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By R. W. Diamond

PUBLIC debts, and the policies guiding public finance in Canada today, are in such a state that every intelligent citizen should be familiar with them, and should be concerned about them. None of you have robe reminded that taxes have already risen to a point where they both annoy and hurt you, but they should also alarm you; alarm you, not so much because of the taxation, but because of the mounting expenditures represented by that taxation. I have no hesitation, therefore, in presenting a paper dealing with public finance at a meeting of the Mining Institute, since all present are concerned,. both as individuals and as representatives of the industry. Moreover, it is important that engineers, particularly, should become better acquainted with the interlocking relationships of economics, public finance, government, and technology. While I am neither an economist, a tax expert, nor a chartered accountant, I shall try to tell you, from my viewpoint as an engineer and an interested voter, the story of public finance in Canada today and of certain causes and effects, and I shall venture certain conclusions. In doing so I may merit criticism by experts, but I will risk this in the hope that sufficient interest will be stimulated in the subject to persuade you, as individuals and as groups, to advance, or to institute, your own studies in public finance, and in turn to interest others. I hope that some of the ideas which will be expressed, or which may develop, will bear fruit. I fully realize that several eminently qualified men have spoken on this subject during recent months, and that many authoritative articles have been written. However, I approach it with confidence, because I propose speaking to you not as an authority, bur as one of you, having similar interests and similar engineering knowledge, who only a few months ago became particularly interested in the subject, studied it, and who now sets before you a summary of his findings, with the conviction that the situation is so serious that constructive planning and constructive action by all thinking citizens are imperative.

Jan 1, 1939

By J. D. Campbell

"Coal is one of Alberta's major fuel resources, but its distribution, especially in the flat plains region, has been somewhat obscured by surficial deposits. After a period of neglect, easily strippable plains coal is presently approaching a position of dominance in electrical power production, a position it is likely to retain for a number of decades in the face of strong competition from hydro and nuclear power. Accordingly, the Research Council of Alberta has undertaken an inventory survey of the province's supplies of this resource.In the southern part of the province and in the north-central forest-fringe area, some strippable coal is found in the Belly River Formation and its equivalents, but major strippable coal reserves in large areas of central Alberta occur within the Edmonton Formation. The survey is planned on a reconnaissance scale, drilling test holes at 2-mile intervals in selected large areas. It appears to show that, in well-settled regions, large reserves of strippable coal are only to be expected where they have long been known; major presently unknown bodies of coal must be sought in unsettled regions or at depths too great for strip mining. However, such bodies might still be economically competitive with hydro and nuclear power in the production of electric power for some time to come."

Jan 1, 1967

By Renliang Shan

Site conditions of China?s coal roadways are complex and changeable, and scientific classification of them is the fundamental basis for coal roadway support design, with great significance for ensuring proper roadway service. Upon analysis of the issues, a commentary regarding the research progress on classification of the stability of rocks surrounding coal roadways in China has been achieved from the point of view of classification methods and indexes. The shortcomings and applicable scope of rock stability classification methods related to coal roadways have been analyzed. It has been asserted that combining artificial neural networks with fuzzy mathematics, combining fuzzy mathematics with grey theory, applying new avenues such as support vector machine algorithms or unascertained average classification, and making classification indexes more scientific are future directions for development of rock stability classification for coal roadways.

Aug 1, 2013

By G. W. H. Norman

"During the past few years emphasis has been placed on the importance of major faults, fault zones, and associated structures in localizing ore deposition. This interest has developed partly through experience in mining camps in other parts of the world, and partly by the discovery of such structures associated with ore deposits in the Abitibi region, northwestern Quebec. The recognition of these structures has been brought about chiefly by detailed mapping that has been gradually extended along most of the southern gold belt of Quebec and across adjacent parts of Ontario. In the Chibougamau region of northern Abitibi, progress has been made in mapping major faults by using aeroplane photographs with a scale of about 1,000 feet to 1 inch for field mapping. These studies have shown that many large faults occur in the Abitibi region; also that there is a relationship, direct or indirect, between faults and mineral deposition. The faults are, however, of more than one type and age, and this should be clearly appreciated in any planned programme for prospecting this great region adequately.Geology of the Abitibi RegionGeneral GeologyFaults of more than one age and type occur in the Abitibi region. In order to appreciate some of the age relationships of the faults, a brief summary of the historical aspects and major structural features of the geology (fig. 1) is necessary. These historical aspects may be briefly summarized in chronological order as follows:(1) Accumulation of Archæan lavas and associated pyroclastic rocks, either alternating with, or essentially followed by, deposition of sedimentary rocks, and interrupted at least once by local and perhaps regional folding and erosion."

