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By G. R. Lane

My opportunity to serve as President of the prestigious Southern African Institute of Mining and Metallurgy (SAIMM) was made possible by an Anglo American scholarship 39 years ago—a pivotal moment that set me on a career path spanning various roles and start-up ventures in the mining industry. Over the past decade, I have been privileged to broaden my experience by consulting across diverse industries globally. This exposure revealed something profound: what I had previously considered mining-specific challenges are, in fact, universal across many sectors. At its core, a mining operation is a complex system of interconnected activities—from exploration through mining operations like drill and blast, load and haul, to beneficiation, and outbound logistics. My cross-industry work has clearly shown that diverse sectors, such as chocolate manufacturing, tissue paper production, toilet paper converting facilities, labgrown diamonds, or high-tech equipment lifecycle management, all rely on value streams of interconnected activities to transform products. The objective is to maximise throughput while effectively managing performance variability. The primary difference lies solely in the specific technical expertise required for each industry, such as chemical, mining, processing, or metallurgical engineering. Across all these industries, I have observed a consistent pattern, that is, performance is primarily driven by individual efforts, where people react and work diligently as situations unfold in real-time. General managers and their teams often operate tactically, focusing on explaining yesterday’s poor performance rather than proactively setting up operations for success. This often resembles an ‘‘under-7s soccer match’’, with everyone chasing the ball. The common response to issues is to add more ad hoc meetings. This effort-driven organisational behaviour persists regardless of whether operations are greenfield digital manufacturing facilities, advanced digital mines with advanced process control, or operations run on paper and Excel spreadsheets for data acquisition. Paradoxically, more real-time data can lead to increased data noise, greater indecision, and sometimes, lower performance. Despite value streams often operating significantly below capacity, organisations continue to invest heavily in additional equipment or in ‘‘glossy brochure promises’’ of Industry 4.0 digital technology and real-time data solutions, which frequently fail to deliver value. This leads to a critical question: Have we underinvested in our most valuable resource— people? Even Tesla faced this challenge with their underperforming fully automated Model X facility. We must shift our focus to designing the ecosystem, or operating model, of our organisations. This extends beyond the traditional triad of people, process, and technology, and moves beyond simplistic views of change management. Artificial Intelligence (AI) has the potential to add significant value, but it also introduces another layer of complexity into designing the organisation of the future. My full presidential address below at the SAIMM AGM discussed the symptoms of an effort-driven organisation and covered the fundamental building blocks and requirements of an operating model, including recommendations on implementing a people-centric approach.

Oct 2, 2025

By L. Kühnel, H. Lieberwirth

Confined bed comminution in High Pressure Grinding Rollers (HPGR) and Vertical Roller Mills (VRM) is gaining substantial attention in many applications. Previously used mainly for milling coal or construction materials, HPGR and VRM have started to complement or even replace tumbling mills in ore beneficiation. Materials like coal or clinker are relatively homogenous, however, in comparison to metal ores and wall rocks. This characteristic poses a new challenge to the confined bed comminution but also an opportunity. Fuerstenau and Abouzeid have investigated the selectivity in comminution of a mixture of particles of different strength in a particle bed. The median particle size and particle size distribution (PSD) of the two constituents used were kept constant. Only the proportion of the two constituents was modified. The competence of a material is, however, also a function of particle size. Smaller particles tend to be more competent than larger ones of the same material. If selective comminution is applied on ores, this size influence has to be understood. The paper presents research results on this topic based on experimental investigations with model materials as well as with natural particles, which were stressed in a piston-die press. It appeared that the comminution result depends substantially on the material characteristics and the composition of the mixture. Conclusions will be drawn for the application in future applications of selective comminution in mineral processing. Keywords: Confined bed comminution, HPGR, VRM, piston die press, particle size

Jan 1, 2020

By H. Möller, L. Mashigo, C. Gassmann

Wire-arc additive manufacturing (WAAM) is a directed-energy deposition technology that uses arc welding procedures to produce computer-aided designed parts, such as three-dimensional printed metal components. A challenge of additive manufacturing is the anisotropy. Interstitial elements play a significant role in the mechanical properties of Ti6Al4V of different grades. In this research, the mechanical properties of Grade 5 and Grade 23 Ti6Al4V were compared for this application. Samples were extracted from WAAM-produced Ti6Al4V walls in different directions (horizontal and vertical) and at different positions (top and bottom). The samples were subjected to optical microscopy and tensile and hardness tests. Grade 5 Ti6Al4V samples were found to have greater strength, greater hardness, and lower ductility, owing to the higher content of interstitial elements compared with Grade 23. The bottom samples had higher strength than the top samples, which is attributed to thermal cycling during manufacturing, resulting in different microstructures.

