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By A. J. S. Benade, N. B. Strydom, W. H. Van Der Walt

The performance of the improved microclimate suit by N. B. STRYDOM M.Sc., Ph.D. (Illinois) (Fellow), A. J. S. BENADE, B.Sc. (Potch.) (Visitor), and W. H. VAN DERWALT, M.Sc. (Potch.) (Visitor) An assessment has been made of a new improved microclimate jacket when worn by men working for four hours in a hot environment (wet-bulb temperature of 33,9°C and an air speed of 0,4 m/s) and at work rates of 35 Wand 70W. At the lower rate of work in heat, the use of microclimate suits maintained the rectal temperatures of the men at almost the same level as when they worked without that protection at normal room temperature (20°C). At the greater rate of work without protection, the men's rectal temperatures rose to 40°C within two to three hours, so that they could not complete four hours of work. When they wore microclimate suits, they easily completed four hours of work, and their rectal temperatures were lower than when they worked at the lower rate without protection.

Jan 8, 1975

By D. Duncanson, R. J. Davidson, C. G. S. Schmidt, G. A. Brown, J. D. Taylor, N. W. Hanf

The development of a cyanidation route for the treatment of gold-plant gravity concentrates is described. This work was carried out as a natural consequence of earlier improvements to the recovery of gold in the gravity sections of existing gold plants. Concern about the environmental aspects of the conventional amalgamation process was further motivation in the development of an alternative procedure. It was found that the partial pressure of oxygen in solution was the most critical reactionrate determining factor. The rate of gold dissolution was shown to be controlled by the reaction rate below approximately 25°C and by diffusion above that temperature. Thus, the efficiency of pulp agitation and oxygen partial pressure permitted a high degree of control over the rate of gold dissolution. The use of oxygen rather than air significantly increased the dissolution rate of both gold and silver. The solubilities of sodium, calcium, and potassium aurocyanide complexes under simulated reaction conditions were studied, and it was established that the values for the sodium and calcium complexes were limited, requiring the use of lower pulp densities and higher reaction temperatures for the treatment of very high-grade concentrates. The presence of excessive amounts of tramp iron in such concentrates of up to 25 per cent by mass was found to result in poor gold dissolution owing to the cementation of gold under certain reaction conditions. The maintenance of high oxygen partial pressures, together with high cyanide concentrations, high pH levels, and the presence of calcium in the system, all aided in passivating the tramp iron. Copper, gold, and iron were shown to be the main cyanide-consuming elements. Optimum gold dissolution was obtained in a closed bench-scale reactor incorporating a flotation-machine type of agitator for effective pulp agitation and oxygenation, the oxygen being recirculated. The reactor was designed to operate under a very small positive pressure. After reaction times of 2 to 6 hours at temperatures in the region of 30°C, both the gold and the silver dissolution averaged 99,S per cent. In the case of very high-grade concentrates, it was shown that gold could be floated in the same reactor by drawing off the flotation concentrate through a port in the reactor. A flotation recovery of 87,4 per cent of the gold in 3,9 per cent by mass was obtained. The recovery of osmiridium from cyanide-leach residues and the electrowinning of gold from the pregnant liquors were also considered as processing aspects in the treatment of gold-plant belt concentrates. Final table tailings with a gold concentration of 10to 12 gft were obtained. The results of the investigation strongly suggested that an alternative cyanidation route for the treatment of gold-plant concentrates was technically feasible, provided the system included effective agitation and oxygenation. In the case of lower-grade concentrates, cyanidation followed by the electrowinning of gold appears to be the simplest route, while, for high-grade concentrates, flotation and smelting of the concentrate followed by cyanidation of the flotation tailings are suggested. The use of oxygen rather than air for sparging the pulp would depend largely on the grade of material to be treated. A preliminary comparison of the costs related to the amalgamation and cyanidation processes for the recovery of gold from such concentrates indicated very similar capital and operating costs. It was concluded that other considerations, e.g. toxicity, safety, and lower labour requirements, were more important than such small cost differences. Furthermore, the 'opening' of the gold-plant gravity circuit, which would be made possible by a cyanidation route, would further reduce the operating costs because of the subsequent decrease in the tonnage to be treated.

