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By M. E. Rossi

In mineral resources, geologic and mining data are acquired, processed, analysed, interpreted and modelled, eventually serving as basis to generate predictions and production plans. This is a complex process, and the resulting predictions are impacted by uncertainties related to the data itself and the processing methods and techniques used. They are also impacted by the subjective decisions made by the modeler(s) at each step of the way. Knowledge, biases, skills, and prior experience come into play in the long mineral resource evaluation development workflow. It is meaningless to discuss uncertainties without evaluating the associated risks that those uncertainties imply. It is important to quantify and assess uncertainty, and to evaluate and mitigate its consequences. This paper discusses (1) conceptual and practical sources of uncertainty; (2) the utopia of an “objective” uncertainty; and (3) the quantification and public reporting of uncertainty using geostatistical conditional simulations. The objective of this paper is to postulate that the industry is running out of reasons and excuses to ignore uncertainty and risk in project evaluation. This is done in two parts, with this, the first one, presenting a more conceptual discussion. Part 2 will present case studies from different types of mining projects and operations showcasing the impact that risk assessments can have in a mining project.

Feb 22, 2026

By K Luthbom, A Lagerkvist

According to the Swedish Environmental Protection Agency, the number of potentially contaminated sites in Sweden is approximately 40 000. The funding for remediation from the Swedish Government alone amounts to $A 60 - 80 M (300 - 400 MSEK) annually for the period 2003 - 2006. Uncertainties will arise when obtaining samples in field, preparing them in laboratories and analysing them. Different procedures give rise to varying errors. Using data for decision-making that does not truly represent the site could be fatal. Misclassification of soil could lead to unnecessary costs or to risks to human health and the environment. The total uncertainty of an environmental sample can be split into analytical uncertainty and sampling uncertainty. The analytical uncertainty is usually known and reported from routine analysis. The size of the sampling uncertainty is less well known. Hence, the question is how big are the sampling uncertainties for contaminated soil and how big is the analytical error compared to the total sampling error? A scrap yard and two landfills within a workshop area were investigated. An excavator dug trial pits and samples were taken with a trowel from the walls of the trial pits. Samples were put into plastic bags and taken off site for preparation and analysis using XRF. Sample preparation included drying and sieving. The samples were homogenised by kneading the sample bags prior to analysis. The sampling and sample handling were performed in an intuitively way without knowledge of sampling theory. However, Pierre GyÆs sampling theory was used for subsequent evaluation of the data from the site investigation. The theory defines seven sampling errors, which can be applied to sampling of soil. Some errors have a variance that can be calculated or at least estimated, while other errors can give some idea whether the bias is positive or negative. The total sampling error varied over three orders of magnitudes from sample to sample. The single largest contributor to the large variation in error was the contaminant level. When comparing the analytical error and the total sampling error the ratio varies more than three orders of magnitude.

Jan 1, 2005

By B. Panton, J. Carvalho, E. T. Brown

High-capacity, post-tensioned anchors have found wide-spread use in initial dam design and construction, and in the strengthening and rehabilitation of concrete dams to meet modern design and safety standards. Despite the advances that have been made in rock mechanics and rock engineering during the almost 80 years in which post-tensioned anchors have been used in dam engineering, some aspects of the rock engineering design of high-capacity rock anchors for dams have changed relatively little over the last 30 or 40 years. This applies, in particular, to the calculations usually carried out to establish the grouted embedment lengths required for deep, post-tensioned anchors. These calculations which involve a number of aleatory and epistemic uncertainties, usually make simplified assumptions about the distribution and values of rock-grout interface shear strengths, the shape of the volume of rock likely to be involved in uplift failure under the influence of a system of post-tensioned anchors, and the mechanism of that failure. The resulting designs are generally conservative. These aspects of the rock engineering design of large, post-tensioned rock anchors for dams could be improved by making greater use of modern, comprehensive, numerical analyses in conjunction with 3D models of the rock mass structure, realistic rock and rock mass properties, and the results of prototype anchor tests in the rock mass concerned.

