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By Graham E. Brown

Since the beginning of time, people later to be known as engineers and architects have strained to create methods whereby they could improve technology to assist them in their various fields of endeavour. Some of these improvements would be the change from linen paper, french chalk and ink pens to drafting film , mylar an d pencil for the production of drawings, the drafting machine in lieu of the tee and set squares, even tap e to attach drafting media to the board instead of thumb tacks and man y, man y more. All of these taken individually are insignificant but combined evolve to the current state-of-the-art in the computerized engineering environment. Ten years ago the major topic o f conversation was the hand-held calculator which for a cost of around $150 would give most trigonometric functions. Today the equivalent calculator can be purchased for around $25, is about one third the size, and if inflation were included over the last ten year s the item should cost around $550 in today' s dollars, it can be seen that tremendous advances not only in the technology but also the cost saving. The following paper is intended to outline some o f the significant aspects o f the latest technology in the computerized engineering office namely Interactive Graphics Systems.

Jan 1, 1985

By Gary Hawthorn

"Laboratory testing, by Lakefield Research determined that, in spite of the relatively high pyrite content of the Golden Rose (GR) orebody, it would respond well to gravity concentration followed by either direct cyanidation or cyanidation of a flotation concentrate.Economics favoured the former choice which became the adopted process flowsheet.During the latter stage of the feasibility study, the Dekalb 500 tpd copper flotation mill became available in the Highland Valley of British Columbia. This plant was purchased by Emerald Lake Resources, and was moved to the Golden Rose minesite.The crushing and grinding circuit were retained and the original flotation circuit was replaced with a 400 mtd gravity plus cyanidation circuit. The plant commissioning commenced in August 1987, and by early September was processing 300 tpd.HistoryThe Golden Rose Mine was operated by Cominco during the period 1935 to 1941 processing 146000 tons grading DAD oz/t Au at a rate of 110 tpd .The process flowsheet consisted of gravity plus amalgamation followed by cyanidation.Metallurgical TestingThe underground mining areas were below the level of Emerald Lake, and had flooded on abandonment in 1942.Samples for metallurgical testing were collected from exposed faces underground once the mine had been dewateredin 1984.In spite of the anticipated high pyrite content of the ore samples, it was apparent from the success of the previous operation that the pyrite did not interfere with the gold recovery.Laboratory testing, at Lakefield, determined that, from a technical perspective, two metallurgical options existed, as shown in Tables I and 2.Note that the very high pyrite content of the ore precluded the possible direct marketing of concentrate. The process flowsheet, therefore, had to contain a cyanidation circuit for the operation to succeed financially.Although the anticipated metallurgy was excellent with either option, the 2.1 % increase in gold recovery with the gravity plus cyanidation option made this the clear choice."

Jan 1, 1989

By P. Harvey

"Following initial discovery in 1991, BHP Billiton Diamonds Inc. opened Canada’s first diamond mine, the EKATI Diamond Mine (EKATI) in the Northwest Territories on October 14, 1998. Four short years later, on November 29, 2002, saw the opening of North America’s first underground diamond mine, the Koala North mine. Nestled between the original Panda open pit and the new Koala pit, which is in the early stages of production, Koala North represents the only underground kimberlite mining venture in Arctic conditions outside the new underground mines being developed by ALROSA in the Yakutsk region of eastern Russia. Extensive underground kimberlite mining has been practiced in the Republic of South Africa for much of the 20th century and continues today.Underground mining represents a key component of the long-term business plan for EKATI. As various open pits reach their economic limit, continued recovery of high-value ore at depth is dependent upon the ability to productively mine the kimberlite pipes by underground methods. As a function of its location, size, and value, the Koala North pipe is ideally positioned to host the first underground mine at EKATI. Koala North is designed and approved as a learning mine, from which to gain valuable experience in preparation for the potential mining of other larger, higher value pipes by underground methods in the development, the Koala North mine is well into its production ramp-up phase and currently producing at around 1,200 t/day from the first two production levels."