Jan 1, 1978

By P. R. Jochens, D. D. Howat, M. S. Rennie

The slags arising from ferrochromium plants were simulated by additions of CaO and Fe2O3 (6 per cent each), Cr2O3 (7 and 12 per cent), and Fe2O3 and Cr2O3 together (6 and 12 per cent respectively) to slags in the MgO-Al2O3-SiO2 system. These additions were made to slags having an SiO2 content of 45 per cent and an MgO-to-Al2O3 ratio of 4 to 3 or 3 to 4. The effect of these oxide additions on the liquidus temperatures, electrical conductivities, and viscosities was determined. The additions of CaO and Fe2O3, although having little effect on liquidus temperatures, decreased viscosity and increased electrical conductivity. The addition of Cr2O3 raised the liquidus temperatures considerably, and tended to decrease viscosity in the temperature range 1 700 to 1 800°C and to increase electrical conductivity.

By H. W. Read, L. G. D. Napier

Change is endemic in our society. Future change will be accelerated by an explosion in technology, communication, and political thought. To meet these challenges, rapid structural changes have been taking place in mining organizations both here and abroad. The management of shaft-sinking projects is a case in point. Shaft sinking is a seminal element in the sustained well-being of a deep level mining venture. Its accomplishment is fraught with risk, involves a high level of capital expenditure, and is a precursor to profitable mining investment. The purpose of this paper is to present a concise and practical picture of the concepts, methods, and techniques of professional project management as applied to shaft-sinking projects.

Jan 1, 1994

By J. D. Koch

A 'project' is defined here as a process in which an idea is developed from its inception until either it is discarded or the product of the idea has been accepted by the ultimate user. The phases in a project, particularly the early phases, are examined, and project organization is described and contrasted with a functional line-management type of organization. Emphasis is placed on comprehensive definition, which is vitally important to the achievement of the goals of time, cost, and quality set for a project.

Jan 1, 1981

By D. F. Malan

Considerable practical knowledge and effective use of empirical evidence is required in the design of tunnel support systems. In many instances, it is unclear how individual support elements interact with fractured rock and which elements of the support system are critical in controlling and containing the movement of material proximate to the excavation. The present paper outlines a displacement discontinuity approach that allows the coupling of surface constraints, in the form of liner or mesh material, to an explicit representation of time-dependent rock discontinuity creep movements. The method is illustrated for a simple square-shaped tunnel profile in which the fracture zone is mobilized by an imposed stress field. A crucial aspect of the model is the computational treatment of the coupling between the liner material and there presentation of the fractured rock mass. This allows the response of the liner material to be assessed quantitatively in terms of the possible reduction of movement in the rock mass. The importance of installing the liner timeously after the excavation is formed is illustrated in a specific example. A number of computational difficulties in simulating liner-rock interaction mechanisms are identified.

