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So many emergencies that crop up in mining necessitate a departure from ordinary methods that the writer has been led to illustrate a few of the examples that have come under his notice during a somewhat lengthy career; and as most of the methods illustrated are certainly outside the ordinary, it may be hoped that while to many they may convey little that is new, to the larger number some acceptable information may be gleaned whenever the occasion calls for it. Experience has shown that there can be no hard and fast rule in mine timbering that will fit the varying- necessities of different localities, and the engineer must divest his mind of all prejudices that his practice of any particular system or systems may have induced, and must direct his attention to the character of the local timber and its fitness or otherwise for the purpose he has in view. Fortunate indeed are the man and mine that can claim an abundance of good and cheap mining timber it simplifies, oftentimes, what would be, under unfavourable timber conditions, a difficult problem. In many parts of the States there is either none or at best a scrub if the latter, he has to either pigstye, balk, or bulkhead, if his ground will permit; if, not, and the necessary timber has to be imported, then some system of recovering his timber and using it over and over again may be possible. As an illustration of this, Fig-s. Nos. I and 2 show a method applied to the copper deposits of the LyellTharsis, Tasmania. The workings were wide; varying from 30 ft. to 50 ft., and the deposit a taIcose schist of fairly good...

Jan 1, 1902

By Jeffiey B. Austin, Maurice Tagami

"The ores of the Iberian Pynte Belt are typically massive sulphide ores with very fine grained mineral textures. EuroZinc Mining Corporation is currently evaluating one of the massive sulphide deposits located near the town of Aljustrel, in South Central Portugal. The deposit contains significant grades of lead, zinc and silver. The ores are comprised solely of sulphide mineralization consisting of pyrite, sphalerite, galena and some secondary copper minerals. Liberation requirements for these ores are typically 22 to 25 microns. A selective flotation process has been utilized to produce separate lead and zinc concentrates for sale to off-site contract smelters.This paper outlines the process test results and describes the process parameters required to optimize the process parameters. Ths test program has been conducted in support of the re-opening of the facilities in Aljustrel. The 3500 tpd mining and milling facility was commissioned in 1990 and operated for 18 months before closing. The previous facility was designed to produce three products using a selective copper-lead-zinc flotation process. EuroZinc Mining Corporation is proposing to re-open the operation, selectively mining from a lead-zinc phase of the massive sulphide deposit and produce only lead and zinc concentrates.Results are presented and discussed.PROJECT HISTORY AND CURRENT PROJECT OBJECTIVESThe EuroZinc Aljustrel Project is a potential major producer of lead, zinc and silver located in the Iberian Pyrite belt of south-central Portugal. The town of Aljustrel is historically associated with mining dating to the time of the Romans. The area is rich in pyrite deposits, and sections of the pyrite deposits contain significant zones of copper, lead, zinc and silver. Mining in Aljustrel during the last century (1900’s) included a major pyrite mining operation, which produced feed for sulphuric acid production. Pynte mining operated from the 1930’s to the early 1970’s and a short-lived base metal operation from 1989 to 199 1."

Jan 1, 2000

By C. Vipulanandan, M. Dawood, Dongmei Pan

"With the aging infrastructure, there is a need to maintain and extend the service life of steel structures in general and steel piles in particular. Steel piles support not only vertical loads but also dynamic horizontal loads in onshore and offshore applications. In order to select the appropriate methods to repair corroded steel piles used in onshore and offshore application, corrosion mechanisms were investigated with the rate of corrosion in various environments. The corrosion rate of steel in soil, water and soil-water interface varied from 2 to 500 µm/year. Based on literature review and analyses, the repair methods can be broadly characterized as protective coating, electro-chemical methods, wrapping and encasement and partial replacement of steel. Also, methods to evaluate the repair materials and the repair configuration have been documented.IntroductionOne of the biggest challenges facing the aging infrastructure is the materials loss and deterioration due to corrosion. Many studies indicate that in the US alone, costs due to corrosion loss is more than $276 billion annually (Michiel et al., 2010). Corrosion is the major cause of deterioration of steel structures and components (MNC, 2005). Load bearing steel piles are used as foundations for various types of structures and hence corrosion is very much influenced by the environment such as soil, water and soil-water interface. Corrosion of steel pile foundations may result in reduced capacity in the axial and lateral directions. Hence, understanding the rate of pile corrosion is essential to select the appropriate repair methods to avoid excessive deflection and failure (Decker et al. 2008).To prevent the deterioration mechanisms that attack a pile, it is fundamental both to identify and understand the deterioration mechanism that has been the cause of damage. Understanding the deterioration mechanism allows the engineer to design a repair that will combat this type of damage. It is widely recognized that the corrosion of carbon steel in soil, water and soil-water interface proceeds according to the following simplified anodic reaction and cathodic reactions in the presence of oxygen (Decker et al. 2008)."

