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By C. W. Eggert

"The idea for this talk came to me last year when I was attending the Canadian Gold Metallurgists Meeting. I talked about it to a friend of mine who is an authority on mineral dressing, particularly the theoretical end of the business. He remarked that this was an excellent technical note, why don't you write it up. This is what I have for presentation this morning. I hope in presenting this type of idea in this way it is in keeping with the tradition of the Canadian Gold Metallurgists which was to function on a not too sophisticated level and where operators could get together and trade ideas in an informal way.My basic thesis is that it should be possible to evaluate screen analyses by the application of the standard statistical probability theory. In any statistical analysis the sample is the first consideration. If we look at existing methods of size evaluation we find it is usually based on the fact that a given particle will pass one square aperature and not another. One system of standardizing how these aperatures will be set up is based on Rittenger' s work with the ratio of hole sizes proportional to the square root of 2. Keeping in mind the limitation we have accepted this as our method of 11 sizing"" in attempting to apply standard statistical methods to screen analysis."

Jan 1, 1968

By W. E. Roscoe

The probability of making an exploration discovery in Canada can be calculated from Derry's (1970) data on exploration expenditures and number of discoveries over the last nineteen years. Considering an average exploration "try" to be $30,000, the probability of a discovery with one try has decreased tenfold from about 0.01 in 1951 to 0.001 in 1969. A plot of these probabilities can be extrapolated to the future, giving a 1969-71 three-year average probability of 0.00096 with 90 per cent confidence limits of 0.00042 and 0.00153. Using this probability, various calculations can be made, such as (1) the probability of making at least one discovery for any given exploration expenditure, (2) the probability of ultimate ruin or survival of the exploration investment process and (3) the expected value of an exploration investment. There is a critical minimum amount per discovery that must be re-invested in exploration, no matter how large the original investment is, for exploration to survive at all in the long run. Currently, this critical minimum is $31,200,000 with 90 per cent confidence limits of $19,600,000 and $71,400,000.

Jan 1, 1971

By A. F. Silva, R. Dockendorff, J. M. Girao Sotomayor, V. F. Navarro Torres, C. Castro

This paper shows the importance of performing probabilistic analyses in open pits, especially for mine planning, which can lead to more efficient ore extraction and meeting the acceptability criteria for safety in mine slopes. Three-dimensional stability analyses were performed to evaluate the future geometry of a large open pit for iron ore extraction in Brazil. The strength parameters of the lithologies were calibrated using ruptures in the pit walls. After determining the factors of safety (FoSs) from the calibrated parameters, probabilistic analyses were performed using the total range of values of each parameter under different field conditions to verify the reliability of the initial analysis. In this sense, it was possible to plot the probability of failure (PoF) and the FoS on the graph of slope height versus slope interramp angle (IRA) for the future pit in each lithology. IRA recommendations are made for two scenarios: (1) the best scenario: dry without ubiquitous joints and (2) the worst scenario: the water table at 10 m depth with ubiquitous joints in the most unfavourable direction. The results show that probabilistic evaluation is an important tool for establishing alert mechanisms in slopes that can be termed stable.

Jul 2, 2022

By John G. Kovac

A computer simulation has been developed to estimate the chances of a miner making a successful escape while wearing a SCSR. The model takes into account: (1) training in the use of SCSRs, (2) apparatus integrity, and (3) the oxygen cost of a mine escape. This Bureau of Mines report examines survival odds for a prototypical escape, and illustrates how these odds change when SCSR training is improved.

Jan 1, 2009

By John G. Kovac

A computer simulation has been developed by the US. Bureau of Mines to estimate the chances of a miner making a successful escape while wearing a self-contained self-rescuer (SCSR). The model takes into account (1) training in the use of SCSR's, (2) apparatus integrity, and (3) oxygen cost of a mine escape. This report examines survival odds for a prototypical escape, and illustrates how these odds change when SCSR training is improved.

Jan 1, 2009

By Calvin L. Stevenson

The probability of a particle passing through a maze is predictable and consistent. This principle may be utilized to effect a particle size separation of materials by presenting a physical maze to a stream of material that will allow the fine particles to pass, while deflecting the coarse particles. A maze is effective even though all apertures encountered are many times larger than the particles being separated. By designing a machine that allows the probability parameters to be controlled and varied without changing physical dimensions, probability sizing becomes a useful tool for the separation of granular materials.

