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By Thomas M. Plouf

Getting optimal performance from flotation cells can, in many cases, be critical to a project's economic viability. Simple testing procedures can sound early warning signals as well as maintain optimum recoveries from the flotation cycle. The materials required for a simple testing laboratory include: (1) pH meter or pH paper, (2) bottles of reagents used in plant flotation, (3) stop watch, (4) calibrated eye droppers. (5) laboratory flotation machine (1000-g tank, open impeller), (6) froth collection pans, (7) magnifying glass, (8) sizing screen sufficient to retain 10% of the flotation feed coarse fraction, (9) sizing screen for the size particles at which desliming of the plant flotation feed is to take place, and (10) a set of screens covering the complete range of feed particle size.

Jan 4, 1978

The prospect of utilization of phosphate ores which contain high P205 values associated with Al and Fe has produced a great deal of interest over many years. Processing options have generally been based on the utilization of by-products which were required to offset the processing costs.This paper presents a range of processing options which have been investigated at laboratory or technical scale on phosphate ores which predominantly consist of crandallite, CaA13(PO4)2(OH)5.3H20 and millisite, Ca(NaK)Al6(PO4)4(OH)9.3H20. Christmas Island (Indian Ocean) and Mt. Weld (Western Australia) phosphate ores are good examples of such feedstocks. It is expected that these processes may also be applicable to such phosphate ores from other locations.

Jan 1, 1990

By Mills JC, Belcher CB

X-ray fluorescence spectrometry is used videly for routine quality control of the mining, )lending and agglomeration of iron ores. Most )f the procedures used, cannot tolerate significant changes in matrix composition or be Lpplied to a wide range of elements. Accord- ngly, a graphite briquette technique which is Lpplicable to some fifty elements in widely Tarying iron ore matrices is described. The ignificant advantages are suitability of the ame preparation for both optical emission and -ray spectrometry, a complete elemental overage for the range 5bcg/g to 100%, and the recision and accuracy of the methods are om.parable with the standard chemical.methods hich have been superseded in the authors' boratories. The proposed methods become ore attractive and economical as more prehensive information is sought.

Jan 1, 1975

By Burt Ensley, Viatcheslav Dushenkov, Ilya Raskin, David E. Salt

Roots of many hydroponically grown terrestrial plants, including sunflower (Helianthus annuus L.) effectively remove toxic metals such as Cu+2, Cd+2, Cr+6, Ni+2, Pb+2 and Zn+2 2 from aqueous solutions. It should be possible to scale up this process such that plant roots can be used to treat large volume aqueous waste streams. It can be extrapolated from laboratory results that to reduce the Cd concentration in a waste stream, from 1 ppm to below 4 ppb, with a flow rate of 4000 L/min, would require 3500 sq. m of plant roots with a density 5 kg fresh weight per sq. m. These results suggest that the roots of hydroponically grown terrestrial plants may provide an attractive alternative to the accepted water treatment technologies.

Jan 1, 1995

Gallery Stoping, an old but little used stoping method, has been reintroduced to workings at the Paringa South Shaft.Orebodies which are amenable to such a method are being mined in this manner with considerable advantages and savings.The advantages of gallery stoping as used at Paringa, compared with traditional mining methods are:1. constant cash flow2. low set up cost and initial stope development3. nearly 1005 recovery 4. no access problems 5. quicker tonnagesAs compared with highly mechanized mining methods, it has been found to be slower but requires less development, gives improved grade control, has less impact on the surrounding rock and fragmentation is much better, reducing secondary blasting costs.This paper examines the mining method and illustrates the advantages of gallery stoping at Paringa.

Jan 1, 1985

Since gold was first discovered in Colorado in the late 1850s' mining has been a major part of the state's economic history, according to Stanley Dempsey, chairman and chief executive officer of Denver- based Royal Gold Inc. While the mining industry has seen some lean times throughout the past century, it has always bounced back. Today, dozens of major gold companies are headquartered in the Denver area. The state's coal mines produced record amounts during 1996. And even some of Colorado's uranium mines are resuming production. Dempsey joined other speakers in addressing the state of Colorado's mining industry during the Colorado Mining Association's (CMA) National Western Mining Conference. Some 800 people attended the CMA meeting, held Feb. 2-5 in Denver. The meeting was the association's 100th since it was incorporated in 1897.

