the rate of dislocation climb through diffusive [4] and non-diffusive [5] mechanisms. Over the last few decades, numerous studies have been performed to gain an insight of the dislocation-obstacle interactions at a fundamental level. These include the interactions responsible for the hardening effect, in addition to those pertaining to the non-conservative motion of dislocations.Although the elementary mechanisms of the various dislocation-obstacle interactions have been vastly explored and understood by means of analytical theory and numerical simulations, it remains difficult to quantitatively understand their effects on the macroscopic deformation behavior. This is due to the fact that their influence on the gross plastic deformation of a bulk sample would be the collective outcome of a large ensemble of such interactions. As a result, it becomes infeasible to predict the bulk deformation behavior of a material until the statistics of pinning of the dislocations at the localized obstacles is available. In the context of precipitate hardening, some well known attempts to extract the pinning-statistics were made by Friedel-Fleischer [6] and Mott [7] by analytical means, which were later tested through simplified 2-dimensional in-silica modeling [8]."

Jan 1, 2014

By Scott D. Thayer, George H. Milly

INTRODUCTION Ambient concentrations of radon and its daughter products have been measured and analyzed by a number of investigators for a variety of purposes. Principal among these purposes have been: (1) descriptive, to characterize the distribution and changes in concentrations under various conditions; (2) research in the use of radon as a tracer gas in the study of atmospheric characteristics and motions, such as eddy mass transfer, diffusivity profiles, large scale circulations, and the like; and (3) the use of radon as an atmospheric tracer in exploration for uranium deposits.* This information forms the basic data for this paper and for its placing the ambient natural, or non-anthropogenic, radon concentrations into the perspective of ambient radon health standards and lung cancer risk calculations. To enable better understanding of some aspects of the ambient radon data, review and analysis is also performed on selected measurements of radon emanation or flux from the surface of the earth into the atmosphere. These measurements have generally been made for purposes similar to those for ambient radon, i.e., (1) description of radon emanation characteristics; or (2) to support and justify the use of ambient concentration measurements in atmospheric research; or (3) in exploration for uranium. Interest is also developing in the use of such measurements for earthquake prediction. In addition, to complete the perspective, brief examination is given to anthropogenic ambient and flux radon measurements related to the mining and milling of uranium, so that comparison can he made with the values from natural sources. As a frame of reference we cite here previous summaries of studies which have presented representative values and ranges of ambient concentrations and emanation rates. H. Israel, in the Compendium of Meterorology (1951), cites eight studies of ambient radon concentrations which we have selected as representative of non-anomalous continental values. Their means generally range from [0.06 to 0.15 pCi lit-1 with the smallest reported minimum of zero and the largest maximum 0.53 pCi lit-1. The overall mean is 0.10 with a standard deviation of 0.03 pCi lit-1. Means over oceans are much smaller, and the data scarcer, with only three values ranging from 0.0004 to 0.003 pCi lit-1 and a mean of 0.0016 pCi lit-1.] Thirteen studies from Israel's list were selected as representative of mountainous terrain. These data, except for the cases of higher elevations, frequently show significantly higher values than the average cases in non-mountainous terrain described-above. The averages range from 0.10 to 0.59 pCi lit-l; the smallest minimum is zero and the largest maximum is 9.2 pCi lit-1. The overall mean is 0.30 with a standard deviation of 0.17 pCi lit-1. Israel also cites five studies of radon emanation (flux) from the earth's surface. These show a mean of 0.40 pCi-2m-2 sec-1 and a range of from 0.21 to 0.74 pCi m-2 sec-1. Data on flux are naturally scarcer in the literature than data on ambient concentrations, because of the greater interest in and utility of the ambient information. In this paper we also give special consideration to observations of the variability in time and space of radon flux rates, and to the impact of these phenomena on the use of such data for a variety of purposes. NATURAL(NON-ANTHROPOGENIC)AMBIENT RADON CONCENTRATIONS We have examined the following reports for the data selected for this category; these studies were generally intended to describe radon characteristics in the atmosphere. Jonassen and Wilkening (1970); Bradley and Pearson (1970); Wilkening (1970); Lambert, et al (1970); Pearson and Moses (1966); and DickPeddie, et al (1974). Another set of studies which was reviewed was selected because the investigators made ambient radon measurements in the course of examining the use of radon as a tracer in atmospheric research. This set consists of: Israel and Horbert (1970); Carlson and Prospero (1972); Subramanian, et al (1977); Larson (1978); Cohen, et al (1972); Hosler (1966); and Shaffer and Cohen (1972). Finally, unpublished data from uranium exploration activities (Milly and Thayer, 1976) was analyzed. [Treating the ocean cases first, the mean values are generally consistent with those quoted earlier from Israel (0.0004 to 0.003 pCi lit-1); they range from 0.001 to 0.011 pCi lit-1, with 0.003 the most frequently reported value. Continental values, from eight studies, range in means from 0.07 to 0.41 pCi lit-1 (not including mineralized areas, or "uranium country", discussed later), with maxima as high as 2.4 pCi lit -l. For comparison, the means from Israel are 0.06 to 0.15 pCi lit-1, with a maximum of 0.53 pCi lit-1. Some of these studies also present the typical decrease of-1 concentration with height to 0.01 to 0.04 pCi lit at 5 to 7 km. The vast numbers of uranium prospecting radon data of]

Jan 1, 1981

By Ali Dehghani Ahmadabadi

Gravity separation technique is widely used in mineral beneficiation practices for its low cost, ease of operation, and eco-friendly nature. The most commonly used gravity methods for beneficiation of iron ores are shaking table, jig and spiral methods which aren't very effective for iron mineral fines. Multi-Gravity Separator (MGS) is suitable for the treatment of fines with a maximum particle size of approximately 500 µm. This study was performed on a low-grade haematite iron ore from Chadormalutailing dams. Detailed mineralogical, physical and chemical characteristics of a goethiticlateritic iron ore showed that the sample contained porous and friable oxides and hydroxides of iron. The ore sample had a feed grade of 35% Fe, 1.1% FeO, 15.5% SiO2 and 8.5% Al2O3. Haematite and goethite are the main iron-bearing minerals while quartzite and kaolinite are the major gangue mineral constituents. In this paper, the statistical evaluation and optimization of grade and recovery using a factorial design of experiment (DOE) method has been carried out for Chadormalulow grade ultra-fine haematite tailings with MGS. The input process parameters considered are drum speed, tilt angle, wash water flow rate and pulp density. The results show considerable improvements in both the quality characteristics such as grade and recovery with statistical evaluation and optimization, compared to the initial value of grade and recovery. Keywords: multi-gravity separator, mgs, statistical evaluation, optimization, haematite

Sep 1, 2012

By G Anders

The effectiveness of two types of powder used in long-wall slashing was compared. The evaluation of the results can serve as a good example of how the application of statistical methods to underground test data can help to minimize the number of tests to be carried out. The conclusions are stated concisely, including a definite assessment of the reliability of the tests. Introduction AN assignment at the Algom Nordic mine called for a performance comparison between 70 per cent Cilgel B and 75 per cent Dygel in longwall stope slashing, particularly taking into account, in both cases, the build-up of bootlegs as dependent on hole deviation. Stopes were usually 8 to 10 ft. high and inclined at about 17 degrees. Starting from a raise, they were widened by consecutive longwall slashes to 60 ft., and, al-lowing for drift pillars, were approximately 300 ft. in length along the incline.

Jan 1, 1964