Jan 1, 1967

By C. W. Hoffman

A fairly recent development in the field of particle separation is now under investigation to determine its value to the mining industry. The method employed is probability sizing through a vibrating network of decreasing screen openings. While probability sizing as such is not new, the possibility of using it for coarse, highly abrasive ores at high tonnage rates has only recently appeared to merit practical consideration. The advantages to be gained by the use of probability sizing vs. conventional screening methods are: reduced space requirements for a high capacity unit, fewer moving parts, more versatile product sizing selection, reduced maintenance requirements and lower power consumption.

Jan 1, 1968

By Randal J. Barnes

In, any open pit mine the ability to make accurate production estimations for the shovel-truck system is an important asset. This is true in an operating mine wishing to estimate production under a set of system modifications (i.e. more trucks, fewer loaders, change in roads, etc.), as well as in the pre- mining planning stages of a property. Many different methods have been proposed for solving this problem; some of the methods rely heavily on "rules of thumb" while others are highly mathematical and require access to a high speed digital computer. Analysis of shovel-truck systems with the use of simulation models is a widely accepted technique within the industry. Through the use of such models it is possible to account for much of the inherent variability of the system and thus produce meaningful results. However, simulation studies are expensive. Formulation and setup of the actual simulation model requires a significant commitment of time and energy. In addition, the cost of the necessary computer runs is often of considerable magnitude.

Jan 1, 1979

INTRODUCTION TO PROBABILITY THEORY The mathematical theory of probability provides the foundation for the interpretations and inferences that can be made from statistical techniques. Probability theory is a broad field of study in itself, and can only be touched on here in order to provide the necessary back- ground for a more complete understanding of statistical analysis. Probability is concerned with the outcome of random events. It had its beginnings in the theory of games of chance which were of great interest to European mathematicians during the last half of the 17th century. The outcome of a random process or experiment is defined as an event. The collection of all mathematical points associated with each event is called the sample space for an experiment. Consider a random experiment having a finite number, n, of possible outcomes, some of which have a characteristic A. What is the probability that A will result from a single

Jan 1, 1980

By G. Pan

The production data of many mines have not reconciled geostatistical estimations based on exploration and development drilling. The discrepancies in recovered metals are sometimes as large as 30%. A number of factors are responsible for such unpleasant outcomes. A major cause, however, is the lack of geological controls in the implementation of geostatistical techniques. Geological modeling establishes geological constraints and mineralization/ore envelopes. Geological constraints are usually established through drill hole interpretation. Mineralization and ore envelopes have been delineated manually based on assay grades. The issues associated with manual methods are: •Time requirements . •Inconsistent dilution. •Uncontrollable implementation variance. Although the time issue may not be a big concern for some companies, the other two have been responsible for many undesired estimation errors. A new geostatistical approach described in this study is designed on the basis of indicator and ordinary kriging. The central component of the method is the procedure for automatic delineation of mineralization and ore envelopes. The method, referred to as probability assigned constrained kriging (PACK), is demonstrated on a Carlin-type gold deposit. The estimation results are compared to blast-hole based production panels, showing that the estimated tonnage is about 2.1 % higher than the actual production, and the average grade is about 2.4% lower.

Jan 1, 1995

By B Mohanty, G Yamin

A number of parameters, aside from blast design and pre-existing rock conditions, can change the performance of the explosives system in actual blasting practice. Sympathetic pressures caused by detonation of preceding holes have been identified as a major contributor to explosive system malfunctions, leading to uneven blasting performance. These effects can occur both within a hole or across several holes. These can consist of high transient pressures related to the shock phase of the explosion or the relatively longer or quasi-static pressures associated with the explosion gas expansion phase. This study presents the findings from an on- going investigation on measurement and analysis of these pressures between donor and receptor holes in a granitic outcrop for representative inter-hole distances and borehole conditions, employing single cartridges of emulsion explosive in 45 mm diameter holes. The results, despite wide scatter in the measured values, show the very short duration pressures to range up to 7 MPa and arriving within a few milliseconds after detonation, whereas the much lower amplitude pressures arrive after tens of milliseconds. Both have the potential to seriously affect the performance of an explosives system.