Jan 1, 2005

By A. A. Wessels, D. P. Allison

"Mine hoists are built to handle a certain nameplate capacity; they are specified and designed according to the required duty. However, as production capacity increases in other parts of an operation, the hoist capacity can become the critical constraint. Such a situation occurred at Lundin Mining’s Neves-Corvo operation. This paper examines how each component of the existing hoisting system was examined and optimized. Through a combination of engineering study and hoist simulations, the annual hoisting capacity was improved by 24% through increases in payload capacity and available hoisting time combined with a reduction in cycle time, while no changes were made to the hoist motor, drum or headframe. The additional payload capacity was achieved by reducing the mass of the hoist ropes and skips, and improving load monitoring systems. The cycle time was reduced through the shortening of the creep distances and increased availability through the installation of a shaft collar safety platform, alternative guide rope bushes, and superior liners for both the skips and underground measuring flasks. Enhanced cooling of the hoist electrical system was also incorporated to increase hoist availability by reducing downtime during hot summer months. The changes will increase the capacity from the current 4.5 mega tonnes per annum (Mtpa) to a planned 5.6 Mtpa and are being implemented over a 2-year period whilst maintaining the mine production during the upgrade work. INTRODUCTION Neves-Corvo Mine Neves-Corvo is primarily a copper and zinc mine producing copper, zinc and lead concentrates. The operation is owned and operated by Somincor, the Portuguese subsidiary of Lundin Mining. Located in the Alentejo district of southern Portugal, the operation is situated approximately 15 km southeast of the town of Castro Verde, where summer temperatures can reach as high as 45ºC, and approximately 220 km southeast of Lisbon. The principal means of mine access is via a ramp from surface, with the vertical shaft used to hoist ore and waste from the 700 m level, while conveyors descend from the 700 m level to transport ore and waste up from the deeper levels of the mine. The mine is highly mechanized and several different stoping methods are employed, with the most significant being bench-and-fill and drift-and-fill. The Neves-Corvo mine currently exploits five orebodies: Neves, Corvo, Graça, Zambujal and Lombador for copper and zinc-lead ores which are processed in one of two plants. All the orebodies are currently exploited over their full elevation with the exception of Lombador which is only mined down to the 220 m level, approximately the top 50% of the orebody, known as Lombador Phase 1."

Jan 1, 2019

By T. Bhambhani, Mukund Vasudevan, Partha Patra, D. R. Nagaraj, P. Somasundaram

Selective Ni separation from ultramafic ores rich in serpentines has been a huge challenge in the mineral processing industry, and therefore highly inefficient. Analysis of the root causes of the challenges and consequent development of robust processing solutions were the main goals of the Cytec-Columbia. University-Vale Joint Development Program. In this context, the subject of this paper is limited to one of the key findings of this research program which is the influence of fibrous serpentines on grade-recovery characteristics. Specifically, the poor flotation behavior is characterized by an atypical reverse C-shaped grade-recovery curve.

Jan 1, 2011

By G. Frithum

In the present paper a new and highly economic route for Fe-separation from HCl leaching processes in hydrometallurgical applications is described. In most ore leaching processes, Fe is involved and needs to be separated; HCl has become an interesting leaching agent, because it can be recycled. Usually a mix of Fe2+ and Fe3+ is obtained which can be hydrolyzed directly (in case only Fe3+) or roasted via pyrohydrolysis (in case of Fe2+) to ferric oxide. Economic oxidation of Fe2+ to Fe3+ is described, and potential technologies for regeneration of HCl with separation of Fe are shown and compared.

Jan 1, 2014

By M. A. Creaney

"The Construction Group is responsible for the construction of all of Placer Dome’s major projects and contributes to the development of most major feasibility studies. This group includes an international collection of Placer Dome people who have built mines in Papua New Guinea, Australia, Chile, the United States and Canada. This paper outlines the changing role of the Construction Group from the early days of single projects to today, when several projects are in various phases from feasibility to construction. The projects’ total annual budgets have from time to time exceeded one billion dollars. IntroductionAs the competition increases globally between the major gold mining companies, the impetus continues to build mines at the lowest cost with the shortest construction schedule. Placer Dome has more than met that challenge by building mines around the world at a pace that was not contemplated 15 or 20 years ago. Since 1960, Placer Dome has built 30 mines and expansions at a cost of nearly 4.5 billion dollars.In the last six years alone, Placer Dome has built 14 mines and expansions, worth 2.6 billion dollars. The company’s success is due primarily to Experience, Innovation, People and Standards.The diversity between projects, let alone the pace, has been a challenge. Placer Dome has built mines around the world in a variety of extreme climates and distinctive cultures. The construction experience gained from these projects has allowed Placer Dome to develop an extensive knowledge and data base making it easier to “fast track” projects.Through the years Placer Dome has developed a human resource base. It now has an experienced and adaptable core team of people able to set up construction projects and build mines anywhere in the world. By developing standards and systems to support the projects they can act as soon as a new project is approved, and complete the projects quickly and effectively. The result is that Placer Dome now has the construction expertise to build its own mines, giving them the competitive advantage that allows them to design and construct a mine in the least time at the lowest capital cost. This was demonstrated in March 1997 with the completion of the construction of two new mines in 12 months."

