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By J. C. Weimer

The goal of Bethlehem's mining research program is to improve both the safety and productivity of our mines through the use of new equipment, new technology and new mining methods. Although we can all agree on the value of such goals, achieving them can be a costly, time-consuming and sometimes frustrating experience. However, the potential benefits of lower costs per ton and better safety in an increasingly more stringent and confusing regulatory environment make the expended effort worthwhile. At Bethlehem we feel that the mining companies are in the best position to determine the needs of the industry, and coal companies have the incentive as well as mine sites at their disposal for testing. Therefore, the mining industry should be leading the research effort

Jan 1, 1979

By M. Hawker, M. Kreuh

The mining and metallurgy industry is known to be of cyclical nature associated with price volatility. As such, some years are quite lucrative and other years require mining companies to tighten their belts. The field is a mix of junior, mid-tier, and major mining companies. One thing that is common to all of them is the time required and the cost to develop a flowsheet in accordance with best practices. Although a long list of factors can impact flowsheet development, this paper will include the impacts of: experienced metallurgical engineers and laboratories, representative samples for high quality and valuable testwork results, and following engineering development stages. The paper also provides typical time frames to complete selected engineering flowsheet development steps.

Jan 1, 2014

By D. G. Ball

Other than being used to convey fill material for the gob stowage or building of ribside packs on advancing longwell faces, pneumatic conveying has not been used for the transport of materials on a large scale in mining operations. The technique is extensively used in the wood products industry for conveying wood chips, limestone and other ingredients for the manufacture of paper, for the transfer from railcars, barges or ships to silos or stockpiles and further transfer into the pulp mills. This method of material transfer has the distinct advantage of transporting suitable material over horizontal and vertical distances within the same system. In considering material associated with mining, this includes, ore, coal and rock up to 4 inch cubed size, throughputs of 200 tons per hour over horizontal distances of 3000 feet or vertical lifts of 2000 feet. In recent years tests have been carried out to determine the physical and economic limitations of pneumatic hoisting, the results of which have led to the installation of two fully productive coal hoisting systems at mines of the National Coal Board in Great Britain. The equipment used for the pneumatic hoisting of coal or waste rock is described in this paper, together with a brief history of the tests which led up to the installation of the two hoisting systems in Great Britain.

Jan 1, 1977

By J. C. Konopka, S. A. G. Poppen, E. K. Roesner

Many shafts have experienced stability problems during shaft sinking because the designer failed to fully appreciate the conditions he would encounter. Some shafts have failed during construction because the ground supports provided to compensate for the expected conditions were inadequate despite the most careful investigations and analyses. To design a ground support which is ultimately safe to achieve stability during shaft sinking would be too costly and impractical and, therefore, many shafts would simply not be constructed. The design of a ground support for shaft sinking based on an intimate understanding of the expected ground behaviour and stress development during excavation combines the art of mining with the science of geotechnical engineering. Where no historical design data is available, the designer of the ground support must: 1. classify the rocks and soils and assess their behavioural characteristics; 2. calculate the primary and secondary stresses; 3. design and/or select a ground support system which will ensure stability of the excavation during shaft sinking.