Jan 1, 2008

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

By W. K. Loftus, H. S. Simpson

Discussion I. R. M. Cheston (Visitor): I should like to congratulate the authors on this interesting paper which graphically illustrates the overall effects of the gradual developments in diamond concentrating processes which have taken place over the past few years. These final stages of diamond concentration represent only a minor factor in the cost of diamond production but because of the shortage of highly trained people for this work, any easing of the burden on the sorting staff has an importance far beyond the immediate economic sphere. The search for the solution of problems posed by the economic and social conditions of industry is never-ending. The Diamond Research Laboratory is, even now, carrying out further work to improve still more the operation of general diamond recovery processes as described in the paper. Before looking at some of the latest developments in this field of final recovery, there are a few points arising from the paper on which I would like to comment. On page 321, reference is made to the X-ray sorters originally developed by the DRL. The paper gives a figure of 100 per cent recovery of diamonds from +7 mesh concentrates in two passes through the prototype machine. Not wishing to claim miraculous powers for our group, I would prefer to see this given as virtually 100 per cent recovery of all fluorescing diamonds. Firstly however much care is taken, there is bound to be an occasional operating loss. In the test work, 100 per cent recovery was made on many occasions but this was not always so. Secondly, although most diamonds fluoresce strongly under X-rays, some diamonds only fluoresce weakly. Type IIB diamonds, in fact hardly fluoresce at all, but the incidence of this special type of diamond is very low in most deposits. However, in operating the commercial X-ray machines, there is a certain background level of reflected radiation from other feed particles. Unless the diamond fluorescence is several times greater than this, it is not possible to achieve sufficient sensitivity in ejection. A certain small but variable proportion of diamonds from each deposit is always found to fluoresce too weakly to be recovered by the X-ray machine. Tests have shown, that for the De Beers mines, this proportion is considerably less than I per cent. These diamonds are nearly all dark brown or black in colour and therefore of low value. The degree of fluorescence does not, however, depend entirely on the colour or quality of the diamond and some of the brightest fluorescence comes from the lowest quality of boart diamonds. Investigations into the property of the diamond which causes this low fluorescence are being carried out. On page 322 it is suggested that zircon fluoresces in the same colour spectrum as the diamond. This is not quite accurate. The total light given out by zircon under X-rays is of the same order as that of diamond. However the zircon radiation has a much wider spectrum band than the diamond fluorescence. Reference is also made on page 322 to the effect of selective milling in small laboratory mills on diamonds. Perfect diamonds are very hard and very strong and are extremely difficult to break. Imperfect diamonds, which form the majority of diamonds recovered from most deposits, although hard, can be very brittle. Even under slight impact some of these diamonds may shatter to powder. Milling conditions must therefore be extremely closely controlled to minimize breakage, and even so, some breakage will always occur. As suggested in the paper, the necessary conditions are: the use of small balls, slow speed mills and very limited water addition. Tests elsewhere have suggested that the water content of the pulp in such a mill must be less than 25 per cent by weight of pulp to prevent diamond breakage reaching significant proportions. The skin flotation techniques described on page 323 operate on a very small scale. It is of interest to note that in West Africa a large-scale continuous skin flotation machine is used to recover the fine diamonds. In this operation the feed is dried and, after standing, is mixed with water and fed in a single layer onto a woven phosphor-bronze conveyor belt. This belt runs at a shallow angle into a water bath and as the particles are carried through the air-water-interface, the diamonds float off and over a weir into a collecting box. The bulk of the particles, being wettable, sink to the bottom of the tank and are continuously removed. If treated without prior drying, the diamond recovery is poor. If material is treated immediately after drying, a lot of the gangue particles also float. During standing, in the hot and humid atmosphere of West Africa, it is found that the gangue particles recover their wettability much faster than the diamond particles. Optimum selectivity is obtained after standing for approximately 24 hours. At the DRL we have been experimenting with optical filters to differentiate between the fluorescence of diamonds and zircon. By limiting the light transmission to the fairly narrow range emitted by diamonds, it is

Jan 4, 1970

By G. Rebel

Owing to the helical construction of the wires and strands in a triangular-strand rope, a torque is generated when the rope is restrained and tensioned. When a rope is suspended vertically, there is a load differential along its length due to the self weight of the rope. This load differential gives rise to an initial torque differential m the rope. Since the rope is constrained only at the conveyance and sheave wheel, the torque along its length must be constant ID order to maintain equilibrium, a variation in lay length occurs so that the lay length at the conveyance end decreases, and the lay length at the sheave end increases, from the manufactured state. The tension-torsion testing of steel-wire ropes is discussed, and it is shown how the results of the tests can be used to predict static in-shaft torsional behaviour. The expected changes in strand lay length in very deep shafts (deeper than 2500 m) are calculated, and the associated problems and of severe changes m lay length on rope endurance and safety are discussed. Examples of current in-service rope distortions such as kinks and corkscrews are shown.

Jan 1, 1996

By Alan Bauer

SYNOPSIS A discussion is presented of the advances that have been made in rotary drilling in recent years and it is indicated how and why these drills have replaced percussive equipment even in the hardest formations at larger than 7 in. diameter. A method is presented showing how it is possible to estimate drill requirements and how to optimize drilling and blasting costs for a particular situation. To do this it is necessary to have, in addition to drill performance data, a knowledge of comparative explosive performance. Current methods of doing this are therefore critically appraised. As hole diameters have increased for overall drilling and blasting economies the question of fragmentation arises. In North America this has been approached on a try-it-and-see basis giving results that, in general, have been very satisfactory. The current drilling and blasting practices in North America are reviewed and reference made to the factors of importance in slope control.

A number of issues relating to the computational aspects of pillar design are addressed in this paper. The computation of average pillar stress values is important when attempting to establish criteria for pillar design and in the analysis of the stability of tabular pillar layouts. One of the default ?classic? numerical methods that are used to determine pillar stresses is the displacement discontinuity method. In many instances it is not clearly understood that this approach does suffer from some limitations, particularly in relation to the fact that in coarse element simulations, the simulated average pillar stress (APS) can depend on the chosen mesh size. The nature of this error is highlighted in this paper and some strategies are suggested to bound the magnitude of these errors. It is demonstrated as well that the popular linear stiffness approximation to pillar or seam compressibility does appear to allow reasonably accurate estimates of the average pillar stress when either the pillar height is varied or when the seam modulus differs from the host rock modulus. A practical implication of this study is that if the seam modulus is noticeably lower than that of the host rock, such as for coal seams, it is important to use a linear stiffness constitutive model for the pillars rather than a ?rigid? pillar assumption. This added complexity seems unnecessary, however, when simulating hard rock pillars in mines where the seam modulus is very similar to that of the surrounding rock.