Jan 1, 2015

By Robert B. Parsons

"Income tax legislation is not keeping pace with federal and provincial environmental legislation. There is a vast array of new environmental regulations at various stages of implementation across the country. Unfortunately, there are serious concerns about the deductibility of significant payments which mining companies will be required to make under these new rules, and the Department of Finance seems to be reluctant to act on these concerns. IntroductionWhile the federal and provincial governments are racing ahead with obvious fervour to introduce new envirorunental laws, the tax rules relating to envirorunental costs are being allowed to lag far behind. In a nutshell, the tax treatment of envirorunental costs is not keeping pace with the new envirorunental legislation.One of the most serious concerns of the mining industry is the deductibility of mine reclamation or closing costs. The producing provinces are well advanced down the road toward mandating upfront deposits, bonds, or similar financial guarantees to protect the envirorunent from the operation and eventual closure of a mine. These requirements are not small. In some instances, they can amount to tens of millions of dollars. And, if there is no tax deduction for these sums when they are set aside by the mining company, then the costs have to be paid out of the company's after-tax earnings."

Jan 1, 1991

By B. Samanta

This paper highlights the use of an innovative mine production scheduling scheme for grade-control planning tasks that take into consideration grade-model uncertainty. The scheduling exercise has been carried out with the help of a multiobjective genetic algorithm (MOGa) for the production scheduling operations. The underlying motive behind the use of MOGa has been the generation of a set of pareto optimal solutions to meet the goals of the target-grade specifications for the considered multiple grade attributes. Several new concepts related to MOGa formulation, in particular the mutation operation and the convergence criteria of this algorithm, are proposed in this paper. The modeling of grade uncertainty into the scheduling outputs has also been incorporated through a set of conditional simulated grade maps. The proposed scheme of production scheduling operations has been applied for the grade-control planning operations in an iron ore mine to meet the targeted grade specifications of iron, silica and alumina, and a risk analysis has been performed to this end.

Jan 1, 2013

By M. Vasudevan

In sulfide mineral flotation, the efficiency of separation is severely affected by the presence of non-sulfide gangue minerals, such as altered silicates and serpentines. Although this is an acknowledged fact, most studies in mineral processing have focused on value minerals, and studies on gangue minerals affecting flotation performance are quite rare, and even those that do are limited in scope. This paper is an attempt to highlight the use of grade-recovery curves in studying the effects of gangue minerals. Specifically, we present the flotation response of problematic Ni and Cu ores which show highly uncharacteristic but similar grade-recovery characteristics despite the very different mineralogy and try to understand this behavior and the underlying mechanism. Finally, we propose chemical modifiers as solutions to overcome the detrimental effects of these gangue minerals and improve efficiency of flotation performance. Keywords: Non-sulfide gangue, grade-recovery, sulfide minerals, serpentines, talc, shale, slimes, spiking, modifiers

Sep 1, 2012

By Peter Halbach

Hydrothermal activity is well known from many locations on most mid-ocean ridges, however no hydrothermally mineralized area had yet been found at the ultraslow spreading southwest Indian Ridge up to October 98 when the Japanese RV Yokosuka with the submersible Shinkai 6500 investigated this area. A massive sulfide field was discovered near 27º51S / 63º56 E in the 11th segment west of the Rodriguez Triple Junction. The Free University of Berlin had joined this cruise and taken over the responsibility for the study of the respective sulfide mineralizations. Hydrothermal minerals were sampled during two dives at water depth of about 2940 m close to the summit of an axial volcanic ridge called Mount Jourdanne. There massive sulfides occur on the seafloor as small smooth mounds with an average area of about 5 m2. Their surfaces are weathered and have a reddish to brownish colour. In addition to these mound-like structures, small tube-like chimneys were observed. These chimneys rise approximately 30 to 40 cm above the floor and are less than 10 cm in diameter. No indications of hydrothermal fauna could be detected. All the hydrothermal features are spatially related to faults and smaller fissures controlled by an E-W trending graben system crossing the summit region of the submarine volcano. Such tectonized areas are generally considered to be ideal for hydrothermal activity because they may have both a magmatic heat source in the deeper underground and pathways for fluid circulation, respectively.