Jan 1, 1997

By B. Damjanac, S. Maxwell, D. Chorney, M. Grob, F. Zhang, J. Hazzard

"A hybrid discrete-continuum numerical scheme is developed to study the behavior of hydraulic fractures crossing natural fractures. The fully coupled hybrid scheme utilizes a discrete element model for a core domain, within which the hydraulic fracture propagates and interacts with natural fractures, and a surrounding continuum domain to better approximate boundary effects. The results show that the behavior of hydraulic fractures crossing natural fractures is affected by a combination of factors. Nevertheless, three fundamental crossing scenarios can be identified from all of the simulations: no crossing, partial crossing, and direct crossing. Each crossing scenario has a distinct injection pressure history which may suggest guidelines for interpreting field hydraulic fracture injection data. Additionally, the capability for these models to generate synthetic microseismicity makes them appealing for the integration of microseismic field data with the reservoir geomechanics for ultimately providing a practical engineering tool for improvement of well completion and stimulation. The model is capable of examining and verifying four different shear deformation mechanisms associated with a propagating hydraulic fracture. The natural fracture can fail solely due to the stress perturbation of the passing hydraulic fracture or it can fail due to a combination of stress and pore pressure changes across different types of interaction scenarios. The simulations also illustrate that the level of fracturing complexity increases as the number and extent of the natural fractures increase. INTRODUCTIONAlthough hydraulic fracturing technique has been applied extensively as a reservoir stimulation technique in the oil and gas industry for over 60 years (Economides & Nolte, 2000), it is one of the key factors promoting the shale gas boom in the past decade (King, 2010; International Energy Agency, 2014). The hydraulic fracturing of shales can be differentiated from hydraulic fracturing of conventional reservoirs by the fact that shale formations often have a pre-existing discrete fracture networks which greatly impact the hydraulic fracture propagation. Based upon field production data as well as microseismic observations, it is believed that so called “fracture complexity” may result from interactions between a created hydraulic fracture and pre-existing natural fractures and planes of weakness (Warpinski, 2009; Maxwell & Cipolla, 2011)."

Jan 1, 2015

By R. Lestari

Newmont Batu Hijau operates with an accelerated mining rate to optimize life of mine (LOM) project economics. This results in a portion of ore mined being stockpiled for reclaim and processing throughout, and at the end of mine life. LOM economics can be further enhanced by preserving stockpiled ore value by mitigating oxidation effects. A detailed stockpile ore oxidation study was conducted to: ?? Develop a practical understanding of how oxidation affects ore value; ?? Determine how oxidation rate can be controlled, and; ?? Determine how oxidation effects can be mitigated to preserve ore value. The result of the study is a stockpile management strategy that significantly reduces oxidation related losses and, implementation of that strategy within practical constraints. Implementation includes installation of Controlled Potential Sulfidisation (CPS) flotation to facilitate oxidised sulfide copper recovery and, recovery of dissolved copper from stockpile drainage solution into saleable product. This paper describes the study results including managing and predicting stockpile oxidation with time, monitoring performance of implemented CPS flotation and recovery of dissolved copper from stockpile drainage. These are essential elements of successful long term mine operation in Batu Hijau.

Jan 1, 2014

By P Stoker

"An EXTENDED ABSTRACT is available for download. A full-length paper was not prepared for this presentation. Mining and exploration properties have a unique set of technical risks. Privately-owned companies considering investing in the resources sector can optimise their investment decisions by adopting a systematic technical assessment of acquisition assets, similar to the approach commonly adopted by public financial institutions and publicly-listed companies.Technical due diligence provides a process to identify key geological, mining, geotechnical, metallurgical, environmental and social risks and opportunities and determine the most likely business case and valuation of assets. Technical due diligence is commonly carried out in parallel with legal, commercial and financial due diligence, often involving the acquirer, to maximise the understanding of the investment.There are significant advantages in investors conducting a comprehensive technical due diligence, which typically involves site visits and project assessment to international standards by an independent, multidisciplinary team of experts. The outcomes provide the opportunity for the investor to make early, informed decisions and to understand and manage risks.Technical due diligence may be carried out at several stages: when considering and weighing up a number of investment options, prior to and during a transaction or immediately post-transaction. In the first stage, the outcomes will inform the choice of investment and, more particularly, whether there are any fundamental flaws in the projects being considered. In the second stage, due diligence outcomes can inform the level of investment and approach to risk management and planning. In the third stage, risks and opportunities can be investigated in more detail, allowing the investor to consider the best options to reduce risk and maximise the benefit of the investment.This paper presents a summary of the technical due diligence assessment process, its benefits to investors, common risks in mining and exploration projects known to cause mining asset write-downs and principal technical due diligence approaches.CITATION:Keogh, A, Stoker, P and Thomas, M, 2015. Benefits of due diligence in private equity mining investments – maximising value and unearthing common risks , in Proceedings PACRIM 2015 Congress, pp 115–126 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

