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By Gary Peach, Peter Mason

Planning and estimating progress rates and costs for tunnelling is always best done based on experience and historic precedent. Much precedent is available but the use of data monitoring, data mining and other retrieval techniques on modern TBM machines can enable this to be further expanded and refined. Advance rates can be related much more closely to rock types as can associated rock bolt and mesh/ shotcrete requirements. This in turn can lead to a further refinement in best likely combinations of equipment, such as shotcrete jumbos, better selected for the anticipated conditions, rather than the potential advance rates of the machine. Efficient and timely construction of the tunnel will also be linked to times needed for finishing work, such as contact and void grouting and to how this can be initiated while the TBM is still in operation, in order to save overall construction time. Indeed, this in turn may affect the most preferable layout and construction details of the permanent tunnel. Considerable experience has been gained in the use of two large diameter TBM tunnel drives through the Himalayas at the Neelum-Jhelum hydropower project in Pakistan. All the above aspects will be discussed in the paper based on the considerable experience and data which came from that operation, including appropriate measures in highly stressed areas potentially subject to rock burst.

Jun 13, 2021

By S. A. Jeric

In-pit crushing and conveying of waste has been utilized in the mining industry for over 30 years. In recent years, innovations in crushing, conveying, and particularly waste and leach stacking technology have sparked a renewed interest in continuous haulage systems for large-scale open pit applications. A review of the advantages/disadvantages and operating techniques of crushers, feeders, conveyors, and stacking systems currently available is made. The paper examines some operations that are currently using large scale continuous haulage systems. Finally, a case study is presented that evaluates the application of a continuous waste haulage system in a large open pit mine in the Western United States, The case study includes a economic comparison with the existing truck haulage system.

Jan 1, 1997

By Ron Allum, Ed VanDerPas

The application of high speed tunneling in a deep underground copper mine is essential for an ambitious expansion project at Magma Copper Company's San Manuel Mine. At stake is the future of over 1,300 employees at the largest producing full gravity block caving copper mine in the world. A joint venture of Frontier-Kemper Constructor's Inc. and Deilmann Haniel GmbH is helping create that future through the successful application of tunnel boring technology. This paper examines the details required to assemble, deploy and operate a 4.62 m open main beam tunnel boring machine (TBM) in a 1048 m deep operating mine accessible only by shaft.

Jan 1, 1995

By Sihua Lei, Hong Zhong, Shuai Wang, Yu Gan, Zhanfang Cao

High purity MgO is widely used in various fields as an important magnesiumcompound. The separation of Mg and Ca is of great importance for the preparation of high purity MgO from dolomite. In this study, the key effects of carbonization temperature and nano-calcium carbonate agglomeration on the separation mechanism of calcium and magnesium have been investigated. The results indicated that the reaction in the carbonization process was stepwise. Precise control of the carbonization temperature was essential for the formation of Mg(HCO3)2 due to its low reaction efficiency at lower temperatures or decomposition markedly at higher temperatures. Meanwhile, there was a common-ion effect in solutions containing Mg2+ and Ca2+. Nano-CaCO3 particles were formed during carbonization and agglomerated with the prolongation of static time. A product with a purity of 99.56% MgO and 0.16% CaO was obtained under the optimized conditions: ratio of liquid–solid 30 L/g, carbonization temperature 22–25 °C, carbonization time 1 h, and refining time 4 h. This work has important guiding significance for the preparation of high purity magnesium oxide from dolomite.

Apr 21, 2020

By Ronald E. Triplett, George K. Burke, Bernard H. Voor

To accommodate larger double-stack rail cars through a tunnel, the existing active tracks were to be lowered. The tunnel is an elliptical, horseshoe-shape with concrete base support, removal of which would jeopardize the tunnel integrity, particularly since the soils beneath part of the tunnel floor included soft, saturated silt overlying rock. Grouted bar anchors combined with a SuperJet soilcrete strut replaced the existing support in situ prior to floor lowering. Close cooperation and detailed timely engineering support provided a quality project. Project design and construction, ground improvement methods, and the performance of the work are described.