Jan 1, 2017

IN the underground department of a mine, we may fairly say that "good management is based upon three elementals: first, sound engineering; second, proper coordination and efficiency of every human unit; third, economy in the purchase and consumption: of supplies.This paper is practically an analysis of the second element; which stands out prominently as the most important in the winning of successful results. The human units are divided into officers and men. The officers intermesh. One man takes responsibility where another throws it down; incessantly new conditions are arising where they may be doubtful of their powers; and always, on account of the three shifts, varying methods of work are coming into conflict. This very often results in disorganization. What is most necessary to guard against this is an esprit de corps, which would influence officers to stifle personal feelings for the general welfare of the department, To secure co-operation and loyalty of the staff, the writer recommends for the mines of the field a system of profit-sharing. Distributed on a salary basis, together with liberal holidays (not less than three weeks in each year) on full pay...

Jan 1, 1912

By J. D. T. Steyl, C. A. Biley

"The chemistry of electrolyte systems containing iron remains generally poorly understood despite their prevalence in many natural and industrial processes, particularly in hydrometallurgy. These systems are typically challenging to study and model due to their affinity for complex formation and precipitation even at low pH. Recent developments in the hydrometallurgical processing of nickel laterites at Anglo American have called for a deeper understanding of the fundamental chemistry of the Fe2(SO4)3–FeSO4–H2SO4–H2O system. This paper details the development of an internally consistent, Pitzer ion-interaction model of this system, with explicit recognition of important contact ion pairs (CIPs). The primary application of this model is a thermodynamic framework for the interpretation of kinetic processes occurring during iron(III) reduction with SO2. Adopting a rigorous thermodynamic basis for the system chemistry facilitates the formulation of simple rate expressions that are capable of inherently capturing complex effects. While the iron(III) reduction case study remains the focus of this work, the developments have more universal applications and the thermodynamic speciation model can be extended into other systems containing acidic ferric sulfate.INTRODUCTIONIron is present in nearly all hydrometallurgical refining circuits typically as both a necessary and unwanted impurity and needs to be removed and disposed in a safe and efficient manner. This is generally performed by precipitation to form a range of solids such as hematite, goethite or jarosite. Numerous studies in the open literature have focussed on the removal of iron from refractory gold sulfide ore (Berezowsky & Weir, 1989; Berezowsky et al., 1991) and zinc pressure leaching (Buban, 1999; Ismael, 2003), and PGM matte sulfide circuits (Dutrizac & Monhemius, 1986). Moreover, since ferric iron is a strong oxidizing agent, it has been used extensively as a leaching agent for sulfide minerals (Dreisinger, 2006). Given the outlook of challenging economic conditions, declining ore grades and increasing levels of impurities, effective iron management is going to become increasingly critical to all hydrometallurgical processes.Against this background, and considering the widespread importance of acidic iron sulfate systems throughout natural and industrial processes, it is unexpected that the knowledge of the fundamental solution chemistry of these systems contains such significant gaps, particularly at the conditions typically found in hydrometallurgical applications. Existing literature describing the measurement and modelling of solution speciation in these systems have highlighted their significant chemical complexity (Magini & Caminiti, 1977; Magini, 1979; Lee & Tavlarides, 1985; Stipp, 1990; Papangelakis et al., 1994; Gil et al., 1995; Majzlan & Myneni, 2005; Kormanyos et al., 2008; Yue et al., 2014). Partially responsible for the lack of quantitative speciation measurements is the strong tendency of ferric to hydrolyse at even low pH (Flynn, 1984), complicating the laboratory study of such systems. Moreover, the large number of aqueous species that may co-exist simultaneously makes the study of individual species and the modelling of the numerous interactions between these species extremely difficult (Dry & Bryson, 1988; Stipp, 1990; Majzlan & Myeni, 2005; Kobylin et al., 2007)."