Jul 1, 2021

By L. Makua, K. Langa, Ndlovu. S., C. Saguru

"Global demand for the three platinum group metals (PGMs) Pt, Pd, and Rh has been steadily growing due to their widespread use in emission control, industrial catalysis, and numerous other applications. The primary supply of PGMs is currently the mining industry. However, legislative, operational, and environmental challenges faced by many mining operations result in erratic supply patterns and deficits for these three metals. Naturally, recycling scrap material to recover Pt, Pd, and Rh has therefore aroused research interest in the scientific and engineering communities. Given that the majority of the global demand for these three metals is driven by emission control devices, autocatalytic converters are therefore a significant source of already processed and beneficiated PGMs for recycling.Although pyrometallurgical processes dominate the recycling industry, hydrometallurgical processes may offer certain advantages, chief among these being lower emissions and reduced energy consumption. In this investigation, scrap converter material was leached in acidic chloride media and the leach liquor subjected to solvent extraction and cloud point extraction (CPE) to recover the PGMs. The recoveries for Pt and Pd using Alamine 308® dissolved in kerosene with decanol as a modifier were 95% and 81%, respectively. The maximum recoveries using CPE after complexation with 2-mercaptobenzothiazole (2-MBT) in the presence of Triton X-100 and tin (II) chloride dihydrate as a reductant were 97% for Pd, 96% for Pt, and 91% for Rh. This demonstrates that CPE, although relatively new, may have some potential as a breakthrough PGM recovery technology. IntroductionPlatinum group metals (PGMs) have found a wide variety of applications in different industries due to their chemical, catalytic, and physical properties. PGMs are essential in automobile emission abatement, petroleum refining, and the pharmaceutical and electrical industries (Carabias-Martinez et al., 2000). However, the abundance of PGMs in the Earth’s crust is low and their primary sources are fast depleting (Crundwell et al., 2011).The high demand for PGMs, together with social, economic, environmental, and political aspects related to their production, has led to concerns about their future supply. This has resulted in renewed interest in recycling end-of-life material. PGM supply from recycling has doubled over the last decade, and currently contributes 22% to global supply (Johnson Matthey, 2016). This is in part due to the environmental, social, and operational challenges associated with mining of PGMs. For example, labour unrest, energy cuts, declining commodity prices, and declining ore grades have collectively made the mining landscape economically challenging (KPMG, 2015). On the other hand, the high content of PGMs in secondary sources makes their recovery from the increasing quantities of waste products important from a resource conservation viewpoint. Moreover, PGMs obtained through recycling have been demonstrated to have a 1% environmental cost from a life-cycle perspective, whereas PGMs obtained from mining contribute the remaining 99% of environmental cost (Bossi and Gediga, 2017). Sustainable resource recovery and the economic incentive of recycling have therefore been major drivers to justify investment in PGM recycling. The autocatalytic converter industry accounts for about 70% of the global consumption of these metals (Johnson Matthey, 2016) and therefore recycling spent converters has become a major source of Pt, Pd, and Rh (Figure 1)."

May 1, 2019

By D. R. Lawrence

A method for the calculation of the economic optimum spacing of raise connections in 'scattered' mining layouts is described. The method of calculation and the results obtained in a case study are presented. An indication of how the overall optimum spacing (which satisfies both economic and geological considerations) can be determined is also given. " The case study demonstrates that, even with the present strike-cleaning systems,significant savings in working costs can result from an increase in the spacing between raise connections. Furthermore, improvement of the present systems would result in a considerable increase in these savings.