Jan 1, 1998

By W. W. Cummings

The Mineral King Mine, owned and operated by Sheep Creek Mines is located in the Purcell mountain range of southeastern British Columbia. Production of lead and zinc concentrates commenced in 1954 some 60 years after the initial discovery. Low cost mining methods have been employed to extract 16,0C'O tons of ore monthly from large ore bodies formed by replacement in limestone. Extensive areas in the limestone are yet to be explored and success in the search for new ore bodies is anticipated.

Jan 1, 1960

By M. Mirnezami, J. A. Finch, M. S. Hashemi A.

The surface of -30µm silica suspension (2% v/v) treated with 100 ppm Mg2+ at pH 11 was fully coated with Mg(OH)2. Under this condition, the silica is strongly positively charged (+30 mV) and the suspension is dispersed. Subsequent addition of Ca2+ promoted aggregation and reduced the surface charge. At this pH calcium is present as Ca2+ and CaOH+, i.e., positively charged ions interacted with the positive surface. Aggregation by a chemical bridging mechanism is proposed. The observation may be relevant to the widespread practice in mineral processing of adding lime to promote aggregation and settling in concentrate thickeners.

Jan 1, 2004

By Ivor da Cunha

Ontario Mining Association (OMA) represents 57 members that are engaged in exploring, producing & processing mineral resources in an environmentally responsible manner. Conservation Bureau at the Ontario Power Authority (OPA) develops, coordinates and stimulates commitment to electricity conservation and demand management programs ? OMA selected compressed air optimization for high impact cost savings and energy efficiency potential ? Ontario Power Authority (OPA) provided $218k funding for $532k project ? Commenced summer 2006, Final Report June 2007 ? Three representative sites participating: ? Williams, CVRD Inco & FNX McCreedy ? Different levels of energy management ? Small, medium and large mining operations ? Different corporate practices and culture

May 1, 2007

By WENDY MARTIN

The Eastern Townships and Asbestos Hill areas are the current asbestos-producing districts of Quebec. Mining in the two areas began in the /are 1870s and 1972 respectively. Production from the Eastern Townships is derived from rhe Serpentine Zone of ulrramafic rocks, specifically from basal serpentinized peridotite members of what are now considered to be allochrhonous ophiolitic material that was abducted onto the Early Ordovician continental margin. From south west to northeast, the rhree allochthonous asbestos-producing sections of the Serpentine Zone are designated the Asbestos Ophiolite Complex, the Thetford Mines Ophiolite Complex and the Pennington Dyke; the Pennington Dyke is considered to represent a segment of serpentinized Alpine peridotire that was fragmenred from a larger, more complete ophiolire complex. The Asbesros Hill deposir on the Ungava Peninsula lies in what apparenrly is an inrrusive sill found wirhin rhe Chukorar Group, the uppermosr group of Precambrian-aged Cape SmithWakeham Bay Belr of volcanic-sedimentary rocks.