Mar 18, 2015

By N. Damiano, C. Zhou, R. Jacksha, J. Srednicki

Modern electronic devices and systems used to enhance miner safety and health are becoming commonplace in underground coal mines. The ability for these devices and systems to function properly in the presence of electromagnetic emissions from other electronic and electrical devices and systems is not entirely understood. To investigate potential electromagnetic compatibility issues of critical mine electronic devices and systems, researchers from the National Institute for Occupational Safety and Health (NIOSH) are conducting surveys of electromagnetic emissions in underground coal mines. This paper presents the measurement system, methods, and results of electric field electromagnetic emission surveys conducted in three underground coal mine environments in the frequency range of 10 kHz to 1000 MHz. The survey data show that in some environments electric field electromagnetic emissions in underground coal mines approached or slightly exceeded limits as defined by other industrial sectors.

Mar 2, 2022

By Atta Ur Rehman, Kwame Awuah-Offei

"Information diffusion potential of a social media user affects how quickly information about a mineral project can diffuse through that user. If management can use social media and network analysis in community engagement programs to understand how fast and how far information will diffuse to communities and followers of particular social media users, it can selectively focus on the most influential users. This article proposes a method to examine the information diffusion potential of social media accounts. The work uses Gephi, an open source software, to extract and analyze data from different Twitter handles to predict their information diffusion potential. The work uses case studies of real Twitter users (e.g. mining news organizations and bloggers) associated with mining to illustrate the approach. The case study results show that there are significant disparities in information diffusion potential that will demand selective attention. This research will help mines develop effective social media engagement strategies.The mineral industry provides raw material for industrial activity to support society (Martens and Rattmann, 2001). Mines have changed from conventional mining practices to sustainable ones because of the negative impacts of mining in the past and increased public awareness (Wang et al., 2016). The concept of sustainable mining is getting mature, as stakeholders (e.g., governments, investors and host communities) are getting more involved in mining projects (World Economic Forum, 2014). The failure of mining companies to address the demands of these stakeholders might result in the failure to acquire a social license to operate (SLO) (Thomson and Boutilier, 2011). The SLO, if granted, is mutually beneficial to all stakeholders. Mines prefer being granted SLO and keeping it to avoid any kind of social unrest due to their operation (Prno, 2013; Moffat and Zhang, 2014). Mining communities can grant different levels of SLO ranging from withholding SLO to psychologically identifying with the project (Joyce and Thomson, 2000; Thomson and Boutilier, 2011).Most of the previous work to understand community perceptions and SLO in mining is generally qualitative (ICMM, 2012a; Thomson and Boutilier, 2011; Prno, 2013; Moffat and Zhang, 2014; IFC, 2014). In particular, there is limited work on how community perceptions change over time due to information diffusion (Boateng and Awuah-Offei, 2017). However, SLO changes with respect to time (Yates and Horvath, 2013), which can result in risks that are not easy to predict. Mine managers and engineers have a desire to understand these changes so as to mitigate these risks (Que and Awuah-Offei, 2014; Que et al., 2015)."

Jan 4, 2018

As a kind of collector, Xanthates are generally used to make sulfide minerals hydrophobic in flotation process. Xanthate adsorption on a galena surface has been widely studied experimentally. In this paper, DFT methods were employed to investigate the local adsorption interactions about the collectors,such as ethyl xanthate (CH3CH2OCS2?, EO) and ethyl trithiocarbonate (CH3CH2SCS2?, ES), absorbing on two different PbS clusters. From the results, it can be easily found that, on the edge or at the apex, both collectors, with two S atoms bidentate coordinating on the clusters, have surprising interaction energies, while on the surface, its interaction is relatively weak in the form of monodentate ligand. NBO analysis results reveal that there is at least a covalence bond with sulfur atom about 10% and lead atom about 90% when the absorbed lead is on the lattice edge or at apex, but, if the absorbed lead is on the lattice surface, no covalence band would be found. Meanwhile, the S-Pb bond, formed by the absorbed Xanthate and galena lattice, seems to have much more covalence characteristic than that formed in the PbS lattice inner. Furthermore, those data also imply that the difference of the collecting effect between the EO and the ES may be not notable, because of the similar distance and the interaction energy for the same interaction mode.