Jan 1, 2001

By Richard H. Sillitoe

Gold is an important byproduct and, locally, coproduct of porphyry copper deposits, and possesses potential for discovery as the major metal in porphyry deposits in either island arcs or Cordilleran belts. Tungsten and tin occur as major components of several potentially bulk-minable porphyry deposits, as well as being byproducts from the Climax porphyry molybdenum deposit. Whereas porphyry tin systems are localized in Cordilleran back-arc settings, their tungsten counterparts appear to span a range of geotectonic settings, from Cordilleran principal arcs through back-arcs to rifts. Although silver is a common byproduct of porphyry copper deposits, it tends to be preferentially concentrated with lead and zinc on the fringes of all types of porphyry deposits and/or as late-stage superpositions; the latter situation could be of some interest in the higher parts of porphyry systems. As byproducts, rhenium, uranium, platinoids and magnetite are exploited occasionally, and rutile and the rare metals, such as tantalum and niobium, have merited consideration.

Jan 1, 1982

By Y. F. Vasyuchkov

In general a term "unconventional mining or "non-traditional mining technology" getting more and more familiar to the mining engineering media. There are several alternating terminological combinations such as "in situ mining", "borehole mining", "shaftless mining", "mineless mining", "geotechnology" etc.; specific terms denote particular method of unconventional mining technology: "underground coal gasification in situ", "underground coal combustion in situ", "borehole hydraulic coal mining" and others. Principal scheme of unconventional coal mining technology is shown in Figure I:

Jan 1, 1997

By Karsten Beekhaus, Sander W. Odijk, Rabea Bahlum, Mazin Adnan, Ayman Abdelh Al Nuaimat, Hassan Farhat

The Arab Potash Company, APC, is one of the 10 largest potash producers of the world. The solar ponds at the Dead Sea, used for the enrichment of the salt content in the brine, are of crucial importance for the first step in the exploitation of the potassium salt. Targeting at the expansion of production in the since over 50 years utilized facilities, the increase of the brine exploitation capacity, reducing the substantial brine seepage losses from the ponds, becomes a crucially required measure. In this context, the remediation measures on the over 11 km long Dyke 1, being a main dyke of the solar ponds system, became inevitable to reduce the brine losses, prevent further development of sinkholes and cavities and hence assuring the stability of the dyke. The highly aggressive environment, the acting hydraulic conditions and the sensitive stratification and nature of the existing ground represented remarkable challenges for the design, as well as its implementation by the construction activities. Royal Haskoning developed a solution addressing the challenges above and targeting at a high sustainability of the executed structure, especially in view of the various geological and hydrological hazards repeatedly occurring in this Dead Sea region, including sinkholes of several meters by diameter and depth. The construction works, consisting of a cut-off wall, with depths reaching down to 31 m, were awarded to Bauer International FZE, a subsidiary of Bauer Spezialtiefbau GmbH. Upon the execution of the first section of 4.2 km length, additional sections were subsequently commissioned, also on further dykes, totaling to about 300,000 m² of cut-off wall. The specific project conditions, such as utilization of cutter technique for the excavation in Halite rock, the stability of open trench exposed to hydrostatic pressure of salt-saturated ground water, resulted in unconventional requirements towards the supporting fluid. The extremely aggressive saline conditions –with a Dead Sea water density of 1.25 tons/m3; one of the world's saltiest water–, were further a decisive factor for the definition of the backfill material concept. Despite its clear advantage for construction of cut-off walls with installed sheet piles, the single-phase system with hardening slurries, fulfilling both functions of excavation support and cut-off wall backfill material, had to be abandoned in favor of the two-phase system, to construct a hybrid cut-off wall made of sheet piles and plastic concrete.

May 1, 2022

By T. Guerin

More than 370 million litres of oil leak from hydraulic equipment every year, excluding all other sources of plant fluid losses. This item analyses the causes of fluid spills from plants and equipment on resource construction sites, and offers some possible solutions.

Apr 1, 2015

By Foluke Salgado de Assis

Natural fibers are attracting the interest of engineering sectors owing to specific advantages such as lightweight and lower cost as well as for their inherent condition of being renewable, biodegradable, recyclable and environmental correct material with respect to CO2 emission. The banana fiber is nowadays recognized by its mechanical properties. It is known that with the increase of fibers volume fraction the composite significant increases its tensile strength. This was obtained with amounts up to 30% in volume of banana fiber. However no higher volume of fibers was able to be molded in a composite plate until now. Thus the present work aims to study higher volumes of fiber in terms of the influence on the tensile strength of specimens prepared under 5 tons of pressure. The fibers were previously washed and dried in an oven at 60ºC, after that poured together with the epoxy resin and catalyst mixture in the metal molds bone-shaped, and pressured to ensure specimens quality. The tensile strength increased significantly with higher amounts of banana fiber incorporated in the epoxy matrix. This better performance can be directly related to the fracture obstacle imposed by the fibers as well as the type of cracks resulting from the fiber/matrix interaction.