Jan 1, 1984

By G. W. Poling, G. W. Hawthorn

"""Unassayable gold and platinum group metals"" have come into vogue in the 70sand 80s in certain jurisdictions as a means of perpetrating fraud. Usual arguments are that a particular ore is not amenable to ""conventional fire assaying"". Explanations for unassayable gold usually revolve around: evaporation of micron-size gold; vaporization of organic gold complexes; volatization of gold halides; alloying of gold with PGM's which prevents fusion or alloying which prevents collection .This paper reviews several of the myths and truths of gold and PGM assaying with the knowledge that not a single mine operatesin thefree world producing gold from unassayable ore.INTRODUCTIONAccurate analyses of exploration data and estimation of ore reserves are two of the most important functions of professional geologists and engineers in mine development. The problems encountered become particularly acute when dealing with precious metal values where very low grade deposits (in the range of 0.0 I Troy oz per ton or - 0.2 ppm (g/t) by weight) sometimes are economic or constitute ""ore"". To emphasize this ""scarcity effect"", a gold assay of 0.4 g/t (0.01 T oz/st) would result from the presence of a single 420 J.tm (35 mesh) gold flake (which weighs I milligram) in a 5 kilogram siliceous sample.The current high gold price and the prospects of high profit margins awaiting exploitation of even very low grade gold deposits, has spawned a sizeable group of incompetent or fraudulent gold assayers. These ""assayers"" will often report significant precious metal values where no such values occur. Failures of legitimate assay labs to confirm these ""significant"" assays are often attributed, by the charlatan, to their capability of detecting ""unassayable gold"" while the check assayer cannot. Geologists and engineers lacking detailed knowledge of sampling and assaying techniques are often hard-pressed to convince a gold-fever aroused company executive or investor-client to abandon a property on which attention-grabbling values have been reported, often by more than one laboratory. Professionals engaged in such evaluations must acquire an understanding of contemporary precious metal sampling and assaying techniques . Only then can they determine whether misrepresentation of values have been perpetrated"

Jan 1, 1989

By K. C. Marsden, B. Pesic

"Interest in the efficient production and recycling of rare earth elements has increased in recent years along with the prices of these elements. The molten LiCl-KCl eutectic is one ionic solvent which can be utilized for these purposes. The LiCl-KCl eutectic has also been selected as the electrolyte for focused research for advanced pyrochemical recycling processes for used nuclear fuel in several nations. Rare earth elements are fission products with notable neutron absorption characteristics, and thorough understanding of the properties and behavior of these elements is critical to their successful partition from the electrochemically-similar actinide elements. The number of research papers investigating individual rare earth elements has greatly expanded in the approximately 35 years since the last review. These research papers are presented in a variety of languages and technical formats, making data difficult to compare, and are sometimes contradictory. A review and summary of diffusion properties of rare earths in LiCl-KCl eutectic was performed, and the data translated to a common format for evaluation. INTRODUCTIONThe rare earth elements have experienced growing importance in recent decades due to their application in high technology, including optical lenses, lasers, high-temperature superconductors, improved alloys, high energy-density batteries, and powerful magnets for compact electronic devices. Their historic production methods and uses are detailed in several texts (Hampel 1971; Bautista &Jackson 1992; Gupta & Krishnamurthy 2005). A s the p rice o f these e lements has r isen in r ecent years, so has interest in their efficient production and possible recycling options. Rare earth oxides are concentrated through hydrometallurgical techniques, but the high thermochemical stability of their oxides precludes production of rare earth metals in aqueous systems. However, the wide electrochemical window and better control of pO2- in fused salt systems allows the production of these reactive metals from their halides or oxides. The high ionic conductivity and diffusivity of the molten ionic electrolyte allow high currents with limited resistive losses (Fray 1980). Electrolytic methods in fused salts are commonly adopted for the production of bulk rare earths in a variety of molten salt systems. Fluorides are sometimes proposed for oxide electrowinning processes due to ability to dissolve the rare earth oxide, reduced hygroscopic behavior, and the wider electrochemical separation between O2 and halide gas evolution (Mohan Das, Damodaran et al. 1988; Gibilaro, Pivato et al. 2011). However, in most electrolytic production processes, such as that for mischmetal, the rare earth oxides are converted to chloride prior to electrolysis in a chloride bath (Gschneidner Jr. & Eyring 1978; Sharma 1987). Of the chlorides, the LiCl-KCl eutectic is one specific medium in which metal production and production-related investigations have been conducted (Gschneidner J r. & Eyring 1978; Driscoll & Fray 1993). L iCl-KCl eutectic has the advantages o f h igh conductivity, but relatively low viscosity and operating temperature. The low operating temperature allows simpler design, with reduced energy consumption, salt volatility and cell corrosion."