Jan 1, 2016

By Ronald M. Hays

The Duluth Gabbro Complex in Northeastern Minnesota possibly contains a significant domestic copper resource and the nation's largest nickel resource. Exploration has discovered large low-grade copper-nickel (Cu-Ni) deposits between Hoyt Lakes and the Boundary Waters Canoe Area (BWCA). The mining and processing of Cu-Ni will have environmental, economic, and social impacts. The purpose of this study is to relate major environmental, economic, and social considerations to various aspects of Cu-Ni extraction. An open pit and two underground (block caving and open stoping with backfilling) models were developed to generate information on the impact of Cu-Ni extraction. Important considerations having environmental, economic, and social impacts (luring various aspects of Cu-Ni extraction are identified and defined. These aspects are exploration, development, mining, beneficiating, smelting, transportation, and termination of operations. Considerations are grouped into the general categories of site, industrial, energy, climatic, resource, water, air emission, waste disposal, employee, tax and royalty, transportation, and community considerations. Cu-Ni extraction in Northeastern Minnesota presents major environmental, economic, and social risks. Decisions are required on trade-offs between adverse and beneficial impacts. The approach used in this study assists in assessing environmental, economic, and social impacts. It will aid in the examination of potential and projected short-term and long-term advantages and disadvantages and will aid in the development of Minnesota's Cu-Ni resource for the maximum benefit to society.

Jan 1, 1974

By Tim O’Neil

Dressed in black tie and Victorian attire, some 200 people came to Leadville, CO, for a September weekend featuring a National Mining Hall of Fame and Museum (NMHF&M) induction banquet and a scenic mountain train trip to Fremont Pass and the Climax Mine. The 18th annual induction banquet on Sept. 17 began with cocktails and a open house. It was a chance for visitors to tour the National Mining Museum including the new Hennebach Wing, opened in February. The new wing is named in honor of Ralph Hennebach, retired chairman of Asarco. Formerly Leadville Junior High School, the Hennebach Wing encompasses more than1,440 m2 (15,500 sq ft) of floor space in two stories. One prominent feature is a 1923 Wills Sainte Claire touring sedan. Climax Molybdenum donated this first all-molybdenum steel motorcar. Docents were available throughout the museum to give banquet attendees directions and answer questions.

Jan 1, 2005

By Alex Del Castillo

The mineral processing industry has followed the development of database control systems, and various systems have been installed in existing and new plants. The goal is to improve product quality, raise productivity and lower production costs. Improvements in different units for mineral .processing .have been applied. This has led to increasing information for the operators. To support the operators and for an easy overview of the process, a complete concept for an integrated process-control system is required. This paper describes the plant-wide [process control system for the Collahuasi copper project located in northern Chile. The total investment for the project was $1,700,000,000 and included a port area and two copper processing plants, an oxide plant with a cathode production of 50 tons per year and a sulfide plant with a concentrate production of 330 kilotons per year. The main characteristics of the plant-wide process control system include a 200- kilometer long redundant control network and a 24-kilometer long redundant serial network providing coverage for the entire plant. The plants are located around 4,700 meters above sea level, serial communication lids allow the integration of over 2,700 SCADA data units, and the system handles over 7,500 physical signals plus the SCADA data integration. The main equipment consists of 39 different sized controllers, 16 operator stations, 5 engineering stations, 2 information management systems and 4 X- terminals. The project management, control configuration, factory acceptance test, system integration test, training, commissioning and start-up were carried out in close cooperation with the customer. The result was completely satisfactory for the customer.

