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Proceedings of a General Meeting held at the Witbank Golf Club at 19h30 on 3rd November, 1977 Geomechanics colloquy The 27th Geomechanics Colloquy is to be held on 12th and 13th October, 1978, in the Salzburg Congress Hall. The themes of the four half-day sessions will be as follows: Conference on pneumoconiosis The Vth International Conference on Pneumoconiosis is to be held in Caracas (Venezuela) from 29th October to 3rd November, 1978.

Jan 1, 1978

By G. J. C. Young

The new metallurgical plant has a simple, compact layout, being designed for a small team of operators. The reasons for building the new plant are given, and its various sections are briefly described. These include the conveyor plant, milling plant (for run-of-mine milling), thickener plant, agitator plant, filtration, clarification, smelthouse, and central core joining the mill and filtration sections.

Jan 1, 1978

[Consider the situation where we wish to estimate the value of a block of ore W from the values of n samples wt (i = 1, 2.... n). The samples can be located anywhere inside or outside W. The blocks and the samples can have any size or shape (Fig. 8.1). We define ws as the set of all the samples wi: WS = Iw1; W2; W3.. . wn and we wish to estimate the block W using the samples ws. Let xi be the value of the ith sample and µw the unknown average value of the block. We can estimate µw from the average value of all the samples. Let µw be the estimator of µw. As the samples need not be of equal size, the sample average is: µw = wi xi/~ wi. (8.1) The mean squared error made when estimating µw by µw is known as the variance of estimation of W by ws. It is the error made when giving the value of the sample set ws to the block W and is written o2E (WS to W). By definition: o2E (ws to W) = E [(µw - µw)2]. (8.2) If n = 1, this error is known as the extension variance. Since the sum of the weights given to the sample values is equal to 1,0, the estimator µw is unbiased (the question of the absence of bias is studied in more detail in Chapter 9): E [( µw - µw)1 = 0. (8.3) The error (µw - µw) has zero mean and a variance o2E = E (W8 to W). If we assume that this error is normally distributed, we can define confidence limits for µw. Let tP be the value of the standardized normal variance t such that the probability that t is less than tP is p: (t,) = .\/27T f exp (- t2/2) dt = p (8.4) The probability that µw is larger than µw + t1-P oE is p. The probability that µw is smaller than µw- t1-P oE is p. The following approximation formulae are often used to calculate 2p central confidence limits for the block value: 68% central confidence limits (p = 16%): µw - o2E, and µw + o2E. 95 % central confidence limits (p = 2,5 %): µw - 2 oE, and µw + 2 oE. Tables of the function 0 can be found in any textbook on statistics (for example, Fraser, 1958, p. 388) (see Table 7.2). [ ] The last line of Table 2.2, corresponding to f = 00, also contains the value of tP for p = 80, 90, 95 and 97,5 %.]

Jan 1, 1978

Minutes of the Annual General Meeting held at the St. Helena Club on Wednesday, 27th July, 1977, at 7.30 p.m. Book review Advances in extractive metallurgy, 1977. Proceedings of the third symposium organised by the Institution of Mining and Metallurgy held from 18-20th April 1977. London, the Institution of Mining and Metallurgy, 1977. 244 pp. £18,50. Coal preparation A meeting of the Organising Committee of the Eighth International Coal Preparation Congress took place in Moscow on 24th and 25th May, 1977.

Jan 1, 1978

By J. Kitagawa

The principal objectives of a metallurgical test programme for a 'grass roots' mining project are twofold. The first requirement is to establish the metallurgical viability of the project by demonstrating that acceptable results can be obtained by processing of the ore. The second goal is to obtain essential supporting data to determine whether the project is economically feasible. This involves several functions, which include the establishment of a workable flowsheet, the obtaining of design criteria for the commercial plant, and the collection of the evidence necessary to convince management, and often a third-party expert, that the metallurgy predicted for the ore can be achieved in a full-scale operation. The latter task is facilitated if a coherent overall picture is presented considering the geology of the orebody, the mining plan, and the mineralogy and metallurgy of the ore. The purpose of this paper is to provide guidance in the establishment of a test programme to meet the above objectives.