Jan 1, 2001

By Paul M. Jr. Musgrove, Donald C. Moore

Conventional Smelting Practice Conventional copper smelting practice varies from smelter to smel¬ter, but generally consists of some or all of the following unit processes: roasting, smelting, converting, and fire refining. Roasting. Copper sulfide concentrates can be smelted directly or after an initial roasting step. Roasting is used in some smelters because roasting prior to smelting increases smelting capacity, less energy is required to melt hot roaster calcines than wet sulfide concen¬trates, roaster off gases are high in Sot concentration, 5-15% SO2, and some volatile impurities are removed from the concentrate prior to smelting. However, many smelters do not use roasters, because the problems associated with handling hot dry calcines outweigh the advantages mentioned. Concentrate roasting is performed in multiple hearth or fluid bed roasters. If the moisture is low, roasting can be performed autogenously, usually at 500-600°C. High roasting temperatures are avoided because excess oxidation of the iron compounds may lead to magnetite formation. Magnetite is detrimental to reverb operation because mag¬netite can combine with refractory minerals to form a highly viscous slag. This slag prohibits efficient matte-slag separation and leads to excessive copper losses. Also, magnetite can settle through the matte layer, deposit on the furnace bottom, and consequently reduce furnace capacity. Roasting is carried out only on sulfide concentrates prior to smelt¬ing in reverb or electric furnaces. For smelting processes, such as the flash and continuous that rely on the exothermic heat of oxidation of the sulfur minerals, roasting is not practiced. Reverberatory Smelting. The predominate copper smelting fur¬nace for the past 50 years has been the reverb. These furnaces are typically 100-120 ft long, 30-35 ft wide, and 12-15 ft high. A typical furnace layout is shown in Fig. 2. Refractory brick linings cover all internal surfaces of the furnace. Originally the flame was directed to reverberate or reflect off the furnace ceiling and melt the feed material. Current practice is to direct the flame down the furnace length to melt the concentrate. A method of charging the concentrates or calcines, generally along the side walls to minimize refractory erosion, is incorporated in the furnace design. The copper concentrates, calcines, and fluxes charged into the reverb undergo a series of complicated reactions as the temperature of the mixture increases. The reaction of the iron and copper sulfides with the oxygen in the furnace produces a molten Cu25-FeS mixture called matte. Copper smelting metallurgy is based on the fact that sulfur has a greater affinity for copper than for iron and most other common metals. Therefore, in a system containing copper, the copper will preferentially remain as a sulfide compound until all of the other metals have been oxidized. The oxidized metals combine with silica to form a silicate slag that floats on the matte and is removed from the system. Reverberatory furnace smelting chemistry can be approximated by the following chemical equations: FeS2 + O2 - FeS+ SO2 (1) The formation of FeS ensures that any copper present other than as sulfides will be reduced by the relationship: CuO2 + 2FeS + O2 - CuS + 2FeO+SO2 (2) or 2Cu +FeS - Cu2S + Fe (3) As the molten charge travels down the furnace, continued oxida¬tion of the iron minerals and sulfurization of the copper minerals occurs. When all of the copper has been converted to sulfides, the iron sulfides can then be further oxidized as: FeS + (3)2 O2 FeO + SiO2 (4) The FeO reacts with the silica added as flux in the furnace charge. A simplified equation is: FeO + SiO2 -FeO SiO2 (5) The iron silicate slag formed is skimmed from the surface at the end opposite the burners. The copper content of reverb slag is usually less than 0.6% Cu and is discarded. Matte is removed along the side wall and is taken to the converter for oxidation of the remaining sulfur and iron. The main objectives in reverberatory smelting are to produce a molten Cu2S-FeS matte containing 30-60% Cu and a throwaway slag. Production of matte permits complete conversion of all copper minerals into copper sulfides, which can migrate because of specific gravity differences, through the lighter slag layer. Also, the molten matte droplets collect the noble metals, gold and silver, as the matte settles in the furnace. The large settling area of the furnace provides enough separation time to produce a low grade slag, which can be discarded without further processing. High heat losses are associated with reverberatory smelting be¬cause of the large volume of gases sweeping through the furnace. Therefore, an outside source of heat is required to keep the smelting reaction going. Natural gas, fuel oil, or pulverized coal are used as this heat source.