Jan 1, 2012

By Staff

"The Weyburn Oil Field, located 80 miles southeast of Regina, Saskatchewan, was discovered by Central-Del Rio Oils Limited, in January, 1955. As of January 1st, 1959, the field had 357 wells capable of producing an estimated total of 45,100 barrels of oil per day.Highly portable, economical, drilling rigs are used to penetrate the pay at a depth of 4,400 to 5,100 feet. Presently, the complete drilling operation for an average field well, including drilling, coring, testing, and running casing, requires 12 days. Drilling procedures are conventional for a field of this depth and no serious problems exist. Central-Del Rio core the productive section of all their wells, which provides valuable information for well completions and reservoir studies. Production casing procedure is to set through the zone and perforate the productive inter-val. This was found advisable due to the lensing nature of the porosity and permeability throughout the reservoir, and to the high connate water saturation encountered in the tighter sections of the reservoir in the north and northeast areas of the field.Although a few wells in the field have produced naturally by flowing or pumping without acid treatment, it has generally been necessary to acidize the wells to make them commercial producers. To date, acid treatments appear to effect better stimulation of the limestone reservoir than fracturing treatments. Perforation sealing balls have been used as an aid in selectively treating all of the perforated interval.The majority of the field is on pump, producing at a low gas-oil ratio. The main part of the field has water-free production, with most of the water being produced in the north and northeastern area. Salt-water disposal is now available in the field through two disposal wells completed in the Basal Blairmore sand.The Midale Beds ""Marly"" and ""Vuggy"" zones form the principal reservoir, which is a stratigraphic trap, with the north and northeast edges terminated by a porosity and permeability pinch-out and the south-west and west edges bounded by water-laden porosity. There is no evidence to date of a gas cap. The reservoir apparently is producing on a fluid-expansion-type mechanism. The increasing water production in wells on the southwest and west edges of the field indicated water encroachment from these directions, and suggests some recovery energy may be available from this source.The total probable ultimate remaining recoverable reserves have been estimated at° 332,469,000 barrels of oil. Markets have not been able to keep up with the rate of development of the medium crude re-serves. However, it is felt strongly that substantial additional markets for Weyburn medium crude will be developed by the producers in the near future at realistic wellhead prices."

Jan 1, 1959

By S. W. Marcuson, P. J. Mackey

The 1973 Oil Embargo and succeeding disruptions in supply had a profound effect on energy costs and consumption patterns in the developed world. This was especially true in the USA where post World War II growth, fueled by low-cost imported oil, left the country dependent on uninterrupted oil shipments from the volatile Middle East. In this atmosphere, Professor H.H. Kellogg of Columbia University, convinced of the necessity of good environmental stewardship by the writings of the era’s leading environmentalists, developed a methodology for evaluating energy and process efficiency of metallurgical processes and wrote a series of papers describing and applying the techniques. One of these, "Energy Use in Sulfide Smelting of Copper" is recognized as a seminal work which both described the state of energy usage in copper smelting in the mid-1970’s and portended future developments. The background to these papers is examined and the current and past Cu-Ni matte smelting practices in Canada are examined in the context of the results. Data from early 20th century publications describing reverberatory and blast furnace operation is employed to show that energy consumption for much of the century was several multiples higher than that calculated for best reverberatory operation in the 1970’s.

Jan 1, 2015

By Michael W. Hinds

X-ray Fluorescence Spectrometry (XRF) is used at various stages of gold refining. Initially, incoming impure gold is analysed for deleterious elements such as As, Cd, Hg, Se, and Te. Based on the levels of these impurities the material can be returned to the client or accepted for refining. XRF is also used to determine the metal concentrations after the impure gold has been melted and sampled. This information is used to assist the final Fire Assay determination of gold and silver. An energy dispersive XRF is used to determine the end point of chlorination refining step.

Jan 1, 2011

By G. D. Garland

"IntroductionALTHOUGH the presence of rock salt in the Carboniferous basin of northern Nova Scotia has been known for at least one hundred and twenty years, and salt has been mined at Malagash continuously since 1919, certain characteristics of the deposits make exploration by drilling or surface examination difficult. The surface rocks of the basin are, in general, of Pennsylvanian age, while the salt occurs in the Mississippian Windsor group. The latter rocks are brought to the surface only along anticlinal folds, or as irregular fault blocks. Because of the limited areal extent of these Windsor exposures, and their complicated internal structure, geophysical surveys, especially gravimetric, can be of considerable aid in outlining the more favourable areas.The present paper describes the results of recent investigations by the Dominion Observatory, in cooperation with the Nova Scotia Department of Mines. It includes a regional study of that section of the Cumberland basin lying between Springhill and Malagash ( Figure 1), and a much more detailed survey of the immediate vicinity of the Malagash deposit itself. This deposit had been studied by Miller (6, 7) with the torsion balance nearly twenty years before, and a direct comparison between the results given by the two types of instruments is therefore possible."