Jan 1, 1978

The second annual student prize giving function of the South African Institute of Mining and Metallurgy was held in the Van der Byl Hall, University of Pretoria, on Thursday, 10th March, 1978. The main address (see opposite page) was given by Dr T. F. Muller, Chairman of Iscor.

Jan 1, 1978

By W. J. Van Den Berg, J. G. Taylor

The paper discusses the introduction of blindhole boring on the South African gold mines of Anglo American Corporation. It covers the boring trials conducted, and outlines the progress made in the development of blindhole borers. The operating costs, and performances, of the latest 1,52 m diameter borer are given. Future trends and requirements In the application and design of blindhole borers are discussed, as well as factors that are of importance in the design of future machines.

Jan 1, 1978

By G. H. Grange

Details are given of three legal controls for the pollution of the air, the water, and the land, together with brief histories of the developments leading up to these controls. Attention is drawn to the fact that legal action may be instituted against a mine under common or other laws where pollution causes proveable damage or loss. It is suggested that an international conference should be held to define the philosophies and principles on which to base not only the necessary legislation for environmental control but also the machinery by which the controls can be administered.

Jan 1, 1978

By G. P. N. Venter

A method of evaluating the possible effect of an industry on the environment is presented, and the method is illustrated by its application to a hypothetical problem. An analysis is offered based on an actual survey of four industrial sites in the Lydenburg area of the eastern Transvaal. The survey showed that there is a high incidence of potentially unfavourable conditions, and there is a distinct possibility that a topographically induced eddying motion will extend over the town and the industrial sites. This moving air could entrap air pollutants, resulting in high concentrations of pollutants over the town. It is concluded that none of the sites is suitable for industries that pollute the atmosphere.

Jan 1, 1978

By F. Botha, J. S. Adams, W. T. Ruhmer

The report describes the Amuran project in the Welkom area, which is being conducted by six members of the Anglo American Group. The project comprises three plants for the flotation of pyrite, a twin-stream uranium plant in which 'high-grade' slimes and pyrite can be leached separately, a pyriteburning sulphuric acid plant, and a plant for the recovery of gold from calcines. Details of these plants including capital costs and estimated production are given. Mention is made of the adsorption of gold onto activated charcoal and wet high-intensity magnetic separation as possible suitable processes for these residues.

Jan 1, 1978

By S. J. Patchet

The use of fill in deep-level gold mining presents the possibility of achieving considerable economic and operational benefits if conventional support can be eliminated. Unfortunately, the combination of the properties of tailings from gold reduction plants and the narrow, flat, tabular reefs being exploited make conventional hydraulic filling very unpractical. Laboratory tests indicate that, with careful control of water content, these tailings can provide an adequate fill material. A variety of bonding agents have been investigated, and the most practical seems to be ordinary Portland cement. Even at very low cement contents some cohesion is achieved. The design and layout for a complete fill support system using hydraulic transport, dewatering, and pneumatic placement are discussed, and a surface field trial indicated that the principles involved are correct and that acceptable results can be achieved. This system and material would completely eliminate conventional timber and brick support, and a preliminary economic analysis indicates that filling is cost competitive on a direct replacement basis. All the operations for a full-scale operation are available or have been developed to a stage sufficient to indicate that the system is practical, although certain operations require further refinement.