Jan 1, 1983

By C. M. Suhr

n order to validate the borehole analysis valuation procedure commonly used in the South African gold mining industry, a simulated orebody was used to create borehole values which would serve as data for the procedure. After confirming the distribution, calculating the variance size of area relationship, estimating the block variance, and calculating a profit measurement for each set, comparisons were made to the known population parameters. Results show only one overall bias (in the estimation of the lognormal third parameter), which is carried throughout the analysis. The remainder of the analysis is unbiased, validating the procedure.

Jan 1, 1987

By Isobel Clark

This paper reviews some of the traditional methods of reserves estimation based on lognormal distribution with or without an additive constant. In the rush to computerize mine planning and grade control generaly, proven estimation methods, such as Sichel's t, seem to have been overlooked. By use of a personal microcomputer, the traditional methods were investigated thoroughly, the results being tested against existing tables and figures. The fitting of a lognormal distribution, including estimation of the additive constant, is discussed, and the calculation of Sichel's t estimator and its associated confidence limits is described in detail. Payability calculations for a lognormal distribution are also covered briefly. The advantages of personal computers, particularly speed and ease of use, are emphasized. This low-cost approach permits detailed investigation of some of the assumptions and approximations inherent in the established methods of calculation. Several disturbing discrepancies are revealed in various factors, and some generalized statements made by previous authors are found to be over-simplistic. Full details are given of acceptable approximations and computer algorithms, and concern is expressed over the possible loss of proven methods under the welter of new, sophisticated computer software.

Jan 1, 1987

By A. Santana, J. Jankolovits, G. S. Reyes

The flotation of sulfide ores that contain carbonaceous gangue requires significant operational and chemical intervention to achieve suitable metallurgical outcomes. Carbonaceous gangue dilutes concentrate grades, alters the froth behaviour, reduces operational stability, adsorbs reagents, and reduces value recovery. Carbon management processing strategies like preflotation and depression are often presented as point solutions. Moreover, oversimplified mechanisms of carbon depressants belie their complex and nuanced impact on flotation behaviour. Optimising the flotation of carbonaceous sulfide ores requires a holistic consideration of interactions between the carbon management reagents and the processing strategy, ore mineralogy, flotation behaviour, flowsheet, and all other aspects of the flotation system. Examples are shown where conventional, simplistic mechanisms of carbon depressants fail to explain the observed flotation behaviour. The multifaceted impacts of carbon depressants on froth behaviour, collector performance, and value recovery highlight the need for a holistic approach to carbon management. Keywords: Carbon management, carbonaceous ores, sulfide flotation, carbon depressant