Jan 1, 1983

By R. F. Sharpe

THE Bullion mine, in the famous Cariboo district of British Columbia, is situated on the left bank of the South fork of the Quesnel river, approximately three miles below the outlet of Quesnel lake. A good road leads 63 miles northeast to the property from Williams lake, the railhead on the Pacific Great Eastern railway. The mine may also be reached over good roads from Vancouver via the Fraser canyon, Ashcroft, Clinton, and the 150-mile house, a total distance of 407 miles. In the early days of placer mining on the South fork of the Quesnel, several rich bars were found. The 'pay' on one of these at the mouth of Dancing Bill gulch was followed up the gulch by a Chinese company, who proved to be the discoverers of the present Bullion mine. This Chinese company commenced working in 1884, in what was then referred to as the China pit. Although working under very primitive conditions, it is reported that, during the ten years they operated the property, they recovered in excess of $900,000 in gold. This somewhat large recovery was due to a local concentration, the result of Dancing Bill creek having meandered down that portion of the channel and washed off the overburden. In 1894, a syndicate composed largely of the Canadian Pacific Railway directorate of that time, with J. B. Hobson as their field manager, acquired the property, as the apparent magnitude of the operation was too great for the resources of the Chinese company. Mr. Hobson, during the first ten years of his regime, developed the mine into a large-scale hydraulic operation, and during that period, from 1894 to 1905, recovered approximately $1,234,000 in gold. In 1906, the property was sold to the Guggenheim Exploration Company, who retained Mr. Hobson as Manager and embarked on an extensive programme to bring in additional water. This project was never completed, however, work being suddenly abandoned in 1907 and the mine closed down. Shortly afterwards, the property was purchased by a small operator on what is believed to have been largely borrowed capital. This venture resulted in no production, but in much litigation, which eventually reached the Privy Council in 1920.

Jan 1, 1939

By R. Simard

"Conventional exploration strategies identify many mineral deposits as potentially interesting, although only a few of them turn out to be of economic importance. In the context of exploration for sulphide nickel deposits in the Canadian Shield, a decisional model, based on a statistical study of parameters relative to nickel deposits as well as to barren sulphide occurences, has been developed.Because such geophysical variables as gravimetry, aeromagnetism and topography could be related to the relative importance of nickel-bearing deposits, a statistical analysis of 13 such variables was carried out for 98 targets which were considered promising after conventional exploration. Among these 98 targets are36 sulphide nickel deposits in the Canadian Shield and 62 drill-tested non-economic occurrences. The results of this study led to the development of a linear logistic model that permits evaluation, for each of the targets, of the probability of finding a nickel deposit of potential commercial interest. This decisional model can thus complement conventional exploration strategies.RésuméLes stratégies conventionnelles d'exploration définissent un très grand nombre de cibles comportant un inténet minier potentiel dont seules quelques-unes correspondent à des gisements économiquement importants. Dans Ie cadre de l'exploration des dépôts nickélifères du Bouclier Canadien, nous avons défini un modelé de décision fonde sur l'étude statistique de divers paramètres relatifs tant aux gisements d'importance qu'aux cibles dites stériles.Ayant fait l'hypothèse que certaines variables géophysiques (gravimétrie, aéromagnétisme et topographie) peuvent suffire à fournir des indications sur l'importance relative d'un gisement nickélifère, nous avons entrepris l'analyse statistique de 13 variables évaluées sur un échantillon de 98 cibles considérées comme potentiellement intéressantes par les stratégies conventionnelles d'exploration. Ces 98 cibles se composent de 36 dépôt nickélifères d ‘importance recontrés sur tout Ie Bouclier Canadien et de 62 cibles stériles reconnues par forage. Nous avons défini à l'aide de ces données un modèle logistique linéaire. Ce dernier nous permet d'évaluer pour chacune des cibles les chances de trouver un gisement. Ce modèle de décision peut done s'inscrire comme outil complémentaire aux stratégies conventionnelles d ‘exploration."