Jan 1, 2014

By Omar. M. Arafat, Edgar Pérez, Kyle. M. Bartholomew, Robert. E. McIvor

The “circulating load” confounds understanding of ball milling circuits. Conflicting opinions exist as to its role. Should it be high, or low? Why does it even exist? It is commonly accepted in the plant as a given, the outcome of largely unknown factors. As such, it may often go unmeasured or even ignored. This paper describes the importance of the circulating load in wet ball milling circuits. It is characterized not only in terms of solids mass flow (or ratio of mass flows), but also by its other key physical characteristic, its size distribution. Its effect on grinding circuit performance is explained. The equipment application design steps to achieve a desired circulating load, in terms of both its mass flow and size distribution, are described. Finally, its pivotal role in grind control is specified. Our goal is for the reader to come away with a fresh understanding of the role of the circulating load in wet ball milling circuits, including how and why it should be measured and managed.

Feb 22, 2026

By Albert Tasias, Daisy Jiménez

La gestión de riesgos mediante barreras, conocida como metodología Bow Tie, permite acompañar el día a día de las operaciones y está adquiriendo mayor relevancia debido a su forma sencilla de describir los peligros a través de un diagrama, en donde se pueden ver las causas y las consecuencias. Asimismo, lo interesante de la metodología son las barreras, que evitan que el peligro o las consecuencias se materialicen, para lo que cuentan con un responsable que debe gestionar y reportar su desempeño. Este trabajo realiza un análisis de la metodología Bow Tie, a través de un glosario de términos, la descripción del proceso, su aplicación actual y las ventajas y desventajas asociadas.

Sep 20, 2019

By Rudolph G. Wuerker

Charles T. Holland (Head, Dept. of Mining Engineeri*, Virginia Polytechnical Inst., Blacksburg, Va.) Mr. Wuerker has presented a very interesting discussion of the use of triaxial test methods for investigating the strength properties of rocks. Such methods, no doubt, eventually will develop considerable information of interest to those concerned with the design of mine layouts, particularly in the field of pillar design. From his discussion of my recent article, "Cause and Occurrence of Coal Mine Bumps" (Holland Mining Engineering 1958, p. 933-1002), it is evident that in one place at least I did not make my meaning clear to him and perhaps others. To clear the matter up I think it best to quote from the article, somewhat more fully than did Mr. Wuerker, as follows: "4) In actual operations — because rocksare not perfectly elastic, homogeneous, nor isotropic and because local yield does occur — the maximum stress as demonstrated by Phillips (Ref. 22, pp. 64, 65) and indicated by much experience in mining, does not occur at the walls of the opening but at a short distance inside the pillar. Furthermore, the maximum stress does not reach as great a value as theoretical considerations and laboratory experimental methods indicate.* Actual distance inside the pillar, measured from the wall, at which the maximum stress exists, has not been determined. Observations in many mines, however, indicate that this distance could have a mini-value of one to six or eight times the bed thickness and that it is probably affected by width and height of the opening, depth of cover, and relative values of the elasticity and plasticity of materials comprising the roof, floor, and coal seam. The actual value of the stress produced probably lies between the theoretical maximum and the average stress concentration that would be produced if the weight of the strata above the unsupported opening were evenly distributed over the pillars for a distance equal to the opening width." The footnote reference in the above quotation referred to the following: "*For example, the Pocahontas No. 4 coal bed in southern West Virginia is mined under cover up to 1800 ft thick. Development openings are driven 18 to 20 ft wide, and the bed is about 6 ft thick. According to the work of Panek, the tangential wall stress at mid-bed height under these conditions would reach values between 4000 and 5000 psi. Actual tests of 3-in. cubes of this coal show its compressive strength would be much less than this, perhaps as low as 400 psi. Yet the pillars usually show no evidence of failure in these headings. In this same bed at a depth of 800 ft, the author has seen an opening 225 ft between supports lying between two old groves approximately 1100 ft apart. According to the theoretical considerations, the stress in the pillar walls would have been about 18,000 psi, yet the pillar showed little or no evidence of weight. In view of these observations, it is clear that the wall stress does not attain the maximum values indicated by theory." (Underlining added to original wording.) By referring to Fig. 2A of my paper it will be noted that theoretically the maximum pillar stress would occur at the pillar wall, i.e., at the passageway surface of the pillar. Obviously this cannot be correct in the cases of stress ranging from 4000 to 18000 psi since the coal at the surface of the pillar is under no constraint and cannot have a strength much greater than 400 or 500 psi. Hence, my conclusion that the maximum stress does not occur at the wall but back in the pillar some distance from the wall. Since these stresses are pushed back in the pillar from the wall, it is also obvious that the loads transferred to the pillar from the opening will be spread over a greater area and hence Pillar stresses will not rise to the values postulated by theory and photoelastic experiment. Further since to visual inspection the coal along the pillar wall did not appear to be failed the conclusion was reached that the stress shift was caused by local elastic or plastic yield and by difference in the elastic modulus of the rocks composing the mine floor, mine roof, and coal bed. Later on under the heading "Strength of Mine Pillars" (pages 1000-1002) the effects of constraint is briefly described. Also a formula taking into account constraint is developed relating pillar strength to the uniaxial strength of coal and the L/T ratio of the pillar. Since my paper was written, reports of experiments conducted in South Africa (Denkhaus, et. al., 1959), in Sweden (Hast 19581, and in Canada (McInnes, et.al., 1959) reveal that the conclusion expressed relative to the existence of a low stress area existing around the edges of pillars and solid faces as described above is generally correct. But it seems possible that where the wall stress developed is less than the unconfined strength of the rock composing the pillar and where the roof, floor, and pillar