Aug 16, 2017

By Ross Goodman, Jesse Salai

The Ohio River Tunnel Project encountered multiple unexpected geotechnical challenges such as crown and invert instability due to the overstress condition affecting the strata above, below, and in the tunnel alignment during and after TBM excavation along with the potential for methane inflow. This paper showcases how the orientation of a tunnel alignment has a significant impact on how in-situ geological stress can impact the excavation of a tunnel from the contractor’s point of view and how geological features influence gas inflow to the alignment over time.

Jun 13, 2021

By W. Arthur White

Underclay squeeze is the plastic flowing of underclay below coal pillars into mined-out entries and rooms. Squeezes may be caused either by wet mine conditions where the moisture is taken up by the clay-making it more plastic-or by the presence of certain clay minerals, such as mont-morillonite, which are plastic when there is enough natural moisture. Under either condition, sufficient stress will cause the underclay to flow. Squeezes may fill an entry or room within several hours, or it may be several months before movement stops. Squeeze areas commonly cover hundreds or thousands of square yards.

Oct 1, 1956

By A. Patti, S. Reutzel, D. M. Herlach, L. Ratke, I. Egry

Cu-Co shows a metastable miscibility gap in the region of the undercooled melt. Undercooling of the melt below the binodal leads to separation of the melt into a Co-rich LI-phase and a Curich L2-phase. Experimentally, undercooling into the metastable miscibility gap is realised by means of electromagnetic levitation (EML), processing in drop tube (DT) and by melt flux embedding. As undercooling is large in these experiments, the velocity of the solidification front is high and the microstructure is frozen in instantaneously. Samples have been undercooled and solidified in the TEMPUS-facility (container less electromagnetic processing under weightlessness) during parabolic flight under reduced gravity conditions. Microstructures of solidified samples have been analysed and compared to those processed under gravitational conditions. The influence of convection on phase growth is much lower in reduced gravity. The microstructure shows spherical droplets of the minority phase, statistically dispersed in the majority phase.

Jan 1, 2004

By S. Yin, A. Bogno, H. Henein, P. Natzke

Impulse Atomization (IA) (a single fluid atomization technique) was used to rapidly solidify Al- 4.5wt%Cu and Al-4.5wt%Cu-0.4wt%Sc under argon atmosphere. In addition to the IA-generated droplets, the same technique was used to produce strips by Spray Deposition (SD) of the same alloys on a copper substrate with and without oil coating. The rapid solidification microstructures were analyzed using Scanning Electron Microscopy (SEM). From the SEM images, the amount of eutectic and the secondary dendrite arm spacing (SDAS) were measured. These SDAS results lead to the estimation of cooling rate. The eutectic fraction coupled with the metastable extension of the solidus and liquidus lines of Al-Cu (Sc) phase diagram lead to the estimation of primary and eutectic undercoolings. A comparison of the solidification path of the droplets and the strips was done as well as the analysis of the effects of scandium.

Jan 1, 2015

By Joseph W. Murray

Prior to 1950 Magma's ore production came from two parallel, steeply dipping, east-west striking mineralized faults, one called the Main or Magma vein, and the other the Koerner vein, which lay about 1100 feet to the south, This vein system has been explored and mined over 9000 feet horizontally and 4800 vertically. In 1950 continued exploration led to the discovery and subsequent development of replacement ore bodies in the Devonian limestone zones adjacent to the veins. These replacement deposits occur in the eastern part of the Magma Mine, and follow the strike and the 30" east dip of the host limestone. Strike length of the ore bodies varies from 250 to 500 ft., and thickness from 15 to 125 ft. The ore bodies are large tabular masses with chalcopyrite and bornite being the dominant ore minerals. Hematite and pyrite are the most abundant gangue minerals. Incompetent limestone, shale, or a porphyry sill hanging wall is charactertistic of substantial portions of the replacement beds. In many instances the ore itself is blocky, badly fractured, and intermixed with layers of limestone gouge, pyrite and hematite.