Jan 1, 1980

By Hilde TWC

Synthesis of GLORIA side-scan sonar and other geophysical data has provided morpholo- gical and tectonic details of the interaction between the Nazca and South American plates along the Peru Trench (80S-15¦S). Our analyses suggest that a new propagating rift of the Galapagos type is evolving along the Mendana Fracture Zone (MFZ). Subduction induced rift- ing of the Nazca plate is accompanied by organized seafloor spreading for the last 3 Ma at least. GLORIA sonographs and bathymetric mapping show an 8-10¦ divergence in MFZ width towards the Peru Trench. The fracture zone comprises numerous ridges and troughs and a lack of sediment cover in the axial part. Young magnetic lineations (anomalies 1-2A) are observed within the fracture zone wni.cn are orthogonal to the older Nazca plate lineations. The central anomaly narrows west- ward and can be observed up to 400 km seaward of the trench whereas anomaly 2A is terminated about 200 km from the trench axis. Recent SeaMARC II sonar mapping in the region shows large igneous blocks in the Trench axis to the north of MFZ but absent to the south. We believe these blocks represent young seafloor of MFZ rift/spreading center broken off from the ridges as they subduct along the Peru Trench. The MFZ rift is propagating west- ward at a rate of 115 km/Ma (25 km/Ma relative to the South American plate). Given the present rates of accretion at the East Pacific Rise and of propagation along MFZ rift, the Nazca plate will be divided into two parts in about 35 Ma.

Jan 1, 1987

By A. J. M. Ross

Backfilling of stopes and other underground openings in the Homestake mine with sand tailings was undertaken primarily to reduce surface subsidence, which was wrecking much of the surface plant and a substantial part of the town, and to make possible maintenance of openings into the top of pillar stopes as mining progressed. The progress of this type of filling has been rapid and the results very satisfactory. Sand is now used in filling timbered stopes, shrinkage stopes, and abandoned drifts and crosscuts. A permanent pipe-line system for transporting sand tailings into the mine by gravity has been installed. The close filling of all stopes has resulted in important benefits other than the two major ones. The ore bodies in the Homestake mine occur as replacements in one distinctive layer of the metamorphosed pre-Cambrian sediments along a group of minor folds that together form a complex anticline that pitches at 35" to 40' to the southeast. The ore bodies are extraordinary for their magnitude. Widths of over 300 ft. have been mined and continuous ore has been followed for over 1200 ft. along the strike on some of the upper levels. Mining has been by shrinkage stoping with square-set mining of crowns and pillars. In the standard plan, shrinkage stopes 60 ft. in the direction of strike and the full width of the ore have been taken up to within 25 ft. of the level above. After filling, the crown has been mined by square-set methods, as have also the 40-ft. pillars between shrinkage stopes. In former days, when the supply of ore seemed inexhaustible, the mining of pillars was allowed to lag far behind because of the high cost. Many pillars were rather badly fractured on the level and in some places between levels. Coarse waste was used for backfilling all stopes, but in pillars it became increasingly difficult to maintain haulageways for the transportation of this fill over the top of the stopes as mining progressed. The cost of maintaining these crosscuts was excessive and in many pillars practically impossible. Therefore it became the practice to fill pillar stopes by tapping the back and sides of the stopes.

Jan 1, 1940

OFFICERS AND DIRECTORS President and Director AUGUSTUS B KINZEL, '60, New York City Past President and Director GROVER J HOLT, '59, Ishpeming, Michigan President-elect and Director HOWARD C PYLE, '61, Los Angeles, Calif

Jan 1, 1958

By S. E. Bretherton

MOST metallurgists appreciate the great need of a process for the extraction and recovery of valuable metals from complex ore, where the presence of one metal increases the cost of extracting the other metals to such an extent that not any of the metals can be extracted at a profit. We need only refer to some of the mines in Colorado, Utah, and New Mexico, where oxidation has taken place and the sulphur, zinc, copper, and some of the iron and other metals have been leached out, large bodies of oxidized ore remaining, rich in lead, silver, and sometimes gold. These metals have been concentrated by the removal of the other metals, leaving a very desirable ore for treatment in the blast-furnace for the production of lead bullion, and recovery of the silver and gold. If lead is not present, the gold and silver are usually recovered by some method of milling, or the ore is shipped to a smelter, where it is mixed with lead ore or copper-iron sulphide ore from some other mine. In these same mines, when developed to greater depth below the leached or oxidized zone, the ore is found to contain the original mixture of sulphur, zinc, copper, etc., added to, or I should say left with, the lead, silver, and gold values; but instead of adding to the value of the ore, the presence of these elements, especially zinc, makes the copper, silver, and gold of less value, and often worthless. Such was the experience of the oldest mines in Leadville, Colo., until methods of mechanical separation of the lead from the zinc were developed sufficiently to allow of some profit by the making of a concentrate rich in zinc to be shipped to the zinc smelter, and sometimes a lead concentrate which could be shipped to the lead smelter; but even in these cases the waste of the different metals is a very serious matter. In the very best concentrating plants some zinc will be left in the lead concentrate, to be lost and to give considerable trouble in the lead-smelting furnace. On the other hand, some of the lead, with a large percentage of the copper and silver, will follow the zinc into the zinc concentrate, to be, perhaps, recovered y smelting the cinder or clinker left in the re-

