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By Manuel Calderón

Chile is responsible for 30% of the global copper production; the world ́s largest. However, significant challenges are faced in this industry; declining grades (1.13% in 2002 to 0.61% in 2015), high cost of energy, scarcity of water, and environmental concerns. Mining trends suggest the future of the industry will be focused in the underground space, specifically due to the depletion of economically viable surface mineral deposits. For example, the largest block cave mineat Codelco ́s Chuquicamata mine is expected to reduce energy costs by 50% and dust emissions by 97%compared to the open cut mine. To access these underground deposits, critical infrastructure is required; horizontal tunnel developments, extraction levels, vertical raises, and ore passes with the on-time delivery of the highest quality outcomes being a requisite for successful project delivery (Lift 1 of 3 at Chuquicamata Underground has over 1000drawbells).One aspect that makes this scenario even more challenging for deeper underground operations is the increased risk profile (people, equipment, and geotechnical) that forms part of the general environment. Furthermore geotechnical risks should be considered and they include rock burst and windblast. The safe interaction with this environment must be sustainable throughout the full life of the project. This paper presents the Enaex group approach to addressing the blasting challenges and outlines the solutions created. Aspects such as rock mass damage occurrence as a function of blast vibration frequency content has been studied, as well as the development of blasting methodologies for guaranteeing the full 100% extraction of all infrastructure blasts, including the all-important draw bell volumes. The development of such infrastructure volumes in one single event using electronic detonators and the associated achievement of ambitious productivity goals, are described as a critical part of the successful construction of one of the most ambitious UG projects currently present on the world.

By G. E. McElroy, A. S. Richardson

"Experiments in the determination of friction factors for fan-pipe installations were carried on in a Butte mine during the fall and winter of 1922-23, under a cooperative agreement between the Bureau of Mines and the Anaconda Ccpper Mining Co. The results have been summarized in a separate paper,*** and this report, which is one of several giving more detailed data, discusses the methods used and the application of the results to fan-pipe practice.The use of canvas and galvanized-iron pipe, 8 to 20 inches in diameter, with small fans, usually electrically driven blowers, is an important factor in the ventilation of metal mines and is increasing in coal mines and long tunnels. In the Matte district the standard installation is an electrically driven small blower fan and 8 to 16 inch canvas pipe.The application of available data on friction losses in sheet-metal pipe to mine installations was doubtful, and very little has been published on canvas pipe, except general statements that the friction looses are greater than in galvanized-iron pipe. Experiments by Weeks and others,**** who determined friction losses under laboratory conditions for a few typical materials used in mine equipment, supported the statements.In 1918, one of the authors (Richardson) conducted tests for the Anaconda Copper Mining Cc. on the friction losses in canvas-pipe systems and the beet type of centrifugal blower for use with such pipe lines. He obtained the average total resistance per unit of length in use, without reference to the variable conditions of the lines. The results were of great value in developing more efficient equipment for average service conditions, and indicated that average friction losses for the commercial canvas tubing then used by the company were equal to or lees than these given for galvanized-iron pipe. Later on, the particular canvas tested was discarded for a heavier and more service-material."

Oct 1, 1923

By Ralf Winterberg, Axel G. Nitschke

"Macro synthetic fiber reinforced concrete or shotcrete is seen by many design engineers as offering a viable alternative to steel reinforcement in tunnel linings. The technology is now commonplace for primary and permanent ground support in both mining and civil tunnel applications. It has for instance become the standard form of reinforcement in the Australian mining industry, and has been used for a majority of permanent tunnel linings in recent tunnel construction in Norway. Similarly, macro synthetic fibers are becoming a standard solution for the initial lining in the USA.The use of macro synthetic fiber offers innovative solutions, yielding robust and sustainable tunnel lining designs. Citing recent research and actual projects, this paper presents state-of-the-art design considerations for fiber reinforced tunnel linings relating to structural and long-term performance. Topics include seismic resistance, crack width control, corrosion and durability, as well as sustainment of performance with age.INTRODUCTIONMacro synthetic fiber reinforced concrete (MSFRC) and shotcrete (MSFRS) has reached maturity as an engineered material and is widely used in all forms of tunnel linings, for temporary as well as permanent ground support in both, mining and civil tunnel applications. In the Australian underground mining industry, it became the standard form of reinforcement, where 2014 literally marked the end of steel fiber use in shotcrete [1], and has been used for over 80 percent of permanent tunnel linings in recent tunnel construction in Norway. Similarly, macro synthetic fibers are becoming a standard solution for tunnel initial linings in the USA. Recent examples in civil tunneling are the Devil’s Slide Tunnel and Caldecott Fourth Bore Tunnel in California or the Anacostia River Tunnel Intershaft Connector Tunnel in Washington D.C. In addition, an increasing number of tunnels are adopting shotcrete permanent linings using macro synthetic fibers. Examples include the A3 Hindhead tunnel near Guildford in the UK and the North Strathfield Rail Underpass in Sydney, Australia [2, 3]."