Jan 1, 2020

Fathi Habashi, Chalcopyrite. Its chemistry and metallurgy. New York, McGraw-Hill, 1978. 165 pp. RI9,95. Loss prevention and safety promotion The Proceedings of the 2nd International Symposium on Loss Prevention and Safety Promotion in the Process Industries, Heidelberg, 6th to 9th September, 1977, are now available. Chemical reaction engineering The Proceedings of the 4th International/6th European Symposium on Chemical Reaction Engineering (4th ISCRE) held at Heidelberg, Federal Republic of Ge rmany, from 6th to 8th April, 1976, are available from DECHEMA Deutsche Gesellschaft fur Chemisches Apparatewesen, P.O.B. 970146, D-6000 Frankfurt/ Main, West Germany, at the price of DMlOO plus postage and packing. Books received The Institution of Mechanical Engineers Proceedings Volume 190. Tribos abstracts on friction lubrication wear. Published by BHRA Fluid Engineering, Cranfield, Bedford MK 43 OAJ England. Price £30 (UK), US$72 (Europe), Seawater corrosion handbook, edited by M. M. Schumaker. Noyes Data Corporation Publicity Department, Mill Road at Grand Ave., Park Ridge, NJ 07656. 494 pp. Australian mineral industry quarterly 31(1) 1978 and 31(2) 1978. Bureau of Mineral Resources, Geology and Geophysics, Box 378, Canberra City, ACT 2601 Australia. Subscriptions $8, individual number $2. Mineral and NIM reports Report no. 1996 The extraction of gold from chloride solutions. (10th Nov., 1978). Report no. 1898 Batch and pilot-plant tests on M erensky Reef ore from the Western Platinum Mine. (8th Jun., 1977; reissued 30th Jan., 1979). Report no. 1920 A mineralogical investigation of Mamatu'an and Wessels manganese ores. (15th Sep., 1977; reissued 3rd Jan., 1979). Report no. 1978 The preparation and certification of a referencesample of magnetite ore. (22nd Dec., 1978). Report no. 1998 Electrode response to the addition of zinc during the cementation of gold. (25th Jan., 1979). Report no. 2002 The spectrochemical determination of phosphorus, magnesium, and iron in phosphate rocks and sulphuric acid leach liquors. (26th January, 1979). Report no. 1992 The use of emission spectrometry for the determination of impurities in metals. (24th Jan., 1979). Report no. 2003 An electrodeless conductivity meter of improved sensitivity and reliability. (28th Feb., 1979). Report no. 2005 The spectrometric analysis of manganese-bearing materials with particular reference to ferromanganese slags and metals. (16th Mar., 1979). Report no. 2006 An examination of procedures for the analysis of dry powders by atomic-absorption spectrophotometry. (28th Feb., 1979). Report no. 2007 The instrumentation and computerization of a 25 MV.A submerged -arc furnace. (25th Mar., 1977; reissued 16th Mar., 1979). Corrosion The International Corrosion Council has decided to hold the next Internat ional Congress on Corrosion in Mainz, Federal Republic of Germany, from 6th to 11th September, 1981. Process control The First European Symposium on Real -time Datahandling and Process Control will be held in West Berlin from 23rd to 25th October, 1979. Geomechanics The 28th Geomechanics Colloquy, organized by the Oosterreichische Gesellschaft fur Geomechanik, is to be held at Salzburg on 18th and 19th October, 1979. Geosta tistics A short course on 'Geostatistics for exploration and production planning' is being conducted by the Applied Earth Sciences Department, Stanford University, California, from 27th to 31st August, 1979. Business administration The Twelfth Executive Development Programme of the Graduate School of Business Administration, University of the Witwatersrand, is to be held from 9th July to 17th August, 1979. The engineer and the law A series of four meetings on the above subject is being conducted by the Measurement, Computation and Control SubCommittee of The South African Institute of Electrical Engineers. Lead smelter for South Africa? The National Institute for Metallurgy and Gold Fields of South Africa are making a comprehensive joint investigation of the technical and economic viability of an integrated lead smelter. Conference on titanium The Fourth International Conference on Titanium will be held from 19th to 22nd May, 1980, in Kyoto, Japan.

Jan 1, 1979

By J. Githiria, C. Musingwini

"Cut-off grade is a decision-making criterion often used for determining the quantities of material (ore and waste) to be mined, ore processed, and saleable product. It therefore directly affects the cash flows from a mining operation and the net present value (NPV) of a mining project. A series of different cut-off grades that are applied over the life of mine (LOM) of an operation defines a cut-off grade policy. Due to the complexity of the calculation process, previous work on cut-off grade calculation has mostly focused on deterministic approaches. However, deterministic approaches fail to capture the uncertainty inherent in input parameters such as commodity price and grade-tonnage distribution. This paper presents a stochastic cut-off grade optimization model that extends Lane’s deterministic theory for calculating optimal cut-off grades over the LOM. The model, code-named ‘NPVMining’, uses realistic grade-tonnage realizations and commodity price distribution to account for uncertainty. NPVMining was applied to a gold mine case study and produced an NPV ranging between 7% and 186% higher than NPVs from deterministic approaches, thus demonstrating improved project value from using stochastic optimization approaches. Background on cut-off grade calculation and optimizationCut-off grade is a decision-making criterion that is generally used in mining to distinguish ore from waste material. Consequently, it is used to determine the quantities of material (ore and waste) to be mined, ore processed, and saleable product. A series of different cutoff grades that are applied over the life-ofmine (LOM) of a mining operation defines the cut-off grade policy for that particular operation. The cut-off grade therefore directly affects the cash flows to be produced and the net present value (NPV) of a project at the mine planning or feasibility study stage."