Jan 7, 1914

By G. L. Myers

The Fortitude skarn near Battle Mountain, NV is currently one of the largest producing gold skarns in the world. It contains about 11 Mt (12 million st) of minable ore grading 5.14 g/t (0.149 oz per st) and is the distal portion of a continuous skarn system in the Copper Canyon area centered on the Eocene Copper Canyon granodiorite porphyry. Calcsilicate compositions, opaque mineralogy, and the high gold grades are atypical of other base metal skarns (iron, Fe; copper, Cu; lead-zinc, Pb-Zn; or tungsten, W). The Copper Canyon skarn is systematically zoned from a garnet (AD 70-100) dominant, pyroxene (HD 20-45) subordinate zone, with major Cu mineralization, adjacent to the intrusive (West ore body), to a pyroxene (HD20-100) dominant, garnet (AD90-100 cores. AD 30-60 rims)subordinate assemblage, with major Au, near the distal marble front (Fortitude ore body). An extensive biotite ± diopsidic pyroxene ± kspar alteration halo surrounds the pyroxene > garnet gold-bearing skarn and represents the early stages of metasomatic alteration. Retrograde alteration is limited in areal extent and intensity, and consists of actinolite, chlorite, quartz, and prehnite. Economic gold mineralization begins in the pyroxene > garnet zone and continues to the marble front, a distance of 1 to 1.5 km (0.6 to 0.9 miles), respectively, from the plutonic contact. The opaque mineralogy in this gold zone includes pyrrhotite, arsenopyrite, marcasite, minor chalcopyrite, galena, sphalerite, argentite, hessite, hedleyite, volnyskite, and native bismuth and gold. The pyrite-pyrrhotite geothermometer yields temperatures that range from 450° C to 300°C (842° F to 582° F) and the electrum-argentite-sphalerite geothermometer yields temperatures which range from 290°C (554° F) at the marble front to about 420°C (788° F) more proximal to the intrusive. Log fS2 calculations from the sulfide assemblages yield values near - 10 with log fO2 values of about -30, in a solution of near neutral pH (5-6). Calculations of metal solubility suggest that the metals were transported as chloride complexes in the proximal skarn but that bisulfide complexes were predominant within the distal gold skarn. Relatively low oxidation states buffered by the carbonaceous to argilliceous, calcareous protolith and subsequent ferrous iron-rich skarn assemblages appear to have increased the gold carrying capacity of this large hydrothermal system.

Jan 1, 1991

Marketing of mineral products has not yet succumbed to the degree of pre- dictability and exactitude that is fam- iliar to the engineer or metallurgist in pursuing their profession. Whilst the Great Market of the world economy dic- tates circumstances for the sale of min- eral products, there are more than just buyers and sellers in the determination of the revenue received by the producer. For the engineer or metallurgist he will be required to gain an understanding of these participants and of the peculiar languages of the market place. This will be only one of his tasks in learn- ing to communicate with society, as his responsibilities increase as he climbs the ladder of success. There is un- doubtedly a need for better statistical information so that producers and sell- ers can make an appropriate and earlier response to market conditions. There is in addition, a need for more aggressive concern by raw material producers for the development and promotion of better end use of their products. Undoubtedly the marketing of mineral products will be more influenced by the direct involv- ment of government agencies than has been the case in the past. Whilst that 1. Director - Marketing & Finance, North Broken Hill Limited.