Jan 1, 1985

By Victor S. Sazhin, Alexander Kostenko

The hydrochemical method, which is based on the separation of aluminium oxide and silicon oxide by the hydrothermal decomposition of aluminosilicates by alkaline solutions in the presence of calcium oxide, can be effectively used for the complex processing of high-silicon aluminium ores. In this case, the silica is bound to a slightly soluble compound: Na20.2Ca0.2Si02•H20 (under the conditions: [&k]= 9, CaO/SiO2 = 1.05, alkali concentration in the solution: over 300 g/l Na20, T = 240...300 °C). If alkaline solutions of 100...150 g/l Na20 concentration are used, Ca0•SiO2•H20 or 2Ca0•Si02.0.5H20 compounds, depending on calcium oxide dosage, are formed at 280...320 °C. New methods for the crystallization of Na20.Al203.2.5H2O from concentrated alkaline solutions rand low-concentration solutions are proposed to isolate aluminium from solutions. The hydrochemical method, which involves no sintering process allows one to decrease the expenditure of heat by a factor of two, to reduce the investment and to exclude the pollution of the ambient air by dust-laden gases. The expansion of the raw-material resources base of

Jan 1, 1984

By Haydn H. Murray

Although alumina constitutes about ii percent of the earth's crust, it is expensive to separate and purify for the production of aluminum with the exception off the alumina in bauxite. The United states has a variety of non-bauxite resources that could substitute for bauxite, including high alumina clays, alunite, dawsonite in oil shale, anorthosite, and nepheline syenite. Each of these resources are discussed from the standpoint of geology, geography, processing, potential recovery, and environmental problems. Potential by-products include silica from clays, potash and sulfuric acid from alunite, soda ash from dawsonite, and soda ash and potash from anorthosite and nepheline syenite.

Jan 1, 1982

By Stanley C. Suboleski

1977 was the modern day low point for productivity in the coal industry. At that time, no one could have predicted that the industry was about to enter a productivity rise that would continue unabated through the 1980s. Thirteen years later, the cause of this phenomenon is still not well understood. While many government studies focused on the fall in productivity from 1969 to 1977, none have been undertaken to explain the rise. Some of the likely causes of the gain in productivity during this period will be discussed here. An attempt will also be made to quantify the value of some of the technical innovations that have taken place. The remainder of the gain is assumed to come from non-technical sources. The nature of these sources, although largely non-quantifiable, is also discussed. Since the number of mines that have adopted the technical innovations noted here is largely unknown, the actual contribu¬tion of technological changes to the overall productivity gain can only be estimated.

Jan 1, 1990

By C. V. Deutsch, J. B. Boisvert, M. A. Cuba

The amount of information available for characterizing a deposit increases over time due to the continuous acquisition of data during mining. This additional information is collected from different sources, including geologic mapping, production data and infill drilling. Throughout the lifetime of a mining project, the block model and the mining sequence are periodically updated to account for this new data. In general, the acquisition of additional data increases the accuracy of the block model, reduces uncertainty in ore/waste limits and clarifies the optimal mining sequence. There has been extensive research on mine planning, but current techniques do not consider the decrease in uncertainty as additional information becomes available. Conventional paradigms assume either 1) the kriged model is correct and uncertainty due to multiple realizations does not change the mining sequence, or 2) the mining sequence is unrealistically adapted to each realization. A new paradigm is proposed for evaluating minable reserves of surface mining projects, which accounts for the acquisition of additional information in the design of the long term mine plan. Multiple scenarios characterizing the dynamic nature of mining and data collection are created. In the proposed methodology, the performance of the long-term mine plan depends on both mining and data acquisition strategies. Each scenario considers the same extracted volume for the first period, resulting in a set of scenarios that diverge from a common initial period, accounting for how the mine may develop over time as new data are acquired and provide a more realistic evaluation of reserves with an appropriate level of uncertainty. A synthetic example is presented to illustrate the implementation of the methodology and the benefits over conventional paradigms.