Jan 1, 1955

By C. H. Wright

Introduction The rapidly expanding and increasingly complex Canadian industrial structure, with the mining, metallurgical, and chemical industries as a large integral part, has, in recent years, brought greatly increased importance and value to our industrial minerals. In the modern economy of our mineral industry the importance which is due the non-metallics has been somewhat overshadowed by the great value of our large metal production and, in addition, by the glamour and fascination usually associated with the mining and treatment of gold ores. The term 'Industrial Mineral' is used in this paper in its usual sense and refers to non-metallics other than fuels. Coal and petroleum products, including natural gas, are considered as industrial minerals in those applications in which they are used for strictly chemical process purposes. Certain reduction metallurgical industries are so closely allied to chemical industries that for purposes been of this discussion no attempt has made to differentiate between them. Chemical industry in Canada today is a fairly large factor in our national economy, whereas in 1898, when the Canadian Mining Institute was born, it was very small indeed. Chemical concerns are largely dependent on industrial minerals for raw materials and process supplies and, as the country has developed industrially, so have the demands for non-metallics increased, not only by chemical industry but also by other large consumers, such as the construction and metallurgical industries. At the present time there is a greater than normal incentive prevailing for new discoveries, due to the serious lack of balance that exists in our import and export trade. This fact has resulted in intensive efforts to rectify the situation by locating new deposits and re-assessing those already known in an effort to enlarge and improve our home production of raw materials and also to extend their processing in Canada for our own needs and for export. The rapid advances in science and technology that have taken place since 1900 have also resulted in many cases of beneficiation and utilization of otherwise too low grade materials in order to satisfy current demands. The purpose of this paper is to indicate the history and the trends of the utilization of industrial minerals in established industry and to indicate the important part played by non-metallics in connection with the opening up of new industries. Some consideration has been given to the continual competition between natural and 'synthetic products and to the general tendency towards more rigid specifications.

Jan 1, 1948

By Silvana Costa

The quality of life in remote mining communities is a significant factor that impacts the mining industry?s ability to attract and retain high quality workers in remote areas. The rapid growth of mining development, along with the shortage of skills and training globally are reflected in an increasing need to identify the ideal conditions for employee wellbeing and investigate ways to improve quality of life of miners and their families in remote locations.

May 1, 2007

By Penny C. Stewart

Narrow vein underground stope design engineers in Australia have expressed significant interest in the requirements and methodology for developing site-specific stability charts. This is largely due to a concern that existing stope stability charts inadequately take into account factors influencing narrow vein stope stability, such as the effect of backfill abutments and the effect of in stope pillars. This paper presents conclusions from a comprehensive statistical examination of case history requirements for a site specific stability chart and critiques literature arguments for site-specific charts. A new statistical analysis technique and a large comprehensive stability database enabled the authors to quantify case history requirements and any site-specific effects the model exhibits. The analyses indicated that a reliable stable-failure boundary requires at least 150 case histories, of which a minimum of 10 percent should be unstable stope surfaces. Marginal site-specific effects were observed for the operating conditions captured within the database. The authors conclude that the apparent site-specific effects noted in previous literature are attributable to operating conditions inadequately represented in the database. Such operating conditions could induce erroneous stability predictions at any site, and are therefore not truly site-specific. Following from these conclusions, a strategy for taking into account operating conditions particularly relevant to narrow vein mining has been proposed. In particular, the development of a chart that accounts for the effect of backfill abutments on stope stability. Backfill abutment effects are particularly relevant to mechanised narrow vein mining methods such as modified Avoca. Collaboration from at least five sites is required to obtain access to relevant data and underground drives for geotechnical mapping. Preliminary estimations indicate that approximately three months fieldwork is required to meet case history requirements. CMS data in conjunction with 3-dimensional design software will be used to calculate equivalent linear overbreak/slough (ELOS). In contrast to stable, failure, major failure and caving categorical variables, ELOS is an objective and continuous stability variable and is therefore, more conducive to mathematical modelling.

Oct 1, 2001