Jan 1, 1999

I HAVE to thank the members of the Institute most cordially for the honour conferred upon me in selecting me President, which position my poor services have prevented my filling adequately. I have, therefore only been able to stumble through my year of office under the guiding direction of our esteemed Secretary. I fully appreciate the honour done to me; and, now that it is over, I can look back with pride and pleasure at having occupied the chair; but I am told that it remains for me to fill one of the requirements of our Institute and present you with what has been dignified by the name of a presidential address. My relief in complying with this is in the knowledge of its freedom from the usual discussion which appertains to papers presented by our worthy members. It has been usual in the past for the subject chosen to be specially connected with the work immediately engaging the attention of your president, and on this occasion I would like to break away from this time-honoured custom and engage your attention for a brief space on what is equally dear to us all namely, Ideals of the Profession. In doing so, the retort of Whistler to an art student gives me, I must admit, much misgiving, for, on being asked how he developed his artistic talents, replied that he painted what he saw, which produced the immediate reply, "Ah, but the tragedy will come when you see what...

Jan 1, 1909

By Ammar Henchiri, Godfrey McDonald

"Breakwater Tunisia S.A.’s Bougrine mine is located in a semi-arid region of Tunisia characterized with Triassic salt domes. Due to extensive agricultural land-use in the mine area, a zero-discharge tailings facility design and high water recycling rates to the concentrator were chosen to minimize the environmental impact to the surrounding area. The process water supply has an accumulation of naturally occurring salts due to high evaporation rates and the need to recycle 70% of the process water. The elevated salt content of the process water had an adverse effect on the efficiency of the flotation reagents, which led to the production of lower quality zinc concentrate.The impact of the water salinity on the zinc concentrate quality was documented by extensive laboratory testing. A feasibility study was prepared and a decision was made to install a reverse osmosis plant for desalination of the process water. A plant was constructed during 2000 which currently supplies up to 85 m3/hr of de-mineralized water, equal to approximately 45% of the total process water requirement. The salinity of the process water decreased from about ten to twelve grams per litre before installation to less than three grams per litre. Together with minor modifications to the concentrator circuit, Breakwater Tunisia has increased the zinc concentrate grade from 50% zinc to 55% zinc without compromising the zinc recovery rate of approximately 84%.This paper discusses the successful installation of a reverse osmosis desalination plant that allowed Breakwater Tunisia to improve the grade of the Bougrine mine zinc concentrate and thus increase the net smelter return.INTRODUCTIONBreakwater Resources Ltd., through a wholly owned subsidiary, Breakwater Tunisia S.A., acquired the Bougrine underground mine and related assets in September 1997. During the winter of 1997/1998, the company rehabilitated the mining equipment, modified the concentrator circuit, developed a new mine ventilation system and prepared a new mining production program. The mine was reopened on May 2, 1998 and was in commercial production as of June 1, 1998."

Jan 1, 2003

The wealth of a nation can be measured many ways, but one of the most important measures is its natural resources, particularly minerals. Minerals provide the foundation upon which economic prosperity and defense preparedness rest. Assessing our energy and mineral resources and assuring their development is in the best interests of all our people continues to be an important national goal. Since its founding in 1910, the U.S. Bureau of Mines has established itself as the world's premier minerals information and research agency. Its authoritative, comprehensive data and pioneering research have contributed significantly to a strong U.S. mineral position in the world.

Jan 1, 1990

By Juan Kobashicawa, Bernardo Falcón

En este trabajo se explican los controles automáticos desarrollados (In-House) e implementados en el circuito de Molienda de Compañía Minera Antamina, el cual abarca Molinos SAG, de Bolas y los Hidrociclones respectivos. Los controles implementados son basados en el Control por Lógica Fuzzy y las Bandas de Bollinger; así mismo se indican los criterios en el diseño de los controladores y las variables del proceso que se han tomado para la implementación donde se controla un indicador de distancia del centro de masa de la carga respecto al centro del molino de Bolas. Asimismo, se muestra el impacto positivo logrado con la estabilización del circuito.