Jan 1, 2013

By W. Norman Sims

A number of forces are at work that are now having an influence on coal handling systems. Changes are occurring and will be occurring at an increasing rate during the next few years. 1. Environmental concerns will dictate that dust pollution and spontaneous combustion and its resulting problems be rigidly controlled. 2. Slurry pipelines will be a reality despite the opposition of the railroads because they are economical and make good business sense. Artifical roadblocks can only survive for a limited time. 3. Coal is now and will remain the most economic fuel, particularly for power generation. This is true in most of the developed nations not just the United States. Increase in demand requires a close inspection of transportation systems. 4. A projected major increase in the export of U.S. coals may never occur without major port developments not the least of which will be the ability to accommodate large ships without demurrage time now affecting such shipments at U.S. Ports.

Jan 1, 1982

By CADEN VITTI, Barbara J. Arnold

Mine tailings, the byproduct of mining and mineral processing, are increasingly mass produced as a result of increased demand for metals and minerals as well as the advancement in technology that allows for the exploitation of lower-grade ores. Lower grades can increase the volume of tailings that may contain new gangue minerals that should be evaluated for the presence of critical minerals and other valuable metals. The practice of reprocessing, while relatively new, is crucial to reducing environmental damages, obtaining valuable critical minerals from waste, and contributing to more sustainable repurposing and disposal methods. With the increase in tailings dam failures in recent years, there is a large motivating factor in remining and removing the potential hazard to benefit the safety of potentially impacted communities. In analyzing the perspectives of various domestic and international studies, this literature review will determine the feasibility of reprocessing and reutilizing mine tailings waste for a more sustainable future while exploring current practices that have benefitted ecosystems and communities.

Jan 1, 2022

By Jr. Winters

The United States continues to be the largest producer and consumer of copper in the world. Table 1 on the following page shows several production statistics for 1974, the most recent year which the non-communist world copper industry might consider a good year, and for 1976 and 1977. In 1974 an estimated 24 percent of the non-communist world's newly mined copper was mined in the United States, and. 87 to 89 percent of that was from the western porphyry coppers. In 1976 U. S. new mine production was down to 22 percent of the non-communist world's newly mined copper, and the percentage of U. S. new mine production supplied by the porphyry coppers had risen to 89 to 91 percent. In 1977 the statistics remained the same as in 1976. U. S. porphyry copper production represented about 65 percent of U. S. refined copper consumption in 1974, rose to 75 percent in 1976, and dropped back to 61 percent in 1977 as imports of foreign copper into the United States began to swell.

Jan 1, 1978

By Farrukh M. Mazhar, Philippe P. Martin

Electrical Vertical Sounding (EVS) profiling has proven to be a valuable tool to set the alignment and guide the design of a 17 km-long, 4.7m diameter water-conveyance tunnel in the Peruvian Andes at an altitude of 4,260 m. EVS profiling helped determine where to locate boreholes, and reduce the amount of drilling to 1,200 m of vertical and inclined boreholes. EVS profiling allowed the designer to identify and verify by drilling the existence of zones with difficult tunneling conditions that were avoided by realigning the tunnel. The rock quality was checked by drilling and a combined scheme of excavation by TBM and conventional drill and blast technique was developed for the final design.