Jan 1, 1978

The theory of geostatistics covers a branch of .applied statistics aimed at a mathematical description and analysis of geological observations. Geostatistics can be used in pure geology (for example, for the analysis of trace elements in a metamorphic rock), in mineral exploration (for example, for the analysis of geochemical exploration data), as well as in mine valuation. This book is intended to provide a practical introduction to the theory of geostatistical methods of mineral evaluation. Over the years, various mathematical models have been developed to represent the distribution of values in mineral deposits. The simpler models are based on the assumption that the values are randomly distributed. Classical statistical methods, based on this assumption of the random distribution of values, are used to analyse mineral deposits to which these models apply or are assumed to apply. In all mineral deposits, however, one recognizes the presence of areas where the values are higher or lower than elsewhere. Also, the values of two samples in a mineral deposit are more likely to be similar if the samples are taken close together than if they are taken far apart. This indicates that there exists a degree of correlation between sample values, and that this correlation is a function of the distance between the samples. Models have been developed which take this correlation into consideration, with the degree of correlation between sample values being usually measured by the semivariogram function. In these models the fact that two samples taken next to each other will most probably not have the same value, must also be considered; even for very short distances the correlations are usually not perfect and a purely random component is present in the value distribution. The mathematical models will therefore assume the presence of two sources of variability in the values: a correlated component and a random component. Finally, one must consider the particular and very common case of mineral deposits in which the values present a systematic variation in space. This variation is usually referred to as a drift, or a trend. For example, the grade of an ore body may increase with depth of the ore, or it may decrease when one moves away from a central volcanic pipe. The earlier models did not give a satisfactory representation of drifts, and more complex models have been developed, in which three sources of variation are represented. These models are made up of: a deterministic component, a correlated component, and a random component. The deterministic component is used as a model of the drift. The correlated component explains regular changes in values which are not represented by the drift. The random component represents variations which cannot be explained by any of the above factors. The simpler models, based on the assumption of a single random component, will be described first (Chapter 2). The models based on the hypothesis of the superimposition of a correlated component on a random component, will then be analysed in detail. These models are most commonly used in the analysis of mineral deposits (Chapters 3-1 I). Finally, how to deal with the presence of a drift will be briefly described (Chapter 12). This book has been written essentially for students in mining engineering and for mining engineers who are interested in the background to the theory of geostatistics as well as its practical applications. The assumption is made that the reader has an elementary knowledge of statistics. Some knowledge of linear algebra is useful in part of Chapter 9, and is necessary to read Chapter 12. A proof is given of all the equations related to geostatistics, and which are not usually found in elementary textbooks on statistics. Understanding of these proofs is not necessary for practical application of the theory, and the reader may wish to skip them on a first reading, concentrating attention on the numerous simple practical examples given. Although the theoretical geostatistician will not find much new material in this publication, it is anticipated that he will develop some interest in the practical approach chosen to prove the various geostatistical equations. Many people and institutions contributed to the preparation and completion of this work. I am much indebted to Dr D. G. Krige and the Anglo Transvaal Consolidated In- vestment Company Limited, who gave me the opportunity to spend a considerable amount of time working on geostatistical problems, both theoretical and practical, during the time that I was in their employment. Dr Krige contributed greatly in developing my interest in studying both the theory and practice of geostatistics, always insisting that a correct balance be kept between theory and practice. I am grateful to Professor H. M. Wells and the Mining Department of the University of the Witwatersrand for inviting me to give lectures in a post- graduate course on geostatistics. The notes 1 prepared for that course became the foundation of the present work. I am also indebted to the Centre de Geostatistique of the École des Mines de Paris, where I received my first formal education in geostatistics during a summer course given by Charles Huijbregts, after many years of my lonely plodding through the published literature. Many graphs in the present volume are reproduced with the permission of the Centre de Geostatistique. The Department of Metallurgical and Mineral Engineering of the University of Wisconsin-Madison has also contributed in making this work possible, by allowing me to spend a considerable amount of time and resources in the writing, typing, and correcting of successive drafts. I am thankful to Lynn D. Kendall, who typed the entire manuscript under constant pressure.

Jan 1, 1978

It is shown that, when a flat-bottomed indentor is pressed into the surface of a strong rock, the normal force necessary to cause failure of the rock is reduced substantially if a shear force is applied to the indentor. A mathematical analysis is described, which shows that higher stresses are induced in an elastic material close to the free surface of the material ahead of a punch when a shear force together with a normal force is applied to the punch. Therefore, failure of the material would occur with lower forces applied to the punch. Stress trajectories show that fractures develop in the rock along lines of maximum principal stresses.