Jan 1, 1975

By D Cioclea, I Toth

Coal mining can lead to the occurrence of spontaneous combustion events. If these events are not prevented they can give rise to fires that have major adverse effects on the mine plan. After studying the chemical structure of coal, the theories of self-ignition and of the oxidation reaction of the organic compounds, two new technologies have been developed for fire prevention based on the inhibition of coal oxidation. The first technology consists of spraying water drops mixed with inhibiting substances into goaves. The second consists of the infusion of a mixture made of several chemical compounds. Tests performed in situ showed the new inhibition technologies to be highly effective even for longwalls mining coal with a high reactivity from the point of view of self-ignition.

Jan 1, 2005

By Trevor Ellis

The following is extracted from a report by the author to the International Valuation Standards Committee (IVSC), with minor modifications for the purpose of publication. The author represented the IVSC at the annual session of the Ad Hoc Group of Experts on Harmonization of Fossil Energy and Mineral Resources Terminology. This is a body organized by the United Nations Economic Commission for Europe (UNECE). This second session, held in Geneva, Switzerland, achieved an important agreement for advancement toward uniform global standards for the classification of minerals and petroleum reserves and resources. Attendees discussed the possibility of enhancing the United Nations Framework Classification for Energy and Mineral Resources (UNFC) for implementation globally as the classification standard for use in financial reports under the International Financial Reporting Standards (IFRS). Presently, there are between 100 and 200 mineral and petroleum resource classification (or definition) systems throughout the world — a similar number to what there are countries.

Jan 1, 2006

By J. F. Wolff

The iron formation of the Gogebic Range in northeastern Wisconsin and the northwestern part of the Upper Peninsula of Michigan, resembles that of the Mesabi Range in Minnesota very closely in lithologic character and the subdivisions and horizons that can be recognized. It contains numerous interbedded slaty layers and considerable intraformational conglomerate in certain horizons. In contrast to the flat dip of the Mesabi formation, the Gogebic dips steeply to the northwest at an average angle of about 70". It has a quartzite and siliceous slate foot wall and a hanging wall of conglomerate, graywacke and slate. The black and gray Tyler slate has been designated the hanging wall of the Gogebic iron formation in U. S. Geologicial Survey monographs, but between the true Tyler slate and the commercially important Gogebic iron formation, and apparently unconformably upon the latter, is a series 600 ft. or more thick of conglomerate, slate, graywacke, and cherty iron formation, the latter being of no commercial importance on the Gogebic Range as far as now known. This series is probably that described as the "Capps" on the eastern Gogebic by the Michigan Geological Survey. The Gogebic iron formation proper can be subdivided into three main horizons, a lower cherty and an upper cherty with a banded or slaty horizon between them, corresponding to the three lower horizons of the Mesabi. Several minor subdivisions can be made of these major ones. Orebodies occur in all three horizons of the Gogebic series and in some places ore is developed across practically the entire series. Dikes and Sills The Gogebic iron formation has been intruded most intricately by basic dikes and sills, most of the former pitching east but some pitching west. One very extensive sill is intruded near the base of the lower slaty or banded horizon, in the formation known locally as the Yale slates. One extensive bedding or strike fault is associated with this sill and a great many transverse faults occur at different places along the Range. The combination, or association, of steep dip, faults, dikes and sills has produced conditions very favorable for the development of orebodies through the leaching, oxidation, and consequent concentration effected