Jan 1, 1961

By Madan M. Singh

This section is unique to the Handbook in that it is the only section that deals with underground excavations for nonmining purposes. The editors were of the opinion that the section should be incorporated because the subject matter covered by the chapters is closely related to mining, and many mining engineers are currently involved in these activities. As we enter the decade of the 1990s activities in this category will increase, enhancing the relevance and utility of the material discussed. As the population increases, especially in metropolitan areas, the necessity to go underground will be greater. At the present time, not only are subsurface shopping malls and pedways connecting buildings becoming commonplace, but structures as diverse as the Civil and Mining Engineering Building on the University of Minnesota campus, a road-and-fleet maintenance facility in Multnomah County, OR, and even an ice cream parlor (Dairy Queen) in northern Wisconsin have been constructed underground. Placing utilities below the surface has numerous advantages and is now customary. Rapid transit and highways through tunnels in urban areas have been the norm for many years, but subterranean stormwater reservoirs, power plants, industrial warehouses, and food storage silos are relatively new innovations. The philosophy of underground defense installations is ancient, but their requirements and designs have trans-formed radically as technology advances. The use of under-ground space for disposition of wastes is modern, since it is recently that environmental concerns and waste disposal costs have assumed increased significance.

Jan 1, 2008

By D Baas, D Bennett

This paper describes how Brisbane-based PanAust Limited develops process control strategies that are implemented at all operations and are used in functional descriptions for plant upgrades and new projects.The process control strategies are determined by operating management philosophies designed to maximise returns from the company’s assets.The approach is endorsed in the project planning and design phases to ensure facilities and equipment that form the major production assets are fit for purpose and capable of enabling the production managers and operators of the projects to maximise shareholder returns.PanAust’s process control approach has been to develop sets of process control standards which focus on two key areas. The first area covers hardware requirements and architecture, software objectives, control models and individual loop tuning methods. The second area defines control room layout, graphic standards and the alarm philosophy. The application of these standards in a new plant or upgrade decreases the time required to achieve design capacity and optimal performance.The PanAust process control strategy changes the operator’s role from one that controls a number of individual loops to one that sets the control objectives of the processing plant. To achieve optimal performance, all the process areas of the plant are analysed to identify opportunities to improve throughput, recovery and stability. Once a key opportunity is identified, a process control strategy is developed which defines the objective of the control, its functionality and how an operator will interact with it. After development of the control model the operators assist engineers to test and debug it. Once the model is robust, it can then be duplicated throughout the group and developed as a group process control standard.CITATION:Baas, D, Bennett, D and Walker, P, 2014. Developing process control standards for optimal plant performance at PanAust Limited, in Proceedings 12th AusIMM Mill Operators’ Conference 2014 , pp 325–334 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 1, 2014