Sep 1, 2017

By Moskovits E. E

Spodumene was recovered from pegmatite by flotation in laboratory and pilot-plant tests using an anionic collector emulsion. A similar process applied to beryl pegmatite gave encouraging results.INTRODUCTIONOver the past two decades lithium and beryllium have aroused increasing interest in the metallurgical world. Both these light metals have potential uses in nuclear shielding and cooling and in lightweight alloys, and there is a growing demand for lithium chemicals for ceramics, air conditioning and lubricants. The use, technology and history of lithium has been surveyed by Schreck (1961).For many years, the only commercial production of lithium and beryllium was from pegmatite deposits amenable to hand cobbing. The most important minerals of these ores are spodumene and beryl, which are respectively lithium aluminium silicate and beryllium aluminium silicate. Norman and Gieseke (1940) investigated the treatment of lithium ores by froth flotation. The process of flotation of the pegmatite constituents away from the spodumene was applied commercially in 1951, and the operation has been described by Goter, Rainey and Hudspeth (1953). Subsequently, the flotation of the spodumene from the pegmatite was studied by Munson and Clark (1955) and Browning and McVay (1961), and this method has superceded the reverse flotation process commercially. Muskett, Tasker and Hobson (1962), in applying the method of Browning and McVay in pilot-scale tests, reported difficulty because of activation of quartz and felspar by iron salts introduced during milling of the ore.The flotation of beryl, reported by Ashton and Weir...

Jan 1, 1963

This report describes the development of training materials for the operators of underground mining equipment in the underground metal and nonmetal mining industry. The objective was to determine the effectiveness and acceptability of these training materials and to provide the validated training materials to the industry. Ten modules were developed, based on industry need according to accident frequency, accident severity and exposure to the equipment. The final modules were an average of 20 minutes in length and used slides with synchronized narration on cassette tapes. Testing materials are included for use by the mines.

Jan 1, 1984

By O. M. Arafat, J. A. Finch

"The Functional Performance Equation calculated from a plant grinding survey defines two distinct ball mill circuit efficiencies and how they relate to total production rate through the target grind size. The survey data are also used to calculate a complete ball mill size distribution model, represented by the energy specific grinding rates, not just through the target grind size, but through all the size classes. Cyclone separation performance is represented by individual size recoveries to underflow. When these two unit operation performances are entered into the circuit modelling program (Streamline™), along with the circuit feed rate and size distribution, all the circuit survey size distributions and mass flows are perfectly regenerated by the program. The many issues associated with the historical Epstein (breakage-selection) models are eliminated. Once the circuit program is populated, pump and cyclone performance changes can be evaluated using a step-by-step procedure in order to maximize Classification System Efficiency. Mill water use and media sizing opportunities are also diagnosed in order to maximize Mill Grinding Efficiency at the size of interest. An example is provided. This circuit analysis and modelling system, and related training, is provided through a web-based application.IntroductionSince its development (McIvor, 1988), the Functional Performance Equation for ball milling has facilitated new understanding of industrial circuit cause and effect relationships, leading to significant strides in operational performance. Success stories of this refreshing approach to plant circuit performance improvement are now too numerous to list. Finch and McIvor (circa 1986) also discovered that the Functional Performance “Mill Grinding Rate” at the size of interest was the same cumulative grinding rate that is calculated from mill feed and discharge size distributions using a first-order rate equation. By calculating these cumulative grinding rates for all screen sizes, a complete ball mill model is generated (as used by Finch and Ramirez, 1981). Others in industry, Hinde and Kalala (2009), for example, have noted the same. Lacking the complexity needed to maintain their interest, most researchers have ignored this model, broadly opting instead for Epstein’s (1948) characterization of grinding as a chemical reaction, combining “selection rate” and “breakage size distribution” functions. The much simpler ball mill model presented here has previously been incorporated into a proprietary circuit modeling program (McIvor, 2005) and used for plant improvement work (for example, see McIvor and Finch, 2007, and McIvor, 2014). Now, by combining this extremely business-friendly ball mill model with optimization criteria from Functional Performance Analysis, a circuit modeling system (including the needed supplementary steps to assure successful plant implementation of circuit design changes) is at the disposal of every plant metallurgist, grinding equipment/material provider, and circuit designer."