Jan 1, 2016

By Carl Lausen

Within recent years several mining companies have sent expeditions co the east end of Great Slave lake co determine the mineral possibilities of that area. Little was known of the geography of the region, and even less of the geology; and, not until Blancher's survey was made and the results published, was an accurate map of the lake available. Early explorers followed the Inconnu channel and the north shore of McLeod bay to Port Reliance, and, just prior to Blancher's survey, Hornby showed that the southern passage was feasible. Apparently, but few geologists have ? travelled through the country, for geological information is meager. In 1900, Robert Bell, of the Geological Survey, made a trip to Fort Reliance by way of the north shore of McLeod bay, and he gives a brief description of the geology. The present paper is the result of an expedition into this little-known region by Mr. Geo. M. Douglas and the writer in the summer of 1928. The south shore of Great Slave lake was followed to the east end of Tochatwi bay, and an extensive exploration was made of Kahochella and Pethei peninsulas. The prime object of the expedition was co determine the presence or absence of the copper-bearing Keweenawan basalts.

Jan 1, 1929

By F H. Henrfquez, A G. Oroz

Design and operating conditions of large size mechanical flotation cells were evaluated by comparing them with actual operating conditions in a plant. The objective was to determine the time scale-up factor, typically based on empirical rules. Experiments were conducted on the rougher flotation circuit at Minera Escondida Ltd. The circuit consisted of self-aerated mechanical cells of 160 m3, arranged in six parallel banks with nine cells each. The rougher circuit flotation kinetics were evaluated from direct sampling and local mass balances around each cell of the bank. Adjusted overall mass balances were also developed. This information was used to fit different kinetic flotation models, and it was found that the rectangular distribution function was the most appropriate to describe the distributed rate constant for industrial operation. Then, a rougher flotation simulator was developed to describe the actual operation in terms of the operating variables (mass flowrate, solid percentage, feed grade) and the actual volumetric flowrate entering to each cell. In this study feed pulp samples were taken in parallel from the rougher circuit and were simultaneously floated in the laboratory. The kinetic behaviour was then modelled at a laboratory batch scale in order to determine the time scale-up factor between laboratory batch flotation data and industrial size flotation. The time scale-up factor observed for large sized cells, 160 m3, was found to be reasonably similar to those previously determined for self-aerated mechanical cells, but of lower size, operating at similar recoveries. In addition, the relative effect of mixing, between laboratory batch and an industrial flotation bank, was quantified by the parameter, separating the impact that kinetic and mixing changes have on the time scale-up factor. In general, the rougher flotation operation was found to reach the predicted metallurgical target, and the optimal separability criterion was also respected. The diagnostic generates information about the internal state of the process and helps to identify potential improvements for design, operation and control of the circuit.