Jan 1, 2011

To determine the characteristics of a mineral deposit, the usual practice is to take samples, analyse the properties of those samples and infer the characteristics of the deposit from these properties. This analysis can be done using statistical methods. In the present work we are concerned with two types of statistical approaches, classical statistics and spatial statistics. If one uses classical statistics to represent the properties of the sample values, the assumption is made that the values are realizations of a random variable. The relative positions of the samples are ignored, and it is assumed that all sample values in the mineral deposit have an equal probability of being selected. The likely presence of trends, zones of enrichment, or pay shoots in the mineralization, is ignored. The fact that two samples taken close to each other are more likely to have similar values than if taken far apart is also not taken into consideration. In contrast, spatial statistics will be used if one chooses to consider that the sample values are realizations of random functions. On this hypothesis, the value of a sample is a function of its position in the mineralization of the deposit, and the relative position of the samples is taken into consideration. The similarity between sample values is quantified as a function of the distance between samples and this relationship represents the foundation of spatial statistics. There are few situations where classical statistics can be used. The assumption that all sample values in the mineral deposit have an equal likelihood of being represented will be satisfied only if the sample values are randomly distributed, or if the sample positions are random. Sample values are in fact never randomly distributed within a mineral deposit. Further- more, geologists usually avoid taking samples at random (random sampling), as it is correctly accepted that samples located on a regular grid, or approximately on a regular grid, give more information than randomly located samples. In practice, classical statistics should be used only in the early stages of exploration, when the number of samples available is relatively small and the distances between samples are large. In these circumstances, and whenever the information available is not sufficient to permit the use of spatial statistics, application of the methods described in this chapter is justified.

Jan 1, 1978

Brigadier R. S. G. Stokes of Sherborne, Dorset, is the oldest surviving member of the South African Institute of Mining and Metallurgy. He joined in 1904 and has been a member for 77 years. Book review Sittig, M. Hand book of catalyst manufacture. Park Ridge (U.S.A.), Noyes Data Corporation, 1978. The detailed information in this book is based on patents issued in the U.S.A. that deal with catalysts and their commercial technology. Project management The South African Institute of Mining and Metallurgy is to hold a Colloquium on Project Management in the Metallurgical Industry in March 1980. Ingenieurs-in-opleiding in die weermag Op 'n onlangse vergadering van die Suid-Afrikaanse Raad vir Professionele Ingenieurs is daar besluit om kwytskelding van jaargeld aan geregistreerde ingenieursin- opleiding wat tans met hulle tweejaar nasionale diensplig besig is, te verleen met dien verstande dat.... Engineers-in-training in the army At a recent meeting of the South African Council for Professional Engineers it was resolved that a remission of annual fees would be granted to registered engineers in- training who are doing compulsory two-year national service, provided that.... Processing of fine particles The Society of Mining Engineers of AIME is organizing an International Symposium on Fine Particles Processing, which is to be held in Las Vegas from 24th to 28th February, 1980. Economics of precious metals International Precious Metals Institute announces a Special Course for all interested in economic aspects of today's precious metals.

Jan 1, 1979

[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

This paper sets out to consider a specific type of corrosion protection system, which is referred to as a Duplex Coating system. The dictionary describes a duplex system as consisting of two elements or a “twofold” composition. The duplex system described in this presentation is such a two-part corrosion protection coating, viz, hot dip galvanizing as the firm base or primer, followed by a top paint system designed to combat severe corrosive environmental conditions encountered in nature. In principle, the duplex system is a cost effective and balanced, designed coating that is suited to the environmental conditions and service life requirements.

Jan 1, 2009

By F. Lombard

We consider in this paper the use of a modified version of Hotelling?s statistic in the analysis of particle size distributions. The statistic can be adversely affected by the presence of outliers among the data. We propose a competitor to the statistic that is based on ranks, and hence is less sensitive to outlier effects. The results of a Monte Carlo study suggest that the rank test is highly competitive with the Hotelling test in its ability to detect differences between two mass size distributions. The calculation of the rank statistic is explained in detail and its application is illustrated on two sets of data.