Jan 1, 2005

By John Reilly

Costs of complex/underground projects have been consistently underestimated and delivery on time and on budget has been problematic. This has been attributed, to inadequate cost estimates and unidentified and/or insufficiently managed risk. Use of probabilistic cost estimates like the Washington State Department of Transportation?s CEVP® process (developed by the author and others) has produced more realistic cost estimates, explicitly identified and quantified risk (as input to risk management plans) and early awareness of key project issues. This paper updates previous work (NAT 2004), adds implementation detail for probalistic cost estimating as used by WSDOT, FHWA and other agencies and will address key issues in risk management, as related to probalistic cost estimates.

Jan 1, 2008

By T. T. Read

A SHORT time ago, one of the large steel companies courteously furnished the author with detailed records of the operations of a considerable number of iron blast furnaces over a period of two months. These will be made the basis of a subsequent study, but in beginning this study one of -the first points requiring consideration was the probable error of the records, for what otherwise might be regarded as significant differences of performance under different conditions were perhaps really due to errors of observation, or failure to observe and record variations. If it is assumed, in blast-furnace records and calculations, that known quantities or factors are constant, when as a matter of fact they are variable, the effects of these variations may erroneously be ascribed to some other cause. This is quite clearly expressed in the following quotation from E. Buckingham:1 Theory always operates on an ideally simplified picture of reality because real phenomena are unmanageably complicated. The results obtained are not exactly true for any, real phenomenon, though they may be for an ideal one; and the approxi¬mation with which a theoretical equation, however obtained, represents the actual facts, always depends on the approximation in essentials between the ideal picture and its real prototype. The purpose of dimensional reasoning is to find out how some quantity which is involved in the phenomenon under consideration is related to certain others; or to find the relation connecting two or more quantities which vary, or may vary, simulta-neously during the course of the phenomenon. Since we know that we must have a complete equation to start with, we begin by thinking the matter over, to see whether the quantities we have in mind are the only ones involved. Usually it is evident that they are not; so we next make a list of all the quantities we can think of which might under any circumstances be important. Upon considering this list, which is often a long one, it is usually evident that under the actual circumstances a number of these quantities may safely be ignored; so we cross them off the list and thus pass from our most general conception of the phenomenon to an ideal simpler one, in which these quantities are not involved at all.

Jan 3, 1925

By John E. Kinnison

The Mission mine, located in southern Arizona near Tucson, is a recently developed open pit which produces 15,000 tons per day of copper ore. The mine lies on a wide and gently sloping bajada sweeping northeasterly from the Sierrita mountains. It derives its name from the nearby Mission San Xavier del Bac, built circa 1700. The ore body is everywhere covered by about 200 feet of alluvium, as are the adjacent Pima and Palo Verde mines. The geology of the Mission deposit is known principally through the study of diamond drill holes spaced 150 to 300 feet apart. The open pit is in an infant stage and has not yet revealed much of the deposit, although information obtained there by the operating staff, and from a few thousand feet of exploratory underground workings, has added significantly to the general fund of knowledge. Permission to publish was granted by the American Smelting and Refining Company. I am indebted to Kenyon Richard and J. H. Courtright for criticism of this paper and for their direction during the several years in which I studied the Mission deposit. Acknowledgment is given to consultant in petrography, Robert L. DuBois of the University of Arizona. The only previous publication pertaining directly to the geology of file Mission deposit appeared in 1959 (Richard and Courtright), and may not be everywhere readily available. Cooper (1960) has published a short paper on the district

Jan 1, 1963

By Dorricott M. G, McAllister J

This paper is concerned with the application of a probabilistic approach to the risk assessment of mining projects.In current practice, sensitivity analysis is the most commonly used deterministic approach of accounting for the uncertainties involved in mining project evaluation, while Monte Carlo simulation is considered to be the best probabilistic method available for the same purpose. The methodology of the approach proposed in this paper is as simple as that of sensitivity analysis. However, the results obtained can be more comprehensive than those obtained from Monte Carlo simulation. Various important statistical features, such as correlation and skewness, of the basic random parameters can be easily taken into account by the proposed approach. Example studies are demonstrated. Lotus 123 was employed for the associated probabilistic calculations.

Jan 1, 1992

By R. L. Schmidt, Williamson. T. N.