Jan 1, 2005

By Binbin He, Baiwei Lei, Rehamutula·Rouzi, Zheng Wang, Chao Li

Methane explosions are highly destructive and constitute a primary hazard affecting mine safety. Seals are commonly employed to obstruct the propagation of methane explosions within tunnels, with the aim of reducing the damage caused by methane explosions. In order to study the influence of the seals’ position on the parameters of methane explosion damage, this study takes the Lake Lynn Experimental Mine No. 501 in the United States as a background case. It investigates the methane/air explosion damage parameters at different positions of seals in a fully sized roadway using the GASFLOWMPI code. The coupling mechanism between methane explosion gas expansion and reflected waves is analyzed. Finally, the variation patterns of explosion damage parameters are analyzed based on explosion damage criteria. The results show that as the distance increases between the seal and the explosion source, the maximum overpressure and impulse at the seal decrease exponentially, and the decrease is more significant when the seal is closer to the explosion source. The maximum velocity and maximum dynamic pressure increase first and then decrease, reaching their maximum values at approximately 115 m. They are approximately 163.355 m/s and 30.485 kPa, respectively. According to the analysis of explosion damage criteria, it is found that overpressure damage is the main form of methane explosion damage. But the damage of impulse and dynamic pressure is not be ignored. The relative position between the seal and the gas expansion area significantly impacts the parameters of methane explosion damage due to the coupling effect of gas expansion and the overpressure reflected wave from the seal. When the seal is set in the gas expansion zone, the further the seal is from the explosion source, the greater the dynamic pressure damage and the more minor the overpressure and impulse damage. The closer to the explosion source, the more significant overpressure and impulse damage changes. When the seal is set outside the gas expansion zone, the further the seal is from the explosion source, the more minor the overpressure and impulse damage to the seal, and the dynamic pressure damage increases first and then decreases.

Apr 24, 2024

By Mark C. Malamphy

AT present the Federal Government represents the only organization applying geophysical methods of prospecting in Brazil. The geophysical work of the National Department of Mineral Production, which will be described in the following pages, must be considered as a program of experimental work designed to demonstrate the applicability of the more or less "standard" methods of geophysical prospecting to various problems of economic interest in Brazil by means of practical examples of results obtained in certain typical areas. Our work is somewhat similar to that of the Imperial Geophysical Experimental Survey of Australia, but our task has been greatly simplified by the ever increasing number of technical publications relative to the theory of instruments and methods.

Jan 1, 1936

Fifty to 75 million years ago, hydrocarbon-bearing rocks were formed in the Green River formation of Colorado, Wyoming and Utah. The hydro- carbons can be extracted from these rocks, marl- stone but misnamed oil shale, after crushing and intense heating. At about 900°F the marlstone decomposes to produce liquid shale oil. A press release from the Colony Development Co. describes a process which may permit, for the first time, economically feasible access to shale oil. Shale oil has resisted economic extraction for almost three centuries. According to the USBM, a patent was issued as early as 1684 in England to produce "oyle from a kind of stone". France produced oil from marlstone in 1838 and a dozen years later, Scotland started an oil shale industry, producing kerosine, that lasted nearly 100 years. In both countries, the process involved crushing the stone and retorting it to decompose the kerogen-a long and costly process at that time. In 1859, Edwin L. Drake brought in the first oil well in Titusville, Pa., and shale oil faded into oblivion.

Jan 8, 1965

By Mark Van Dyke, Ted Klemetti, Jake Beale, Zoheir Khademian, Joe Wickline

In 2016, a 3.7-ML magnitude event caused by mining activity occurred at a longwall mine in southwestern Virginia which was recorded by the United States Geological Survey (USGS) and felt by local residents. The event was the largest of its kind since a global mine design change by the operator was instituted in 2008 following three large events in 2005, 2006, and 2007 (3.4, 4.3, and 3.4 Moment Magnitude (Mw), respectively). Two of the three pre-2008 events (2005 and 2007) damaged ventilation controls in the mine which fueled a mine fire. In 2016, the mine’s management requested researchers from the National Institute for Occupational Safety and Health (NIOSH) to access geological data and determine what parameters could possibly lead to events of a magnitude of 1.0 ML or greater. Evaluation of 2152 geological data points and modeling revealed three major geological factors in common with the majority of the 181 recorded +1.0 ML events from 2009 through 2016. Three levels of seismic potential were identified as follows:

Aug 4, 2023

By G. K. Burgess

THE question of the allotropy of iron, in spite of a vast amount of experimental work and perhaps an even greater amount of theorizing, is not yet settled. That there is a definite transformation in iron near 900,° the A3 point, is generally recognized, as well as the fact that the temperature of this transformation is lowered by the addition of carbon and metallic elements. On heating, the transformation Ac3 is always found at a higher temperature than the transformation on cooling, Ar3. Whether the A3 transformation is sharp like the melting point of a pure substance, or extends over a considerable range of temperatures, embracing perhaps as a lower limit the A2 change, appears to be still an open question for pure iron. The nature and identity of the A2 transformation, it would appear from recent publications, has not yet been satisfactorily settled. In the present paper a critical, historical summary is given of the experimental investigations of the location of A2 and A.3 in pure iron, together with brief mention of some of the theoretical aspects of the subject, and an account is given of a series ?of experiments carried out with several samples of very pure iron which were studied by two methods of thermal analysis in the range from 5000 C. to 1,000° C., and which it is believed furnish a contribution of considerable interest as to the location and nature of the A3 and A2 transformations. Great attention has been given to the details of experimental manipulation and to the preparation of the samples, as it was soon found that some of the discrepancies noted in the work of many experimenters may be traced largely to lack of precautions which we have found essential. For example, to anticipate somewhat, it is necessary to provide a suitable practically gas-free furnace, the heating and cooling of which may be regulated to a nicety. To render a minimum the deforming effects on the cooling and heating curves of the poor conduction of the sample, it must be of a form and mass to pass on its heat rapidly and completely to the thermocouple; and finally the sample itself must be freed from gases which, if present, further mask the definiteness of the heating and cooling curves. We, have also varied within wide limits the several factors which may influence the determination of the exact location and shape of the transformation ranges, especially the mass and preparation of sample, rate of heating and cooling, design of furnace; and finally, as nearly as it is experimentally possible, we have worked with a substance approaching pure iron, free from occluded gases and other impurities, and contained within a vacuum.

Jan 10, 1913

By V. E. Housman

EPA's Mining Waste Section within the Office of Solid Waste is continuing to collect and analyze information on mining waste management practices. Starting in 1991, the Mining Waste Section has continued to conduct site visits and prepare case study reports on the waste generation and management practices of operating mines. In choosing sites to study, a reasonable attempt was made to provide diversity in mining commodity types, geographic regions, geology, climate, and environment. To date, EPA has visited the following mines: Asarco Troy (copper) in Montana, Newmont Rain in Nevada (gold), Cyprus Thompson Creek (molybdenum) in Idaho, LTV Steel (iron) in Minnesota, Phelps Dodge Morenci (copper) in Arizona, Doe Run Fletcher (lead) in Missouri, Brewer (gold) in South Carolina, IMC Four Corners (phosphate) .in Florida, Pennzoil Culberson (sulfur) in Texas, Nerco Cripple Creek (gold) in Colorado, Copper Range White Pine (copper) in Michigan, Magma San Manuel (copper) in Arizona, Colosseum (gold) in California, and several gold placer mines in Alaska, including the Valdez Creek Mine. EPA has prepared a case study report on each facility. The mine operators were provided an opportunity to comment on their respective site visit report and their comments have been included in' each respective report. These site visit reports have in turn been incorporated into technical resource documents which provide a detailed description of each mining sector. EPA is currently reviewing the technical resource documents and plans to release the documents in the Spring of 1994.

Jan 1, 1994

By Marcelo Rebellato, Beatriz Pereda, Beatriz Lopez, Pello Uranga

The classical application of Nb microalloying in the development of thermomechanical processes for flat products has been related to its suitability to enhance strain-induced precipitation and get a pancaked austenite prior to transformation. As new steel grades or new lay-outs are being developed, more complex metallurgical conditions need to be evaluated. In this context, Nb microalloying, alone or combined with other microadditions, needs to intervene in a more controlled way in additional steps of the thermomechanical process, besides its conventional strain-induced precipitation role. For example, the hardenability enhancement associated with Nb to properly achieve lower temperature transformation products, demands a proper balance of the Nb amount precipitated during rolling and the one remaining in solid solution. Similar effects are also sought when the final available Nb is used to increase strength through precipitation hardening. This manuscript evaluates how changes in the rolling strategies affect the interaction between Nb(C,N) precipitation and austenite recrystallization at different steps of the rolling process. As the possible interactions between parameters intervening simultaneously are quite complex, the application of microstructural models helps to properly define the best austenite conditioning combined with the convenient amount of Nb in solution, as a function of the final property requirements. Along the manuscript, several strategies will be discussed for the case of hot rolling of flat products comparing both normal and coarse initial austenite grain sizes.

Oct 1, 2019

By Wangzhi Zhou, Huasheng Chen, Bowen Li, Meng Liu, Mingsheng He, Long Zou

Steel slag is an inevitable by-product from a steelmaking furnace such as a converter, an open-hearth furnace or an electric arc furnace. The yield of steel slag increases with the sharp rise of steel production. Utilizing the slag effectively and comprehensively is one of the important tasks to promote the development of iron and steel industry in China in a sustainable and efficient way. In this study, hot-poured steel slag from a converter was used to prepare ceramics by mixing with fly ash, microsilica, and quartz. After heating at 1100–1200 °C, the ceramics were well sintered. XRD revealed that multiple crystalline phases coexisted in the glass-ceramics, and the main crystalline phases were diopside and anorthite. SEM observation indicated that there was a plate-columnar composite structure in the ceramics. Reaction mechanisms were discussed.