Jan 1, 2012

By F. Lombard

We consider in this paper the use of a modified version of Hotelling?s statistic in the analysis of particle size distributions. The statistic can be adversely affected by the presence of outliers among the data. We propose a competitor to the statistic that is based on ranks, and hence is less sensitive to outlier effects. The results of a Monte Carlo study suggest that the rank test is highly competitive with the Hotelling test in its ability to detect differences between two mass size distributions. The calculation of the rank statistic is explained in detail and its application is illustrated on two sets of data.

Jan 1, 2012

By P. K. Van Manen

Anglo Platinum's Polokwane Smelter is situated outside Polokwane, in the Limpopo Province of South Africa. Wet concentrate is received from various concentrators along the Eastern Bushveld Complex. Approximately 60% of the total concentrate received is from UG2 Reef, and 40% is from Merensky Reef. The concentrate is dried in two flash dryers, and smelted in a single 168 MVA furnace. A PGM-rich nickel-copper matte is cast, crushed and transported to Rustenburg for converting. The plant was commissioned in March 2003. The wet concentrate, containing 12-18% moisture, is weighed, sampled by one of two auger samplers, and off-loaded into a concentrate shed, either directly through a grizzly into a hopper, or onto the floor. From the shed the concentrate is conveyed to 12 concrete silos. Each of the two identical flash dryers can be fed from six silos. From the flash dryers concentrate is transported pneumatically to a 3 000-ton dry concentrate storage silo. The flash dryers are rated at a nominal 66 tph of dry concentrate at 14% moisture, while the furnace can smelt 90 tph of dry concentrate. Therefore both flash dryers are required to operate when the furnace runs at design throughput. Each flash dryer consists of a hot gas generator (HGG), a disintegrator and drying column, and a section for gas/solids separation. In the HGG, gas heated up to 700° C is produced from the combustion of coal peas in a fluidized sand bed. The hot gas and wet concentrate are introduced to the disintegrator at the bottom of the drying column. The disintegrator breaks up any lumps of concentrate, and throws the concentrate up into the drying column, where it travels co-currently with the hot gas. A fan draws the hot gas from the drying column and through the gas/solids separation section, which consists of three primary cyclones, a multiclone and a high-temperature bag house. The dry concentrate reports to a 450-ton dry concentrate storage bin. A portion of dry concentrate is recycled to the wet concentrate feed in a paddle mixer, so that concentrate that is too wet does not enter the disintegrator. The drying column outlet temperature is controlled at 120° C. Coal is received by road, screened for oversize and conveyed to a 400-ton concrete silo. From here it is pneumatically conveyed to a small feed bin at each of the HGG' s. The optimization work consists of process control improvements relating to the HGG outlet temperature, to control the drying column temperature during the ramp-up of the HGG outlet temperature and bag filters. Furthermore a heat balance is used to evaluate options to increase the instantaneous drying capacity of the existing equipment. The coal consumption derived from the heat balance is compared with the actual coal consumption. The purpose of the optimization work is to achieve an operating schedule for the flash dryers such that they operate simultaneously for as short time as possible. Most of the time one flash dryer should operate, allowing maintenance to be done on the other flash dryer, while drawing down the dry concentrate stock. Keywords: Anglo Platinum, Polokwane Smelter, pyrometallurgy, metallurgy, platinum, platinum group metals (PGM), base metals, flash drying, fluidized bed.

Jan 1, 2006

This paper summarises some observations regarding the way SAG and AG mills work based on the last ten years of pilot plant operation, grinding circuit design and operational reviews for various projects in Australia and overseas. The main purpose is to promote discussion on key factors influencing breakage in a SAG mill. The focus of the paper is on two questions: ? How do mill lifters and liners really work and have an effect on grinding? ? How does the mill charge composition impact on grinding performance? The focus of the paper is on observations of mill behaviour in both pilot plant trials and plant operation, particularly on Cadia ore. DEM, by others, and JKSimMet modelling of SAG mill performance have greatly assisted in forming the ideas expressed in the paper and both are valuable tools in developing our understanding of the comminution process. Put in the `extreme' form the major observations and conclusions expressed in this paper are that: ? the main purpose of mill lifters is to reduce mill liner wear and not to promote rock breakage; ? the often promoted theory that balls impacting the ?toe of the charge? is a dominant form of breakage is incorrect; and ? fines production in a SAG mill is primarily a function of the rock load mass, with a secondary dependence on ball load for any given circuit configuration.

Jan 1, 2007

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