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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

By R. J. MacAulay, R. C. More O’Ferrall

Preliminary tests on cement-consolidated gold-plant slime are outlined, together with preliminary underground tests on the behaviour of two paddocks of the material. Further large-scale testing of the same material pumped to the underground workings from a batching plant on surface is described.

Jan 1, 1978

By E. J. Magri, R. M. Murray

This paper describes the application of linear programming to the monthly 'set up' planning of stopers' sections on two gold mines. On one of these mines, the purpose of the exercise was to maximize the total stoping production (measured in centares per month). On the other mine, the maximum stoping contribution (rands per month) was required. Maximization was to be achieved through improved planning, independently of the various other productivity improving activities that were taking place at the same time. The results to date show that, when linear programming is used, an average increase of about 9 per cent in stoping production (or contribution) can be obtained for these two mines.

Jan 1, 1978

By M. G. Spengler

A new type of pack has been developed primarily for the support of narrow stopes. It was shown in the laboratory that it has characteristics that very closely approximate the optimum required by underground support to achieve hangingwall stability.

Jan 1, 1978

In many practical situations, the samples available to estimate a block of ore are not located on a regular grid. The sample sizes and orientations are not constant, and the number and relative position of the samples used for valuation of each block change from block to block. Estimation of a block W might be very complex and time consuming if each sample in the neighbourhood of the block were considered individually. A practical solution consists of grouping the samples in blocks Wi (i = 1, 2, . . . n) in the neighbourhood of W, and estimating µw as a weighted average of the mean xi of the samples in Wi. Possible ways of grouping the samples are illustrated in Fig. 1 1.1. More complex patterns can be found in the literature (Krige, 1966) To calculate the kriging estimator of pw, we must be able to calculate the variance of xi, the covariance of xi and xj, and the covariance of xi and pµw. The purpose of this chapter is to show how these quantities can be calculated when we ignore the position of the samples in the block Wi. We consider the samples to be randomly distributed in Wi; kriging with this assumption is known as random kriging.

Jan 1, 1978

From a consideration of the functional requirements of a stope-support pack, simple design principles were developed. The material and dimensional properties of the different components of the pack were determined from a series of laboratory tests. The most important requirement for an adequate pack is that the cushioning layers of timber between the concrete brick layers should provide sufficient transverse reinforcement. The tendency of the compressed timber to creep is shown to be a serious limitation to pack performance and must therefore be an important consideration in the overall design of supports.

Jan 1, 1978

By T. F. Muller

In recent years, a great deal has been written and spoken, both in our country and overseas, about the dangers posed to the environment and the ecology by mining operations. The object of this address is to put this problem, and it is a real problem, into reasonable perspective. I shall try to present the various facets that merit consideration as objectively as possible. In doing so, I shall examine the following factors: Book review National Coal Board. Gate belt conveyors. London, H.M.S.O. (Price 95p.) Although the preface of this handy little book states that it has been written for the guidance of miningoperation trainees, it will prove valuable to the practising engineer as well. NIM reports Report no. 1733 A mineralogical investigation of weathered carbonatite from Salpeterkop. (14th Apr., 1975; re-issued 28th Feb., 1978). Report no. 1823 The recovery of gold and pyrite from a residue dump at Crown Mines. (10th Jul., 1976; re-issued 28th Feb., 1976). Report no. 1829 An investigation of weathered carbonatite from Salpeterkop. (20th Jul., 1976; reissued 28th Feb., 1978). Report no. 1932 A BASIC computer programme for the evaluation of intensity data from the Telsec Lab-X-250 Analyser. (12th Jan., 1978). Report no. 1940 The extraction of the noble metals with n-octylaniline, and its application to the analysis of platinum-bearing materials. (30th Jan., 1978). Report no. 1945 Analyses of the NIMROC reference samples for minor and trace elements. (28th Feb., 1978). Report no. 1945 Analyses of the NIMROC reference samples for minor and trace elements. (28th Feb., 1978). International futures conference A conference entitled 'The Road Ahead' is being organized by the 1820 Settlers National Monument Foundation to be held in Grahamstown from 3rd to 7th July, 1978. Conference of metallurgists The technical programme has been established for the 17th Annual Conference of Metallurgists sponsored by the Metallurgical Society of the Canadian Institute of Mining and Metallurgy. This year the Conference will be held in Montreal, Quebec, on 27th to 31st August, 1978, together with the 8th Hydrometallurgy Meeting.

Jan 1, 1978

In many practical situations, calculation of the point semivariogram is not necessary. Such a case is analysed in this chapter. The purpose of this analysis is to give a better understanding of the meaning of the mathematical formulae developed in the previous chapters. A similar problem will be studied in Chapter 11, using the point semivariogram.

Jan 1, 1978

The mathematical models of semivariograms can be classified according to whether or not they correspond to situations where the second order stationarity conditions are satisfied (§ 3.3.4). If second order stationarity exists, the a priori variance s2 of x (z) also exists and is finite. For large distances h such that x (z) and x (z + h) are not correlated, the semi- variogram ? (h) will reach a value equal to s2 [this is a consequence of (3.27) above]. This limiting value is called the sill C of the semivariogram, and the distance at which ? (h) reaches the sill is called the range. The range of the semi- variogram obtained from a given type of sample corresponds to the distance of influence of these samples. If only the intrinsic hypothesis is satisfied, the sample variance is an increasing function of the size of the area or volume in which the samples are located, and the semivariogram ? (h) will be a continuously increasing function of h. Remark: It will be shown in Chapter 7 that the variance s2 of x (z) in the ore body O is equal to the average value of ? (h) in O. If ? (h) is a non-decreasing function with sill C, the average value of ? (h) in O will be less than C. s2 and C will be equal only if for some values of h in O, ? (h) exceeds C. In practice, if the range of the semivariogram is small with respect to the dimensions of the ore body, the difference between C and s2 will be negligible.

Jan 1, 1978

A General Meeting, followed by a Colloquium on 'Pilot plants and problems of scale-up', was held on 22nd March, 1978, in the Main Hall, Kelvin House, Johannesburg. The President, Mr P. A. von Wielligh, opened the meeting at 09h15. He thanked the authors and contributors for their co-operation, and announced the names of the undermentioned candidates, who had been admitted to membership of the Institute:

Jan 1, 1978

In the previous chapters we did not concern ourselves with the fact that the geostatistical properties of the regionalized variable x (z) are affected by the size of the support w. Ideally, when analysing an ore body O, we would like to determine the properties of point values in O, i.e. the properties of a regionalized variable with an infinitely small support, say w°. In practice, point values are never known. To measure the value of x at a point z we must take a sample of size w centred at z. For example, if we are interested in the grade at point z, w will be the volume of the sample 'centred in z; if we are interested in the metal accumulation at point z, w will be the area of the cross-section of the sample centred in z. We say that the measured property is a regularized variable, and so the semivariogram (or covariogram) calculated from the values obtained is also regularized. In the majority of the mining problems which can be solved by geostatistical methods, we are interested in the properties of blocks of ore and of samples with a finite non-point support. It will be shown in the following chapters that these problems can be solved by calculating the average value of the point sernivariogram in volumes or areas of finite dimension, or between such volumes or areas. These calculations would be simple if we knew the point semivariogram. This means that the point semivariogram has to be estimated from the observed regularized semivariogram(s).

Jan 1, 1978