Mar 1, 2019

By B. Besa, S. Nalukui

Globally, the demand for mineral products is ever increasing. Extraction of these mineral resources results in the continuous production of a huge volume of waste material, including tailing dumps. The mass of tailings usually exceeds the actual resource and often contains hazardous contaminants. This study investigated the effects of tailings disposal on soil, water, and air quality in the Nampundwe area. Water, soil, and dust samples were collected from different locations in the surrounding communities. The constituents analysed in the samples included copper, cobalt, iron, sulfate, and silica. According to the results obtained, some seepages occurred from the tailings impoundment to the shallow aquifer in the area. However, the general water quality meets the Zambia Environmental Management Agency (ZEMA) statutory limits. Recorded concentrations of sulfate (1500 mg/l), copper (1.5 mg/l), cobalt (1.0 mg/l), iron (2.0 mg/l), and silica were between 0.003 mg/l and 705 mg/l, which is far below ZEMA’s statutory limit. Silica concentration was also evident in the air. The highest concentration recorded was 260 ppcc (particle per cubic centimeter) recorded in July 2019 from the northern direction of the tailings dam. The concentration was below the statutory limit of 350 ppcc. The topsoil from the northern part of the tailings recorded a silica dust concentration of 39.9 ppcc. Iron was evident in the underground soil with a concentration of 8.01 ppcc, cobalt 0.005 ppcc, copper 0.051 ppcc, while sulfate was recorded as 0.41 ppcc.

Oct 9, 2024

By N. O. Lotter

Evaluation errors and value frequency distribution models of the gold ore bodies in the Witwatersrand and Free State systems are reviewed. It is found that the low-grade sections of the data are prone to the largest evaluation errors, and that an understanding of the shape of the value frequency distribution is essential to the calculation of mean grade. The evaluation of a mineral process for a particular ore requires attention to mil-feed sampling, sample processing, and monitoring. In particular, the calculation of a representative mass of mill-feed sample (Ms) should take account of size-by-size value variance. Alternative Ms models are discussed.

Jan 1, 1995

This paper describes an interactive personal computer program, ENVIRON, which simulates cooling and ventilating systems on gold mines. An example of the practical application of the program is given and proposed future developments are discussed. The program consists of two main modules, HEATFLOW and VENT- FLOW. HEATFLOW calculates the heat loads and the effect of air coolers, while VENTFLOW estimates the air flow distribution. As the calculation of the heat loads requires a knowledge of the air flow and vice versa, the two modules are run iteratively until the solution converges. The program is written in Pascal and runs on any IBM-compatible personal computer.

Jan 1, 1987

By R. Lechuti-Tlhalerwa

"Geometallurgy aims to improve mining project value by predicting the impact that ore and waste characteristics will have on mining and metallurgical processes. This requires integration of rich spatial models of orebody characteristics with validated process response models. These models have, until recently, been constrained by the spatial coverage and representativity of relevant data and the ability to validate predictions made.The revolution in the diversity and volume of data and computational power that is now becoming available for integrated geoscientific modelling of orebodies, and stochastic simulation of mining and mineral processes is accelerating. By embracing emergent integrated data analysis and simulation techniques, geoscientists and engineers can lead a transformation in the way the mining value chain, from orebody to recovery, can be conceived, evaluated, and operated by using the geometallurgical paradigm.This paper describes a methodology that is applied to an existing diamond operation. Analysis of spatial and process data is used to build an integrated geometallurgical value chain model (IGVCM). This IGVCM is used to generate geometallurgical options and evaluate their potential outcomes. The model facilitates the use of flexible, highly configurable, and potentially automated intelligent approaches to evaluate mining and mineral process configuration, and results in more robust design outcomes. The approach described here, and its successful implementation has potential to deliver step-changes in value. IntroductionGeometallurgy aims to identify treatability risks – and opportunities – that arise from the interaction of orebody characteristics with mining and treatment. Improved understanding of the rock/process relationships allows project planners and production teams to predict performance, identify potential shortfalls, and thus enable the proactive creation and evaluation of strategies to mitigate these risks. These advanced insights also create opportunities for continually improving operational performance through dynamically adapting and improving the process response to the changing properties of the ore (Figure 1)."