Mar 1, 2018

"Many advances in glass technology and processing are being made and the possibilities for glass as a material in the future appear unlimited. Float glass, glass-ceramics, high-strength sheet and container glass, glass-reinforced plastics, glass for electronic equipment, aerospace glass, glass fibres, glass vehicles, glasses with selective-reflective coatings and glare-reducing glasses, to name a few, provide areas of significance at present and for the future. There appear to be great opportunities, in certain localities of Canada, to develop new sources of raw materials for an expanding Canadian glass industry.New developments in the structural clay products industry have centered around facing brick as a structural load-bearing material, prefabricated brick panels, large-sized units, isostatic pressing of sewer pipe and auto-matic settmg of brick. Fast-firing techniques, using prefired or calcined raw materials, and the development of high-strength products will result in the use of a wider range of raw materials in the whiteware and structural clay products industries.Porcelain enamel, a material used for many years in domestic appliances and for sanitary ware, now is used extensively in architecture, agriculture, water tanks, highway signs and reflectors, and in products where resistance to corrosion-plus-temperature is important. Exotic composites of ceramics and metals, and specialized ceramic coatings applied on metals by various techniques such as flame spray, plasma jet, or vapour and chemical deposition have proved useful in materials for aircraft power plants, rockets, missiles and nuclear applications."

Jan 1, 1967

By Kai Tang, Casper van der Eijk

Natural gas has been used as reductant in the production of iron for several decades. Recently, the use of natural gas as reductant for other metals has been drawing attention because of the low price of natural gas, as well as the reduction of CO2 emissions compared to the use of coke and coal. In this work, the reduction of a mixture of Ti- and Ni-oxides by natural gas has been studied. Within the Ni-Ti system, the intermetallic compound Ni3Ti is thermodynamically the most stable one. Therefore, powders of Ni-oxide and Ti-oxides were mixed in an atomic ratio of three to one and subsequently pelletized. Reduction was performed in a TGA furnace at constant temperature with varying reducing gas atmospheres. In a natural gas containing atmosphere, the Ni-oxide was easily reduced to metallic nickel while the Ti was reduced to Ti-oxycarbides or Ti-oxynitride when nitrogen was present. Depending on the process parameters, several percent of Ti was dissolved in the nickel-based solid phase.

Jan 1, 2014

By Tamas Kekesi, Gergo Rimaszeki, Tibor Kulcsar

The efficient purification of soldering waste material can be achieved in a single operational step by the electrolytic refining in pure hydrochloric acid - tin-chloride media. The complex formation of the ionic species may offer a beneficial level of natural inhibition. Using the PCR (periodic current reversal) technology, is efficient in affecting the morphology of the cathodic deposit. In order to optimize the process, the investigation of the solution stability and the electrode reactions is essential. The natural tendency of the Sn(II) oxidation and precipitation can be overcome by properly controlling the concentration of the main components and the ratio of Sn(IV)/Sn(II) in the electrolyte solution. Polarization curves were obtained for different concentrations tin and hydrochloric acid. Conclusions referring to the electrode reaction were derived from the overvoltage - current plots. The morphology of the deposit can be correlated with the exchange current density, also determined from the polarization curves. The cathodic current efficiency and the morphology of deposited metal are affected by the distribution of tin species and the principal electrolysis parameters.

Jan 1, 2011

By G. R. Hopkins

[Apparent progress in economy at petroleum refineries, as measured by the average amount of hest units required to refine a barrel or crude oil, received a set-back in 1938, when the average rose to 567,000 B. t. u., compared with 562,000 B. t. u. in 1937 (see fig. 1). The primary factor in the rise in average heat requirement's per barrel of crude oil refined in 1938 was the decline in total runs to Invariably the average requirement increases when crude inn to stills decline, and vice versa. In other words, annual gains in fuel efficiency at refineries are masked by the degree to which the capacity is utilized. Additional crude runs give lower average heat requirements in two grays first, because they are mane with the expenditure of cc-comparatively small amounts s of auxiliary heat, and, second, because additional runs generally represent simple topping operations. In 1938 crude runs to stills declined 1.6 percent (from 1,183,440,000 barrels in 1937 to 1,165,015,000 barrels in 1938), but the total heat consumption declined only 0.4 percent, or from. 663,866 billion B. t. u. in 1777 to 660, 56 billion in 1938.]