By M Fuchs

Roadheaders were introduced to mining and tunnelling in the early-1960s. Since this period their main field of application has been for roadway drivages in coal mines and for mineral production, for instance in coal, rocksalt, potash and gypsum mines. Their main field of application in tunnelling is in softer and partly friable rock formations, a suitable area for non-blasting excavation. However, in longer tunnel sections excavators with high ripping forces have replaced roadheaders in many situations. The main arguments against roadheaders have been and still are:a sharp increase in excavation cost with increasing rock strength and increasing abrasivity; and greater risks in conditions which have not been, or could not be, investigated to a sufficient extent. These arguments have, to a great extent, restricted practical roadheader application in production mining and in a lot of æstandardÆ tunnel projects. To address these limitations, factors which could make roadheaders attractive for such conditions and could overcome existing technological difficulties have been investigated. Extension of the economic field of application in hard rock was found to be the most important and the most effective step forward.

Jan 1, 2002

By J. H. Tu

The technical paper correctly points out that the kriging variance is not a good measure of the uncertainty of the estimated (i.e., kriged) value of individual blocks. The au thors claim that their proposed jackknife method, which is a rekriging of each block by eliminating, in turn, one sample from the original sample set and then taking the average of the rekriged estimates, not only gives good block estimates, but the resulting jackknife kriging standard deviation is a useful indicator of the "true uncertainty associated with block estimates." However, they immediately abandon the idea of using the block-by-block standard deviations, reasoning that these standard deviations are not independent and that there is no easy way to utilize them. There may be another reason for not using them. The jackknife standard deviations for individual blocks given in their example are mostly in the range of 0.004 to 0.005 oz/st (0.14 to 0.17 g/t) with only one block having a high value of 0.012 oz/st (0.41 g/ t). These individual block standard deviations are as low as the jackknife standard deviation for the mean grade of the entire shape, i.e., 0.0041 oz/st (0.14 g/t). Do they represent the "true uncertainty" of the individual block estimates? Could the authors explain this? In a global shape consisting of a large number of blocks, any given sample will affect the kriged estimate of only those few blocks within its vicinity. This is the rationale for the authors' selective rekriging, making the jackknife algorithm more efficient. On second thought, why not do away with jackknifing altogether? Just cumulate and normalize, if necessary, the kriging weights of each sample used during the ordinary block kriging process, and then compute the global variance from these kriging weights and their respective sample grades? After all, isn't the global mean grade nothing but the weighted average of the samples used in the estimation? Reply by G.S. Adisoma and M.G. Hester The jackknife is one of the many tools in a practitioner's toolbox to solve estimation problems. The strengths of the technique lies in its simplicity, i.e., it uses the concept of mean and standard deviation and the fact that it can be easily combined with other tools, in this case kriging. Because the jackknife kriging (JK) estimate is also the mean of the pseudovalues, the JK standard deviation is attractive just as the standard deviation of the mean explains the variability of the data. The difference is that the pseudovalue calculation in jackknife kriging uses the ordinary kriging (OK) weighting scheme instead of simple arithmetic averaging. The data used to illustrate the jackknife technique in the paper consist of high values that are roughly three times the low values. The resulting JK estimate of the block grades show that the highest estimate is roughly twice the grade of the lowest estimate. The contrast between the low and the high estimate is more evident in the JK estimate than in the OK estimate, even though the mean grades of the blocks for the two estimates are very similar. Nonetheless, in this paper, we are concentrating more on the need for a more realistic measure of uncertainty, or precision, for the estimate. Unlike its OK counterpart, the JK standard deviation of the blocks clearly reflects the original data variation. The highest JK standard deviation of the blocks is three times its lowest value. This follows our intuition that, when the samples used to estimate a block is more variable, the resulting estimation variance (or standard deviation) should be higher than the case where the samples are more uniformly valued. However, block-by-block standard deviation or variance is of little practical value in reserve estimation and classification, as well as in mine planning. One is usually more interested in quantifying not the variance of the individual block estimate, but the uncertainties associated with a much larger dimension, such as the minable reserve. Thus, the thrust of the paper is to find a simple way to obtain a single estimation variance or standard deviation associated with the reserve grade estimate. The discussion by J.H. Tu did not mention how one would obtain the global variance from the OK weights and the sample grades. As a technique that offers a data valuebased measure of uncertainty for its estimate, the "leave-one-out" jackknife fills this need nicely through the block kriging shortcut approach described in the paper. Note: The first column and the last two columns of Table 3 in the paper should have contained a single number each, namely, an OK estimate of 0.0317, a JK estimate of 0.0333 and a JK standard deviation of 0.0041 oz/st, respectively, for the shape, as are obvious from the text. ?