Jan 1, 1954

By S. Banisi, J. Marois, A. R. Laplante

"This paper compares the behaviour of gold and ore in the grinding circuit of Hemlo Mines Ltd. Particular attention is given to grinding kinetics, classification behaviour, and liberation. For grinding kinetics, laboratory grinding of gold flakes and silica, 840 µm to 1200 µm in size (14/20 mesh), was also performed to provide a standard for comparison and to study in a controlled environment the mechanisms of breakage, folding , smearing and impacting.Grinding kinetics were characterized at laboratory scale with breakage and selection functions. The breakage function showed that 75% of gold disappearing from the 840 µm to 1200 µm class reported to the 600 µm to 840 µm; this figure is much higher than for silica (46%) or most other minerals, and implies that comparatively fewer fine fragments are produced from the breakage of gold flakes, on account of gold's malleability. The selection function of silica was four times that of gold. At plant scale, the ratio of the selection function of ore and gold increased from 6 for at 50 urn to JOO pm to 20 at 500 um to 1000µm.Observation of original flakes and their fragments with the scanning electron microscope showed that the main mechanism of ""grinding"" from the 840 µm to 1200 µm to the 600 µm to 840 µm class was folding rather than actual breakage. This was confirmed by a measure of individual flake weight. The postulated breakage cycle is that relatively globular flakes become increasingly serrated through grinding; they can then regain their original shape through folding and reflattening into cylindrical and spherical shapes, as the majority does; however, some fragments will at this point undergo actual breakage. Photograhic evidence is presented to support the proposed mechanisms.Smearing of gold unto silica was observed when silica was ground after a gold, and embedding of silica into gold flakes when gold was ground after a silica. Both mechanisms occur whenever gold and harder minerals are jointly ground, and result in ""unliberation"" of gold. It is postulated that smearing of gold onto other minerals plays an important role in explaining how gravity recovery can increase over-all gold metallurgy, especially when used ahead of flotation.Classification of gold in the primary hydro cyclones takes place at a much finer cut-size than ore, 20 µm vs 57 µm. This and the slower grinding kinetics result in high gold circulating loads in the primary loop, 6700%, and a gold content in the primary cyclone underflow (PCUF) is twenty-four times that of the ore. The gold size distribution for primary cyclone overflow is much finer than that of the ore, although they are essentially similar in the PCUF.Liberation, or more accurately ""gravity recoverability"", was assessed with a 7.5 cm (3 in.) Knelson concentrator. It varied between the thirties for the primary mill discharge and two cyclone overflows, to highs of 89% and 92% for the PCUF and secondary mill discharge."

Jan 1, 1991

By Nav Dhadli

Tailings from Oil Sands MiningWhat are they? Challenges Solutions Regulatory Environment Definition of the AFD Tailings Treatment Process 2010 AFD Pilot/Demonstration ProgramTechnical challenges Performance and Results Next steps Oil Sands Industry Collaboration on Tailings Technology TAILINGS ?WHAT ARE THEY? Mixture of remaining water and solids following bitumen extraction process Composed of water, sand, silt, clay, small amounts of hydrocarbon (bitumen, solvent, and asphaltenes) A necessary part of production in excavation of oil sands and removal of bitumen

May 1, 2011

By C. A. Born

This paper describes the rejuvenation of a molybdenum mine mill complex at the head of Alice Arm, 500 miles north of Vancouver and 85 miles north of Prince Rupert, British Columbia. It includes a description of the property history of the deposits and of the previous operations, together with details of the project for re-opening the mine.

Jan 1, 1979

By Xiaoguang Zhao

The coal mining area in Northern Shaanxi, China, has been taken as the study area, and the damage mechanism of the ecological environment is discussed on the basis of analyzing the characteristics of natural eco-environment and resource development in this area. Mining subsidence is taken as an example, and by using the Gray Correlation Analysis method, the key impact factors have been selected. An assessment model with fuzzy comprehensive evaluation has been constructed, and 12 coal mines have been quantitatively assessed. This paper also constructs an ecosystem health assessment method and index system in the coal mine area on the basis of ecosystem health theory, and assesses the ecosystem health status in the Shenfu coal mining area from 2000?2006. The research results are expected to help the eco-environment protection process in the designated coal mining area.