Jan 1, 1939

By Guoqiang Lan, Jun Song, Bin Ouyang

Rare-earth pyrochlores, commonly exhibiting anomalously low lattice thermal conductivities, are considered as promising topcoat materials for thermal barrier coatings. However the structural origin underlying their low thermal conductivities remain unclear. In the present study, we investigated the phonon properties of a group of RE pyrochlores, Ln2Zr2O7 (Ln = La, Nd, Sm, Gd) employing density functional theory and quasi harmonic approximation. Through the relaxation time approximation (RTA) with Debye model, the thermal conductivities of those RE pyrochlores were predicted, showing good agreement with experimental measurements. The low thermal conductivities of RE pyrochlores were shown to largely come from the interference between the low-lying optical branches and acoustic branches. The structural origin underlying the low-lying optical branches was then clarified.

Jan 1, 2015

By Zhikai Wang, Wensheng Lyu, Peng Yang

"To better understand the mechanical behavior of the compression deformation of backfill under high stresses corresponding to large depths, consolidation compression tests were performed for cemented tailings backfill with a cement-sand ration of 1:10 and 30% water under confined conditions. After applying different loading stress functions from 0.5 MPa to 32 MPa, the final axial deformation of the test specimen of backfill was obtained, and the micromorphology of backfill was studied before and after consolidation by scanning electron microscopy. Additionally, fitting analysis was performed for backfill confined compression deformation data and device model constitutive equations by the minimum square law. The constitutive model was revised according to the analysis results. The research results indicate that, as the load increases, the void ratio e obeys the functional relationship e=alnt + b (where a and b are fitting constants and t is compression time). Under the high-stress conditions of confinement, the constitutive model of backfill consolidation and creep can be used to describe the creep behavior of the backfill. Under high-stress conditions, after the consolidation of the confined backfill, the space between the tailing particles diminishes, the particles becomes more compact, and particle slippage occurs. INTRODUCTION With the depletion of shallow mineral resources, the mining industry has gradually shifted to deep mining (Zhang, Li, An, and Huang, 2010). Furthermore, with the continuous introduction of sustainable development policies regarding development and utilization of mineral resources, the mining industry must protect the limited available land and make full use of mineral resources as much as possible (Sijing, 1994; Zhihua, 2009). Backfill mining technology offers an unparalleled advantage in fully recovering mineral resources, controlling pressures, and improving environmental protection. As a result, this method has been widely used in various countries in the world (Burd, 2002; Benzaazoua, et al., 2008). Of the underground mines in the world, 45% of the large and medium-sized non-ferrous-metal mines and 37% of the gold mines use backfilling (Fuhrman, et al., 2014; Khaldoun, Ouadif, Baba, and Bahi, 2016). In addition, 45% of underground non-ferrous-metal mines and 37% of the gold mines use the filling method (Mchaina, Januszewski, and Hallam, 2001). According to incomplete statistics, more than 80 metal mines operate at a depth of more than 1 km; the depths of several typical deep mines are shown in Figure 1 (Burd, 2002; Fall, et al., 2009)."

Jan 1, 2017

By M. Ataee-pour, S. E. Jalali

So far, a large number of algorithms have been developed for the optimization of pit limits, most of which follow deterministic rules. In this paper, a new algorithm is introduced, which follows a probabilistic logic using the Markov chain process. The algorithm is implemented on a transition matrix that corresponds to the 2D conventional economic block model of the mining area. The probability of mining a block is proportional to the desirability it may provide. Applying this algorithm, the probability of mining each block is obtained, and finally, the optimum pit limits are defined as the pit, which provides the highest probability of mining. In order to validate the proposed model, a numerical example is given and the results of the algorithm are compared to those of a dynamic programming algorithm. A 2D analysis of the problem is discussed in this paper. Although dealing with 3D problems requires larger size matrices, the optimization method is the same and the algorithm does not need any smoothing.

Jan 1, 2006