Jan 1, 1998

By J. H. Tu

The technical paper correctly points out that the kriging variance is not a good measure of the uncertainty of the estimated (i.e., kriged) value of individual blocks. The authors claim that their proposed jack-knife method, which is a rekriging of each block by eliminating, in turn, one sample from m the original sample set and then taking the average of the rekriged estimates, not only gives good block estimates, but the resulting jackknife kriging standard deviation is a useful indicator of the "true uncertainty associated with block estimates." However, they immediately abandon the idea of using the block-by-block standard deviations, reasoning that these standard deviations are not independent and that there is no easy way to utilize them. There may be another reason for not using them. The jackknife standard deviations for individual blocks given in their example are mostly in the range of 0.004 to 0.005 oz/st (0.14 to 0.17 g/t) with only one block having a high value of 0.012 oz/st (0.41 g/ t). These individual block standard deviations are as low as the jackknife standard deviation for the mean grade of the entire shape, i.e., 0.0041 oz/st (0.14 g/t). Do they represent the "true uncertainty" .of the individual block estimates? Could the authors explain this? In a global shape consisting of a large number of blocks, any given sample will affect the kriged estimate of only those few blocks within its vicinity. This is the rationale for the authors' selective rekriging, making the jackknife algorithm more efficient. On second thought, why not do away with jackknifing altogether? Just cumulate and normalize, if necessary, the kriging weights of each sample used during the ordinary block kriging process, and then compute the global variance from these kriging weights and their respective sample grades? After all, isn't the global mean grade nothing but the weighted average of the samples used in the estimation? Reply by G.S. Adisoma and M.G. Hester The jackknife is one of the many tools in a practitioner's toolbox to solve estimation problems. The strengths of the technique lies in its simplicity, i.e., it uses the concept of mean and standard deviation and the fact that it can be easily combined with other tools, in this case kriging. Because the jackknife kriging (JK) estimate is also the mean of the pseudovalues, the JK standard deviation is attractive just as the standard deviation of the mean explains the variability of the data. The difference is that the pseudovalue calculation in jackknife kriging uses the ordinary kriging (OK) weighting scheme instead of simple arithmetic averaging. The data used to illustrate the jackknife technique in the paper con¬sist of high values that are roughly three times the low values. The resulting JK estimate of the block grades show that the highest estimate is roughly twice the grade of the lowest estimate. The contrast between the low and the high estimate is more evident in the JK estimate than in the OK estimate, even though the mean grades of the blocks for the two estimates are very similar. Nonetheless, in this paper, we are concentrating more on the need for a more realistic measure of uncertainty, or precision, for the estimate. Unlike its OK counterpart, the JK standard deviation of the blocks clearly reflects the original data variation. The highest JK standard deviation of the blocks is three times its lowest value. This follows our intuition that, when the samples used to estimate a block is more variable, the resulting estimation variance (or standard deviation) should be higher than the case where the samples are more uniformly valued. However, block-by-block standard deviation or variance is of little practical value in reserve estimation and classification, as well as in mine planning. One is usually more interested in quantifying not the variance of the individual block estimate, but the uncertainties associated with a much larger dimension, such as the minable reserve. Thus, the thrust of the paper is to find a simple way to obtain a single estimation variance or standard deviation associated with the reserve grade estimate. The discussion by J.H. Tu did not mention how one would obtain the global variance from the OK weights and the sample grades. As a technique that offers a data value-based measure of uncertainty for its estimate, the "leave-one-out" jackknife fills this need nicely through the block kriging shortcut approach described in the paper. Note: The first column and the last two columns of Table 3 in the paper should have contained a single number each, namely, an OK estimate of 0.0317, a JK estimate of 0.0333 and a JK standard deviation of 0.0041 oz/st, respectively, for the shape, as are obvious from the text.

Jan 1, 1997