Jan 1, 1925

By Kazuyo Yokoyama

New environmental assessment model based on the Waste Input-Output analysis has been developed and applied for the "Landfill mining activity". "Landfill mining" implies the digging up of the landfilled wastes, the recovery of valuable material and energy resources and, thus, the reuse of the saved space as a new landfill site. In this study, the landfilled wastes are assumed to be treated by the gasification/melting processes. Two kinds of reactors, the fluidized bed type (FB) and the shaft furnace type (SF), have been considered in this work as the typical gasification/melting processes adopted in Japan. In FB, the dug-up wastes are heated in the sand fluidized bed zone under reducing atmosphere, Fe and Al are recovered in the metallic form, and then, the gasification/melting of residues is made in the second zone. In SF, the waste is charged in the high temperature coke bed, and the gas is recovered together with molten metal and slag. Both processes generate electric power by the recovered heat and fly ash as waste to landfill. It has been found in this study that the both processes can reduce the total volume of waste and save the available landfill space. SF seems to have higher potential for decreasing volume of wastes because of less emission than FB while FB has great benefit to recover metallic Fe and Al individually. The results of scenario analysis have also indicated that the landfill mining activity is effective for sustainable management of landfill sites.

Jan 1, 2006

By Mary Ellen Bruce

Let me first address the issue of the wet grab samples. The wet grab samples that were attempted to take on the Central Artery were hindered by the fact that the way the mixing was being done was only by injecting grout on the way out, during withdrawal of the mixing tools. They would auger down to the required depth (usually with some water being injected), which took anywhere from 45 minutes to an hour, and then when coming out, the grout would be injected with grout. That was leaving a column of grout in the center where the shaft had been (i.e. inside of the blades of the mixing tools), which would end up being something like a foot in diameter because the pipe that was used for the drill shaft was a foot in diameter. So we had 10 inches to a foot of almost pure grout in the middle of our column and then we had 2 feet on either side that was mixed soil cement. So when they went down with the wet grab sampler not knowing where that was in the column sometimes they/we were getting strengths of 1500 psi, and sometimes they/we were getting strength of 500 psi or 100 psi. So what was it that we were taking into the wet grab sampler? In those cases you don't really know, but it wasn't representative of the core samples we were taking. We were purposely not coring in the center because we knew that was going to be high cement content, almost pure grout. So the issue of wet grab sampling particularly on this project, the Central Artery Project, was that we didn't really know what we were sampling. What becomes an issue with wet grab sampling in other projects is that you have to have another device (machine) in most cases, a cherry picker crane or something similar that can raise and lower with a beam that is used to forces the sampler down into the freshly mixed soil-cement. And regarding economics, is it more economical to have that crane standing by with its operator or to have a drill rig to come along later and do the coring and take the material out that's fairly identical to what you're finding in situ? The complaint of micro-fracturing in the core samples as you're taking the cores was raised by Seiko as causing large strength reductions. But, if you're doing it carefully, then I don't think that's much of an issue anymore, on research basis perhaps but not on a practical level.

Feb 10, 2003

By James Lonergan

El presente texto señala la aplicación de Minesight en la operación de Toquepala, así como los resultados de la misma. La minera Toquepala pertenece a Southern Perú Limited y se ubica en la ciudad de Ilo. Sus operaciones mineras anteriores al despojo se iniciaron en 1957 y la producción del mineral, en 1960. En 1994, SPL compró el software de MineSight®/MEDSYSTEM® para los departamentos de Geología e Ingeniería de minas de Toquepala. Dicha aplicación se inició después de la capacitación inicial en las oficinas de Mintec en Tucson. En consecuencia, los ingenieros y geólogos de Toquepala tuvieron éxito al implementar todos los componentes principales del software desde el ingreso de los datos de barreno (drillhole) de exploración hasta tareas de levantamiento (survey) diário y de control de ley.