Apr 1, 2019

By E. Córdova, A. Anani, W. Nyaaba

Optimization of panels, haulage fleet, and waiting area involves deterministic and low-fidelity methods and experiential knowledge. The process is challenging because coal recovery and operational capabilities must be considered in the solution. The approach in this manuscript comprises the development of an integrated stochastic simulation model of a coal room-and-pillar system that addresses these challenges. The decision variables evaluated are panel width, number of shuttle cars, and change-out time (COT). The results show that the mine should implement the shortest possible COT, decreasing the cycle time and thereby increasing productivity and continuous miner (CM) utilization. The highest productivity and CM utilization for a fleet size of three shuttle cars is found in the 15-entry panel width. For the evaluated fleet sizes, the 19-entry panel width is optimal for the four and five shuttle cars. Among the three variables studied, panel width and fleet size had the most significant effects (5% increase) on the CM productivity, cycle time, and utilization.

Apr 2, 2022

By S. Stuurman

Inorganic acids such as sulphuric acid have found use together with certain reducing agents in leaching of copper-cobalt oxide ores. These reagents are not ideal due to the adverse effect the inorganic acids generally have on the environment and the high costs of the reducing agents. In this study a copper-cobalt oxide ore from the Central African Copperbelt was leached in two different environments; sulphuric acid in conjunction with hydrogen peroxide as a reducing agent and tartaric acid. The effects of acid concentration, reducing agent concentration, and temperature were independently determined for both leaching environments. The sulphuric acid concentration was varied between 0.4 M and 1.2 M and the concentration of hydrogen peroxide between 4.0 M and 6.5 M, while the tartaric acid concentration was varied between 0.15 M and 0.35 M. The temperature was varied between 20°C and 50°C. The results showed that the extraction of both copper and cobalt increased with sulphuric acid concentration, reaching a peak at approximately 0.8 M and then decreasing at higher acid concentrations. A similar increase and decrease in metal extraction was observed when the reducing agent was increased. In leaching with tartaric acid, the extraction of cobalt was much higher than that of copper, although extraction of both metals increased with acid concentration. Additions of small amounts of hydrogen peroxide were found to increase cobalt extraction in tartaric acid but had a minimal effect on copper. An increase in the solution temperature had a significant effect in the organic acid environment, with the effect on cobalt extraction being much more pronounced than on copper.

Jan 1, 2014

By D. D. Munro

Finsch Mine is a Kimberlite diamond mine located at Lime Acres in the Northern Cape of South Africa. The mine was founded in 1961 and started surface-mining in 1964. Underground production commenced in 1990 using a Modified Blast Hole Open Stoping method for the mining of Blocks 1,2 and 3. Block 4 is currently being mined as a Block Cave. The process of identifying and optimizing a mining method to mine the Block 5 ore body started in 1991 and in 2006 Inclined Caving was identified as being a technically feasible method. This report aims to document the process employed in developing this method by the Block 5 Pre-Feasibility Team as well as discussing the technical challenges encountered during this process.

Jan 1, 2010

By N. Naude, L. S. Leal Filho, M. P. Tshazi

In this paper, the authors performed experiments in the Denver and Leeds laboratory flotation devices at the University of Pretoria at various particle sizes to evaluate the performance of the devices. Quartz was used in a single mineral system at discrete sizes fractions, -25 μm, +25- 45 μm, +45-75 μm, and +75-106 μm. Hydrodynamic analysis, based on dimensionless power and Reynolds numbers, indicated that the Leeds cell required higher power input to achieve comparable flow conditions. Specifically, the Leeds cell exhibited an average power number of 1.03, whereas the Denver cell averaged 0.77 within the same impeller speed range of 1000 rpm–1500 rpm. For comparative flotation performance, impeller speeds were calibrated, resulting in operating speeds of 1200 rpm for the Denver cell and 1400 rpm for the Leeds cell. The cells performed similarly at two coarser-sized fractions. However, some deviations were observed in the finer particle size range. The -25 μm (fine) fraction initially achieved a recovery of only 15%. An additional reagent dosage was required to enhance the recovery of this fraction significantly. These findings highlighted the influence of particle size on flotation recovery. For all experiments, the Denver laboratory flotation cell outperformed (defined by higher recovery) the Leeds device, while still operating at a lower impeller speed. This advantage can be attributed to its impeller-stator design and air dispersion features, effectively overcoming slurry resistance and resulting in superior flotation performance compared to the Leeds cell.