INTRODUCTION This paper describes one of several research projects funded by the Advanced Research Projects Agency to extend the technology of rapid underground excavation. This study and field research effort are to investigate alternative means to determine rock and geological conditions in advance of a tunnel boring machine (TBM). Approximately 1 year of a planned 3-year program has resulted in the definition of three candidate drill systems. Hardware has been assembled to field test these candidates and testing has begun. The 3-year objective is to develop a single optimum prototype drill and test it in an active TBM operation. ACKNOWLEDGMENT This research was supported by the Advanced Research Projects Agency (ARPA) of the Department of Defense and was monitored by the Bureau of Mines under Contract No. H0210037. The authors and sponsoring agencies are indebted to the quarry operators in California, Virginia, and West Virginia who offered assistance including access to their properties.

Jan 1, 1997

By Daniel Gendron, Luc Morin

"Concentrate sampling is a growing concern in the world's mining and smelting industry. The main modes of transportation for concentrate to the smelter are by truck or rail car in a bulk form, thereby limiting access to sample extraction equipment. In many cases, concentrate is shipped to a smelter by several suppliers therefore requiring individual manipulation of different customer samples in a safe and reliable manner. The Heath & Sherwood Bulk Product Sampler offers this feature as well as an economical and effortless way of obtaining samples in rail cars or truck boxes.In 1994, Noranda Metallurgie in Rouyn-Noranda, Québec purchased a self contained Bulk Product Sampler to extract samples directly from inside rail cars before unloading the concentrate. After testing and comparing the results with the conventional sampling method, the bulk product sampler proved to be a practical and advantageous solution for concentrate sampling both for the customer and smelter. Since its installation at the Horne smelter in Rouyn-Noranda, the Bulk Product Sampler has been steadily used on rail cars which contain concentrates from around the world."

Jan 1, 1996

A Little Book on the Assaying of Gold, Silver, Copper, and Lead. Also on How to Assay and Work profitably All Minds of Metal. Complied with great care for the benefit of all mintmasters, assay masters, gold= smiths, miners, and dealers in metals.

Jan 1, 1949

GOD the Almighty has all things well ordered; in G particular, the effects and attributes of the seven planets whose reign and course (by the grace of God) determine for the most part not only our own life and death but also the growth and decay of vegetable and mineral life, so that the aforesaid planets generate and develop in a wondrous way the ores of gold and other metals in minerals, rocks, and earths. Specifically, the Sun develops the ores of gold, the Moon the ores of silver, Venus the ores of copper, Saturn the ores of lead, Jupiter the ores of tin and bismuth, Mars the ores of steel and iron, and so on. Since, however, no ore is made alone but each is made and wrought so that it is associated with other ores, it is necessary to know the art of separating the thus-made ores after they have become metals; as for instance, silver from lead and copper; gold from silver, and so on. [2]* If this is to be done usefully, you must be able to assay and must understand everything that is needed in connection therewith. It is obviously true and clear as light of day that some kinds of copper contain silver and some kinds of silver contain gold. In order that you may be able to separate them, so that each is obtained by itself and can be worked with profit and re ward you need first of all a true assay for the values of such metal. The assay, by revealing how great they are, whether the pure has been obtained separate from the worthless matter, and what the admixture is, advises you whether it would be worth the expense and the effort to start mining operations. Assaying also indicates how much silver there is in a centner of ore or how much copper and lead there are in

Jan 1, 1949

By L. Gutierrez, M. Pawlik

The rheology artificial mixtures of bitumen with fine quartz of varying bitumen content, as well as actual oil sand ores, was investigated under different physicochemical conditions (pH, temperature). All rheological measurements were conducted using a Haake Rotovisco VT550 rotational viscometer, connected to a fixture specifically designed to measure properties of settling suspensions. It was found that at low bitumen contents (1 %, wt.) the pH of the slurries was the most important parameter that controlled the rheology of quartz-bitumen slurries. At higher bitumen contents (10%, wt.), it was a combination of high temperature and high pH that gave the lowest apparent viscosities and yield stresses of the model mixtures. These model observations correlated well with the rheology data obtained for slurries of actual oil sand ores. The overall results were discussed in terms of aggregation-dispersion phenomena between bitumen and mineral particles.

Jan 1, 2009