May 25, 1998

By K. A. Natarajan, S. Usha Padukone

"An industrial waste liquor having high sulfate concentrations was subjected to biological treatment using the sulfate-reducing bacteria (SRB) Desulfovibrio desulfuricans. Toxicity levels of different sulfate, cobalt and nickel concentrations toward growth of the SRB with respect to biological sulfate reduction kinetics was initially established. Optimum sulfate concentration to promote SRB growth amounted to 0.8 - 1 g/L. The strain of D. desulfuricans used in this study initially tolerated up to 4 -5 g/L of sulfate or 50 mg/L of cobalt and nickel, while its tolerance could be further enhanced through adaptation by serial subculturing in the presence of increasing concentrations of sulfate, cobalt and nickel. From the waste liquor, more than 70% of sulfate and 95% of cobalt and nickel could be precipitated as sulfides, using a preadapted strain of D. desulfuricans. Probable mechanisms involving biological sulfide precipitation and metal adsorption onto precipitates and bacterial cells are discussed.IntroductionIndustrial effluents from hydrometallurgical and mineral processing operations often contain high sulfate and metal concentrations posing significant disposal problems, which require urgent solution to avoid serious environmental contamination. In such waste liquors, sulfate and heavy metals such as cobalt, nickel, zinc and iron originate from the chemical or biological oxidation of exposed sulfide minerals. Reduction of sulfate and precipitation of toxic metal ions from industrial wastes is essential from the viewpoint of environmentally acceptable waste disposal and recovery of associated strategic metals.Many of these heavy metals are essential for metabolic activity of bacterial cells at low levels. But they exert toxic effects at concentrations encountered in polluted water. Removal of toxic metals through biological reduction of sulfates from industrial waste waters have been practiced for several decades. Metal remediation through common physicochemical techniques such as oxidation-reduction, chemical precipitation, filtration, electrochemical treatment, evaporation, ion exchange and reverse osmosis processes is expensive and not suitable in the case of voluminous effluents containing complexing organic matter and low metal concentrations. Further, strong and contaminating reagents are used for desorption, resulting in toxic sludge and secondary environmental pollution. Biotechnological approaches can be more efficient and cost effective for detoxification of such effluents. Biotreatment/ bioremoval offers several advantages over conventional chemical and physical treatment technologies, especially for diluted and mixed contaminants. Biological detoxification, which involves the use of microbes to detoxify and degrade environmental contaminants, has received increasing attention in recent years (Iwamoto and Nasu, 2001). In addition, valuable metals can be recovered from metal sulfide sludge (Boonstra et al., 1999)."

Jan 1, 2015

By C. Yanqui

"Discontinuum Mechanics is based on two foundations: the idealization of the internal structure of substances, and the principle of the arithmetic mean value. For a linear discontinuum, the methods of Crystallography are used to describe their structure, in which nodes stands for the position of the homologous points such as molecules, grains, or any other motif. The principle of the mean value states that the value of any discrete function at a node is equal to the arithmetic average of the values of this function at the neighboring nodes. This principle leads to an elliptical linear differential equation of the second order, with coefficients given by the statistical second moments of the Cartesian components of the metric vector. As long as those coefficients are components of a symmetric second-order tensor, there are three mutually perpendicular directions, in which the variances reach their extreme values and the covariances are zero, showing that the mean value principle transforms the discontinuum into a statistically equivalent orthotropic continuum.The application of Discontinuum Mechanics to linear rock masses is simple and direct. It is sufficient to define the motif as the plane of geological discontinuity, and the metric vector as the normal vector to this plane, whose magnitude is the spacing between two consecutive planes belonging to the same set of discontinuities. Furthermore, heterogeneities of rock masses can be also included in this description by substituting the plane of discontinuity by a zone of weakness. In this way, the magnitude of the normal vector results from the product of the spacing and the RQD or the RMR. In going further in this theory, at least three conclusions show up. First, in the evaluation of rock masses, it is necessary to determine the orientation, spacing, and RMR for each set of discontinuities. Second, the conventional method of finding the principal families from the contours of equal concentration of poles on the stereographic projection excluding the spacing does not have any physical meaning. Third, any problem of rock mechanics can be solved in a rigorous and reliable way by integrating the differential equation of the mean value."

Jan 1, 2015