Jan 1, 1978

The statistical methods described in the previous chapter permit the estimation of the average value p of a deposit, and the calculation of confidence limits for this value. They are based on the assumption of independence of sample values. As soon as a reasonable number of samples has been obtained from a deposit, local valuation, or estimation of blocks of ore within the mineral deposit, becomes necessary. The assumption of independence of values must then be rejected. Local valuation is possible only if there is a relationship between the value of a sample and the value of the surrounding ore, provided this relationship is a function of the position of the sample with respect to the blocks of ore to be valued. Whichever method is used for the valuation of a block of ore, the following assumptions are always made: ? The values of samples located near or inside the block are related to the value of the block. ? The values of the samples located closest to the block are most closely related to the value of the block. These assumptions will hold true only if the following assumption can also be made: ? There exists a relationship between sample values which is a function of the distance between samples. We are saying that the value x (z) of a sample centred at a point z has properties which are functions of this point. A certain spatial structure exists in the sample distribution. We are therefore dealing with a regionalized phenomenon, and we must treat x (z) as a regionalized variable. This can be done statistically by means of a model chosen to represent the spatial structure of the phenomenon. We shall see that the relationship between block values and sample values can be deduced from the relationship between sample values, and all local valuation problems can be solved using the statistical model obtained from the analysis of the sample values. It is important to realize that this statistical model is obtained by analysing the properties of known sample values, and will be used for the estimation of unknown block values. Such a statistical inference is valid only if the model developed represents the properties of both the sampled section of the ore body and the section to be valued: some stationarity conditions must be satisfied, and the model with the least restrictive conditions is preferred. In the following chapters, the most important models used in spatial geostatistics are presented. The models which can be used when there is no significant drift (trends) in values are described in Chapters 3-1 1. These models can also be used to solve some specific valuation problems when a linear drift is present. A general study of the more difficult problem of analysis of an ore body whose values present a drift is described in Chapter 12. Note that the area considered for local valuation of a block of ore is often small enough for any drift which might be present to be ignored.

Jan 1, 1978

By A. E. Hall, R. N. Taylor, J. G. Taylor

The introduction of tunnel-boring machines to South African gold mines has created problems and challenges which accompany any new technique. This paper describes the experience gained in this field, especially in the design and erection of a tunnel borer and in boring and environmental conditions.

Jan 1, 1978

By A. K. Haines

The status of the South African research and development programme on continuous ion exchange, which was aimed at the technical and economic assessment of that process for the recovery of uranium, is reviewed. The first phase of this programme, which has now been completed, involved development investigations on various pilot plants and culminated in the successful operation of a large-scale demonstration plant and the incorporation of the system in a number of new South African uranium plants. This account highlights the engineering aspects and the design fo the system, its adaptation to process flowsheets, and plans for future development.

Jan 1, 1978

By M. G. Adamson, B. D. H. Phillips

This paper describes a procedure that has been found successful in the planning and execution of practical trials of mechanized-mining equipment. The procedure is illustrated by reference to development trials of a rockslotting machine with pneumatic or hydraulic drills that were conducted on South African gold mines.

Jan 1, 1978

By J. J. C. Heynike

The relationship between population growth and steel consumption since the beginning of the twentieth century is indicated, reference being made to the increasing capacity of production units and the resultant increased pollution in the same area. The need for the control of fugitive emissions with its associated high cost is pointed out. There is a direct relationship between energy and pollution, and examples are given of several improvements that have been made to achieve better energy usage and reduced pollution. Several practical examples of air-pollution control systems are described as applicable to the main metallurgical steel processes of today. In conclusion, reference is made to the fact that, with the improvements attained in reducing pollution, the public will not tolerate a decline in the standards already attained. Environmental control and better energy utilization will continue to be important aspects of steel-plant design and operation.