Jan 1, 2017

By David Stephenson, Hugo Granados, Steven Klohn

"HudBay’s Constancia project is a copper molybdenum concentrator located in southern Peru. In 2010 Ausenco was contracted to perform a feasibility study optimization review which resulted in an improved design with significantly increased throughput capacity at a minimal increase in capital cost. Construction began in 2012 with commercial operation commencing in May 2015. This paper outlines the process plant design as well as describing the plant’s major equipment selections, start-up and early operations experiences.IntroductionHudBay Mineral’s Constancia project is located at 4200 meters above sea level (masl) in southern Peru, approximately 630 km south-east of Lima, Peru. The property can be accessed by road from Cusco, Peru, (approximately 110 km to the north), or from Arequipa, Peru (approximately 215 km to the south). Matarani, accessed via Arequipa, is the closest port.Constancia is located within the Yauri-Andahuaylas metallogenic belt. The region contains several large copper-gold-molybdenum porphyry deposits such as Antapaccay (by Glencore) and Los Chancas (by Grupo Mexico), and copper skarn deposits such as Tintaya (by Glencore) and Las Bambas (by MMG). Constancia’s ore reserves contain copper and molybdenum with trace amounts of gold and silver.Ore is mined by an open-pit operation. The process plant recovers copper and molybdenum concentrates, storing tailings in a conventional tailings management facility. Infrastructure at the site includes a grid power supply (via a 70 km overhead transmission line from Tintaya), water supply, workshops and an accommodation camp. Mine life is 22 years.Site construction works began in 2012 with first copper concentrate produced in late 2014. The project was executed for approximately 1.75B$USD.Ausenco’s design approach focussed on developing a capital efficient copper molybdenum concentrator. This paper outlines key features incorporated in the concentrator design, plant layout and equipment selection, as well as start-up experiences and early operational results."

Jan 1, 2016

By V. Petr, G. G. W. Mustoe, T. G. Rozgonyi

We introduced a numerical method that is applicable for the analysis of static and dynamic deformations of elastic media. In this numerical study, each elastic body is modeled with a system of several hundred rigid particles that are joined together elastically. Maximum shear stress fields due to external loading are obtained and compared with those obtained by photoelastic experiment. Preliminary results are presented for the stresses generated in circular disk shaped bodies idealized with connected systems of particles. Extension of this simulation method to fragmentation of brittle materials is also illustrated in an example.

Jan 1, 2000

By N. Andersen

During the preliminary design phases and feasibility study of a proposed vertical shaft, a vertical diamond drill-hole is normally drilled on the site. This paper outlines how rock mass characteristics, in-situ rock stress, rock strength, hydrological characteristics, and structural parameters can be determined using wireline logging of this borehole. In addition, a rock mass classification scheme is developed, based on published work, and in particular the Q-factor is adapted to assess the stability of raise-bored shafts. The ‘stick plot’ is introduced, which combines all geotechnical parameters applicable to the stability of a vertical shaft into a colourcoded format where cross-correlations can readily be made on a day-today basis during the shaft-sinking process.

Jan 1, 2015

By Aram Grigoryan

This paper addresses historical aspects and construction sequencing of the subway complex under Columbus Circle in Manhattan; the structural elements of the rehabilitation and new construction; and the challenges associated with design and construction. PB is providing engineering services to New York City Transit (NYCT) for the rehabilitation of the 59th Street/Columbus Circle Station Complex that services over 150,000 customers daily. The project involves structural repairs, modifications and new construction requiring underpinning and temporary supports, custom framing details, and construction staging procedures to meet stringent limitations within the operating transit station and around the Columbus Circle street intersections.