May 27, 2025

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

By More-O&apos, R. C. Ferrall, J. W. Wilson

Discussion: M. D. G. Salamon* (Fellow): The theoretical principles behind the techniques of calculation used by the authors was formulated and published during the period 1962- 65. These principles, together with their practical implications, were summarized in a review paper in 1966.1 Now, in February, 1970, we have this long and comprehensive paper discussing the practical application of the theory. I think this is good progress. The large number of practical examples treated in the paper clearly demonstrates not only the skill and knowledge of the authors, but also the versatility of the techniques of analysis. I feel that the techniques described by the authors, and their improved versions, will revolutionize mine planning. I suggest that no shaft system or stoping layout should be planned in future without an adequate rock mechanics analysis. It seems that it will be progressively more difficult to white wash mistakes in rock mechanics and attribute their costly outcome to normal mining risk. We should not, however, become complacent. There is still a lot to learn and do in the future. I do not want to discuss tonight the question of further research but instead, I will raise two other problems which may hinder the future progress of practical rock mechanics. To carry out work similar to that described in the paper, mine managements require men who are capable of doing the work and who have the most efficient techniques of analysis at their disposal. As a research engineer I have been associated with the development of techniques of analysis. I can assure you that these have undergone an amazingly rapid development during the last six years. We have seen the change from the use of the electrolytic tank analogue and manual integration to the method described by the authors, that is, to the employment of the automatic network analogue and computer integration. But this is not the end. In a recent paper Prof R. P. Plewman2 and his co-authors described a completely digital technique. Here the process of calculating on- and off-reef quantities is integrated into one computer run. But these sophisticated methods of computation are useless without men to make intelligent use of them. During the last few years a new breed of mining engineers has appeared on the scene - the Rock Mechanics Engineer. I feel it is timely to call the attention of the senior members of this Institute to the fact that this new breed will succeed in carrying out its duties in a valuable manner only if we manage to attract to its ranks young engineers of the right quality. The requirements are high. The top rock mechanics engineers have to be good mine planners and they have to understand the essence of sophisticated theories. Without these attributes they will not succeed in the long term and the industry will not gain the benefit of available knowledge. To attract this quality of engineers the industry will have to ensure that rock mechanics is accepted by all concerned as a career which could lead to the top echelons of our profession. Finally, I would like to make one or two remarks concerning Part I of the paper. In Sections 3.1 and 3.2 the authors describe methods of determining the normal stress on the reef plane and the convergence distribution in the excavations. The description as given applies only to a horizontal reef. When the reef is inclined the situation is more complex since a shear component of stress on the intact reef and a ride component in the excavations must then also be determined. These can be calculated by methods similar to that described in the paper.3 The practical application of the method of calculating the released energy (Section 3.4) is in the comparison of various stoping layouts to establish an order of preference in terms of decreasing rates of energy release. To carry out these comparisons effectively, the calculations must be carried out in a manner by which the values of energy per unit area obtained are comparable. I would like to note in this respect that the method of calculation given in the paper is valid without reservation only if there is no elastic contact between the hanging and foot walls in the mined-out area. If there is contact then the calculated energy values are correct only if the mined out area is increased in small steps during the analysis. My second point in this regard is concerned with the practical method of calculation as described in Sections 3.4 (ii)-(iii). Firstly, I would like to suggest that the energy calculation should be carried out, as far as possible, by using always the same scale on the analogue. Secondly, the reading of current on a pin should be followed by the removal of that pin to obtain the corresponding reading of potential. The product of these two values will be proportional to the energy released during the mining of the small area corresponding to that pin. The method suggested by the authors tends to mask possible danger points in the layouts, since they obtain an average value for a time period, say, for six months.