Jan 1, 1978

By R. P. King

The flotation behaviour of phoscorite from the Phosphate Development Corporation was measured in a pilot plant, the flotation cells in the plant being varied in configuration so as to operate with or without circulating loads. The ore was floated in a batch cell so that the parameters for a kinetic model could be estimated, and these parameters were then used in a flotation-plant simulator, which is based on the kinetic model, in the prediction of the performance of a pilot flotation plant operating on phoscorite. The simulator predictions compare well with the measured performance of the ore in the pilot plant, but the comparison shows that the kinetic model is not completely adequate for the prediction of performance in continuous flotation plants. The model is weakest in its ability to model the behaviour of the froth phase. The flotation behaviour of the ore could be adequately described when it was assumed that the apatite and gangue each consist of floatable and unfloatable components. The effect of particle size on the specific flotation-rate constant of apatite was found to have a maximum at 85 µm and to fall to zero at 400 µm that for the gangue had a maximum at 50 µm and was zero at 350 µm.

Jan 1, 1978

[The following notations will be used: O an ore body. z a point in O. z' another point in O. w0 (z) a point support of infinitely small dimensions w0 centred in z. w (z) a sample (or block) of finite dimensions kv centred in z. W (z) a block of size W greater than or equal to w. W'(z) a block of size W' greater than or equal to W. W" (z) a block of size W" greater than or equal to W'. x (z) value of the regionalized variable x with support wO at point z. p (z) average value of x in w (z). pw WZ) = E[x(z')l zt in w(z) pw (z) average value of x in W (z). pwl (z) average value of x in W' (z). pwU (z) average value of x in W" (z). Note that pW (z), pw (z), pwf (z) and pw,, (z) are (regular- ized) regionalized variables with support w, W, W' and W" respectively. The relative sizes of wO, w, W', W" and O are represented schematically in Fig. 7.1. The variance of pw (z) when w (z) takes all possible positions in O is known as the dispersion variance of w in O and is denoted by a? (w in O) or a\: 0; = a2(w in a = Ew,z, inn {[p~ (z) - p121. (7.1) For convenience, the following simpler notation will be used: a> Ew in n [(p w - pl21. Consider now a large block W (z) in O with average value p~(z), and all the possible smaller blocks (or samples) w (z') of size w in W (z). We can calculate the variance of the blocks w (z') in the block W(z), which is the dispersion vaciance of w in W (z), from the relationship a2 [w in W(z)l = Ewcz,, in W(Z) {[PW (z') -pw (z)l21. (7.2) Provided the intrinsic hypothesis is satisfied (§3.4.4), this variance is a function only of the dimensions of the supports w and W, and is independent of the position z of the block W (z). We can therefore define the dispersion variance of w in W, as follows: u2 (win W) = Ew in w [(ptti - PW)~]. (7.3) In cases where the intrinsic hypothesis is not satisfied, the variance of samples w in blocks W may vary only slightly from block to block, so that the average dispersion variance of w in W (z) for all possible W (z) in O can be used: ayw in W) = Ew(,, ~n n {a2 [W in W (z)]}. (7.4) The following example will help to illustrate the importance of the variance of dispersion. Assume that we plan to develop a bedded coal deposit Q. We consider mining the ore body with only one giant dragline, which will extract each day a block of coal of size W'. The total area mined in a year will have a size W". We want to know whether this scheme is acceptable, given that the daily variation in ash content must not exceed a given percentage specified in the sales contract, which is renewable on a yearly basis. On a given day, if we mine the block W' (z), the ash content will average pwT (z). In a period of one year, the expected daily variation in ash content is measured by the expected variance of pwf (z) in W", i.e. by a2 (W'in W"). An alternative mining method might be to use two smaller draglines, each one mining W'/2 of ore per day, and Wn/2 per year. If the draglines are used to mine two distinct sections of the deposit, the expected daily variation in ash content will be u2 (W'/2 in Wj1/2)/2 Other situations, where economic decisions cannot be made without knowledge of the dispersion variance, are illustrated in § 7.4 and 7.5 below. Remark: The notation a2 (w in W) is used in this publication because of its clarity. An alternative notation, which is increasingly accepted in the literature, is s2w/W. ]

Jan 1, 1978