Jan 1, 2008

M.S. Azun I have many objections to the content of the author's paper. Before discussing it, however, I would like to repeat the property of semivariogram function. Second order stationary properties of regionalized variables (ReV's) such as semivariogram function y(h) are perfectly known in geostatistics. Also, the kriging equations in the language of mathematical statistics using second order stationary properties are well understood. However, the way to use the sample (estimated) semivariogram function in any one of the kriging procedures is vague. The sample semivariogram function is given as follows: [ ] where N is the total number of samples, Xi is the sample value at the i - th location, Xi+h is the sample value at the i + h - th location, and h is the distance among the samples. An estimation variance of sample semivariogram function of first lag is smaller than that of higher order lag. The theoretical semivariogram function reaches the variance of samples asymptotically. But this is not easily observable because of the larger variation involved in the estimate of semivariogram function. In general, an estimation procedure is done for h = 0, 1, 2, up to the greatest integer less than N/2, even though sample semivariogram function can be computable through N-1. After estimating semivariogram function, the critical question of how to model sample semivariogram function arises. As seen in the above equation, sample semivariogram function is discrete and can be smoothed by the model being selected. Therefore, modeling of sample semivariogram function is the most important step in geostatistics. It not only smoothes a discrete function but also affects the results of the kriging procedure. When the only aim is to model the semivariogram function, which is the basic point of the author's paper, one can employ any fitting techniques, such as curve fitting, or any arbitrary functions, which are called submodels in the paper. The term "arbitrary function" is used rather than "submodel" because there is no basic understanding of developing them. The author suggests that the sum of those submodels can also be used for the modeling of sample semivariogram function. The combination of any arbitrary functions brings many problems instead of giving an insight of the domain structure considered. The author used two arbitrary functions and the nugget effect in response to sample semivariogram function (Fig. 10). For the same example, he stated that the parameters involved in the mixed arbitrary function model can be accepted when the discrepancy between sample semivariogram function and the model is small visually. For verifying the fitting behavior of any selected model, one should not be contented with the visual satisfactory. Some statistical measure such as goodness of fit has to be used. The author's practice is no more than an exercise in curve fitting without any fundamental understanding or conceptualization of the underlying physical mechanism. Furthermore, the selection of any model is not an easy task if the purpose is the search for the "best" response to the observed second order properties of ReV's. I suggest that the Markovian model (Azun, 1983), on the basis of a theoretical understanding of underlying mechanism, which gives more information about the occurrence of regionalized variables, is used to respond all properties of ReV's. There are a lot of problems for modeling of one-dimensional sample semivariogram function. Thus, it is not appropriate to go to higher order dimensional sample semivariogram function modeling. In the meantime, I would recommend that one can connect the values of standardized sample semivariogram function rather than simple values of semivariogram function in the two-dimensional estimation. The standardized values can be computed in dividing the semivariogram function value by the number of sample pairs involved in each lag regardless of the directions. In conclusion, geostatistics is an interdisciplinary area in mining that uses the principles of mathematical statistics. Thus, it should not violate any probabilistic and statistical rules. When Matheron was developing the theory of geostatistical study in the early years of geostatistics, many mining people had a reservation accepting the geostatistical tools. However, this does not mean that we, the geostatisticians, might try to convince those people using some "strange" tools or rules as some authors implied (Baafi and Kim, 1984). Instead, we have to develop and explain the geostatistical tools staying only in the framework of statistical concepts and properties. References Azun, M.S., 1983, "Stochastic Process Modeling of Spatially Distributed Geostatistical Data," Columbia University, Ph.D. Thesis. Baafi, E.Y., and Kim, Y.C., 1984, "Discussion - Comparison of Different Ore Reserve Estimation Methods Using Conditional Simulation," Mining Engineering, Vol. 36, No. 3, p. 280. Reply by J.M. Rendu The interactive method proposed by Rendu allows practitioners to develop semivariogram models that take into account not only the numerical information obtained by sampling, but also highly significant additional information that often cannot be quantified. The geology of the deposit - including hypotheses concerning its genesis, sampling methods, assaying methods, and mathematical methods used to calculate the semivariograms - all have an influence on the numerical results obtained and on how these results should be interpreted. If all the information concerning the spatial distribution of values in a mineral deposit was contained in the sample values, it could be argued that statistical techniques alone would produce optimum models. However, this is rarely, if ever, the case. Methods that allow the user to take into account his experience and his geologic understanding of the deposit should not be rejected for the sake of theoretical statistical purity.

Jan 11, 1985