Jan 1, 1973

By J. A. Pigott, R J. Hall

The International Nickel Company of Canada, Limited operates five underground mines on the rim of the Sudbury Basin in the northern part of the Province of Ontario. Four of the mines, the Frood-Stobie, Creigh-ton, Murray and Garson, are located on the south range of the basin with-in a radius of IO miles of the centre of the city of Sudbury. The fifth mine, Levack, is on the north range about 30 miles northwest of the city. The ores are mined primarily for nickel and copper, and the principal minerals are pentlandite, chalcopyrite and pyrrhotite. In 1960 the total ore production was in excess of 16 mil-lion tons, 95 per cent of which was produced from the five underground mines and the balance from the Frood-Stobie Open Pit. Mining at this open pit is nearing completion and underground production has been expanded to replace the open pit tonnage.

Jan 1, 1961

By Joseph W. Murray

GENERAL DESCRIPTION The undercut-and-fill method of mining was devel¬oped by Inco Ltd. in the Sudbury district of Ontario, Canada, to deal with abnormal ground conditions en¬countered in pillar recovery. Although it is now some¬times utilized as a primary stoping method, the main application continues to be in pillar recovery. In any mining method in which fill is employed, pillar systems tend to fail gradually as stoping pro¬gresses. As a result, most pillars are completely destressed and broken by the time pillar recovery com¬mences. Control of the back in such ground becomes a major problem and is contingent on local conditions as they exist in the workplace. In most mining methods, operations such as drilling, blasting, slushing, and tim¬bering can be readily assessed and the mining cycle pre¬dicted. However, in the mining of pillars with overhand methods, the time and effort required to maintain a safe back varies to a quite unpredictable extent. For years the square-set method was the most effective means available for pillar recovery. However, in areas where bad ground was encountered, square setting was a costly and sometimes hazardous method. As the tonnage mined from pillars increased, it was apparent that a safer and less expensive approach was required. Past experience indicated that the best way to deal with broken ground was to mine from the top down. Top slicing systems were examined but were rejected due to the major sub¬sidence which resulted. However, ideas generated from studying top slicing finally developed into the present method of undercut-and-fill. This method, which has almost completely replaced square-set mining, exhibits reduced costs, has improved safety and efficiency, elimi¬nates the factor of bad ground overhead, and allows a closer prediction of the actual mining cycle. The result is more accurate scheduling of pillar production. This factor is of increasing importance as the tonnage from pillar recovery increases in relation to total mine pro¬duction. Undercut-and-fill is a method of extracting a block of ore by mining successive cuts, working from the top down. After a cut of ore is completely mined out, lami¬nated timber stringers are constructed along the sides for the full length of the cut. Round logs covered by a wire screen are laid across the stringers to form a mat. The cut is then tightly filled with hydraulically placed cemented sand fill. Mining is then resumed on the cut immediately below the mat. As the cut advances, the timber stringers are supported by round timber posts seated on the solid bottom of the cut. Drilling, blasting, muck removal, and timbering operations are repeated until all the ore in the cut has been removed. At this time, another log mat is laid and the cut is filled. This sequence is continued until the block has been mined from level to level. The basic principles of undercut-and-fill can be adapted to a variety of mining situations. It can be applied transversely or longitudinally in ore bodies of varying width, that dip from vertical to flat lying. The method can be applied using conventional equipment or it can be mechanized through the introduction of small diesel or air-powered units for muck removal. Undercut¬and-fill is a selective method, ore recovery is high, and dilution can be controlled to an acceptable level. How¬ever, it is a high-cost, labor-intensive method and as such its use is restricted to areas where the less costly meth¬ods of ground support are not successful or where bulk mining methods are not adaptable. One basic require¬ment for undercut-and-fill is an adequate source of hydraulically placed cemented sand fill and a dependable sand plant and distribution system. The success of the undercut method is to a large degree dependent on the competence of the fill placed in each of the successive cuts. In theory, the weight of the fill on each cut is supported in part by the cemented sand itself as it binds to the rough sides of the mined¬out areas next to the pillar walls, and in part by the tim¬ber support. As mining progresses beneath the mat, a downward pressure is exerted within the cemented fill and a voussoir arch develops above the mat, across the full width of the cut. This supports the major portion of the load. The log mat and posts have a double func¬tion in that they carry the remaining weight not sup¬ported by the voussoir arch and in addition prevent any pronounced settling of the fill mass. Excessive settling breaks the bond between the cemented fill and the pillar walls, eliminating the arch effect and transferring the entire load to the mat and posts. The theory of a voussoir arch forming within the cemented sand fill mass is substantiated in practice by the fact that pillars have been mined from level to level with no more significant weight on the bottom cuts than was experienced on the top cuts. In effect, as mining progresses downward, there is no additional transfer of weight from previous cuts to the cut being mined. APPLICATION OF UNDERCUT-AND-FILL Because of their size, the Sudbury ore bodies are, for the most part, mined transversely and, to a considerable extent, by filling methods. Transverse stoping blocks are designed with 9-m (30-ft) crown pillars established be¬low each level and with stopes separated by vertical rib pillars. In past years, floor pillars were left above the level as well, but present practice favors the silling of primary stopes at the base of the rail. Rib pillars are designed to meet the ground control requirements of the primary stoping methods. Local conditions and past experience generally dictate their size. Historically, since the square-set method was to be used for recovery, rib pillars were designed to accommo¬date standard 1.7-m (5'h-ft) sets. A typical rib pillar is four sets wide [6.7 m (22 ft)] when located between two square-set or cut-and-fill stopes having a width of 8.4 m (27.5 ft). When the undercut-and-fill method was de¬veloped, a mat width of two sets was adopted. This di¬vided each cut of the common four-set pillar into two