Jan 1, 2003

By S. Lee, F. Campero

"Past heap leach design has evaluated hydrodynamic parameters based on a uniform particle size of heap material, but has ignored the equal importance of the instability of fine migration within heap stack in the beginning stages of the irrigation process. The proposed probabilistic model evaluates internal fine erosion and segregation potential of well-graded crushed ores by considering the entire particle size distribution shape and site compaction degree. Using this model, unsaturated flow model parameters were successfully evaluated based on synthesized soil-water characteristic curve (SWCC). Additionally, one-dimensional unsaturated transient flow modeling with Hydrus 1D® showed that the different recovery efficiencies of heap material under unsaturated flow patterns depending on the particle size distribution and compaction degree of heap material. Agglomeration preprocess employed by most heap leach sites can reduce the potential of fine erosion within heap material significantly, but internal stability of crushed ores and hydrodynamic-based analysis of heap material’s pore structure is equally important in the prescreening stage in order to improve efficiency of the heap leach and avoid a costly agglomeration process. INTRODUCTION Accurate estimation of heap leach recovery is a difficult task due to the variety of design parameters that need to be considered - such as geochemistry, hydro-dynamics, and geotechnical design aspects, most notably particle size distribution through the process of agglomeration. After agglomeration techniques were introduced to heap leach design, the influence of particle size distribution and compaction degree in enhanced heap leach recovery has been neglected. The main purpose of agglomeration is to prevent fine segregation and internal erosion during and after heap stacking for well graded crushed ores, which will eventually diminish heap reach recovery. Recent studies show that agglomerated heap materials that had been consolidated at 10 meters below heap surface can release the fines after contact time with lixiviant to the compacted heap material and produce poor drainage performance (Milczarek et al, 2013). It must be noted that engineers and practitioners should investigate feasibility of agglomeration benefit prior to heap leach design because the agglomeration process can incur up to 20 or 30% of project costs. Internal stability of stacked heap material is mainly governed by the particle size distribution of crushed ores. Depending on this stability, segregation and internal erosion of fines can be mitigated by the application of moderate compaction effort during heap construction. Investigation of segregation and internal erosion potential therefore takes precedence for well graded crushed ore since reaction time and contact area with lixivant are greater in finer ores."

Jan 1, 2016

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 W. D. Bachman

A study has been made of wet, autogenous grinding of disseminated copper ores, including testing of a large number of samples from Kennecott Copper Corporation's Chino mine. The efficiency with which the various samples could be ground was found to vary over an extremely wide range, even among samples taken from different locations within the same ore body. These variations in grindability can be qualitatively correlated with the composition of the rock and the fracturing and alteration that had occurred. Because of the large-scale non-homogeneity of disseminated copper ore bodies, extensive and careful testing of autogenous grinding is needed. An accurate correlation of the grinding data from various samples with the geology of the ore body and with mining plans will indicate if variations in grinding mill throughput can be avoided in practice by mixing or blending of mill feed and if, therefore, autogenous grinding can be applied successfully.

Jan 1, 1970

By J. A. Matar

Mineralization features at the Bajo La Alumbrera porphyry copper-gold deposit are discussed as they affect gold leaching and copper flotation behavior. Alteration-mineralization geological blocks are assigned in the zoned body, and each required its own geostatistical model. They extend horizontally outward from potassic to the phyllic-propylitic boundary, vertically from surface down to 300 meters, and include oxide, secondary enriched, and hypogene mineralization. Copper and gold values are calculated geostatistically from assays and all available geologic-mineralogic information. Reserves are classified for each geologic block and for each open-pit bench into leach or float ore according to metal grades, geologic characteristics, and supergene-hypogene relations. Finally ore extraction behaviour is briefly described, grouping gold and copper reserves into metallurgical families.

Jan 1, 1986

By Jacques B. Wertz

It is well known that the major fractures and lineaments presently recorded in Western North America are preferentially oriented along a general northwest direction (Figure 1). There are other features, however, more subtle, more elusive as a rule and which can only be inferred, occurring at right angle to this broad NW direction. It is intended a) to examine some of these NE or transverse trends, b) to compare these regional NE breaks to similar ones that transversally cut through the eastern part of the European Tethys, more specifically in Iran and Turkey, and c) to study their potential relationship to mineralization in both areas.

Jan 1, 1973

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