Jan 1, 1982

By Frank Florez

INTRODUCTION The Magma mine, located at Superior, AZ, some 100 km (60 miles) east of Phoenix, was discovered in 1875, and was originally mined for silver. The property was acquired by W. B. Thompson who formed the Magma Copper Co. in 1910. Prior to 1965, square-set mining and cut-and-fill methods were used to mine steeply dipping veins at Magma. Ore was moved to the chute by gravity in the square-set stopes and by slusher in the cut-and-fill stopes. The stopes were gobbed with waste from the surface and development headings in the mine. The original square-set method of mining was modi¬fied in order to extract replacement ore bodies in limestones that dipped at 0.52 rad (30°) and varied in thick¬ness from 4.6 to 38 m (15 to 125 ft). Mining of these ore bodies was done by starting at the upper lateral ex¬tremities and retreating to the access openings. The timber square sets and cribbing were used as temporary support, the ground being allowed to cave as the mining retreated. It was found, however, that mining in such a manner was very inefficient; safety hazards increased be¬cause of the blocky and fractured characteristics of the ore and the weakness of the hanging wall. GENERAL DESCRIPTION The undercut-and-fill method of mining is now the primary stoping method used at Magma, and no pillars are left for later extraction. Four ore bodies are pres¬ently being mined. These ore bodies (see Fig. 1) dip conformably at 0.52 rad (30°) to the east with the host limestone and shale sediments, their average strike length is about 122 m (400 ft), and their thickness varies from 9 to 38 m (30 to 125 ft). The ore bodies are separated by varying thicknesses of barren rock. Three of them come together at various elevations primarily in the area of the main feeder fault, but there is an apparent horizontal displacement of about 23 m (75 ft) on the main feeder fault which complicates stope layout. The method as originally applied has been modified in order to mine more efficiently ore bodies that are 9 m (30 ft) or more in thickness. The modification was made to mine all the ore at a given elevation before dropping down for the cut below. The advantage of this is that mining is done on a horizontal plane and there¬fore muck removal can be mechanized. Also multiple faces are made available, thereby improving overall min¬ing efficiency. Another major change made was to carry a 6.7-m (22-ft) face when mining the top sill and a 6.4-m (21-ft) face when mining under fill rather than the former standard 3.35-m (11-ft) high face. This change lengthens the mining cycle and cuts mat prepa¬ration costs in half. Stopes are laid out (see Fig. 2) so that maximum mining panels are available and yet one stope crew will not tie up too much of the ore reserve. One stope might consist of as many as 20 panels, and these panels are divided evenly on opposite sides of the extraction cross¬cut. The stope layout is planned so that the maximum tramming distance to the orepass will not exceed 30.5 m (100 ft) on the crosscut and 38 m (125 ft) in the panel. Stope panel distances are sometimes exceeded when min¬ing to the extremity of the ore body. Tramming distance limits are determined by the efficiency of the com

Jan 1, 1982