Aug 1, 2013

By S. Broda

Waste rock piles (WRP) are made of heterogeneous, coarse grained waste rock, with inclined layers due to segregation along the slopes and haul traffic compacted layers, creating highly contrasted hydrogeological conditions. The internal structure of the pile has a major impact on water and oxygen movement and pore water pressure distribution. In the presence of reactive minerals, this influences the production of acid mine drainage (AMD) or contaminated neutral drainage (CND) with metal leaching from the WRP. Water flow and distribution may also affect slope stability, particularly following major infiltration events (rain/snow melts).The prediction and interpretation of water distribution in WRP is a challenging problem. Numerous numerical investigations of short and long term forecasts have been conducted, and many of these were found of limited reliability. The shortcomings of existing approaches are typically due to difficulties in representing preferential flow processes in macropores. Such phenomena are in fact often neglected in the assessment of water flow in WRP because these are unattainable with the classical porous media approach typically used in this field. This paper focuses on the use of modeling techniques originally designed for massive fractured rock media to simulate flow in WRP. Waste rock properties used in this study are retrieved from large scale laboratory permeability and water retention tests and from in situ infiltration tests. The effect of WRP configurations on water flow into potentially reactive zones is examined with the numerical 3D fully-integrated surface/subsurface, variably saturated flow model HydroGeoSphere. Material properties retrieved from the laboratory tests are represented by means of stochastic facies distribution generated within a probability framework. Modelled soil water contents and hydraulic head distributions, as well as fluxes within a simple waste rock pile, with compacted layers, are compared with results retrieved from simulations based on the classical equivalent porous medium approach. Results indicate significantly increased flow towards the looser waste rock zone by considering heterogeneous material distribution, causing weak or absent capillary barriers and preferential flow paths. Practical implications for the design of waste rock piles are also discussed.

Aug 1, 2013

By David Thomas, Charles Harper, Brian Watters

The Star-Waddy Lakes area lies withjn the northeasterly-trending early- to mjd-Proterozoic volcanoseilimentary-pl utoruc belt referred to as the La Range Domllin. In the area investigated the domajn is composed of the Central Metavolcaruc Belt which is bordered by metasedimentary belts of the Crew Lake and MacLean Lake Belts to the northwest and southeast respectively. The boundaries between the Central Metavolcanic Belt and the flanking belts are generally marked by prominent zones of shearing. The volcanosed imentary succession is intruded by a variety of ultramafic to felsic plutons which, on the basis of lithology, field relations and geochronology, can be broadly subdivided into three groups or episodes. These are: a) an 'early' (ea. 1866 Ma), possibly subvolcanic, episode marked by composite intrusions ranging from gabbro-diorite to granite, b) an 'intermediate' (ea. 1854 Ma) plutonic event distinguished by more homogeneous felsic intru ions ; and c) a 'later' (ea. 1835 Ma) event characterized by leucocratic quartz-rich grani te intrusions. The La Range Domain has undergone polyphase deformation with a strongly developed northeast-trending structural grain. Large scale folding is manjfested by large regional sy nforms, arcuate and triangular patterns associated with many of the plutons and by tight to isoclinal folds within the adjacent metasedimentary belts. Inhomogeneous strain characterizes much of the Star-Waddy Lakes area. With strain gradients being typically very steep, zones of high strain consisting of zones of extreme extensional fabrics, discrete shearing, as well as broader zones of cataclasis and structural slicing, are often juxtaposed with areas of relatively minimal deformation . Dilation structures tend to favour these zones of highly contrasting strain. Late, brittle fractures, faults and shear zones are widespread and appear to be particularly important as loci for gold mineralization. Metan1orphic mineral assemblages indicate that upper greenschist to middle amphibolite facies conditions were attained. Geological and geochenucal evidence indicates that the Central Metavolcanic Belt evolved in an island arc environment. Metavolcanic rocks from both the Waddy and Star Lakes areas display similar characteristics on variation diagrams (e.g. AFM and the Jensen cation plot) in that the dominant trend is calc-alkaline with some basic to intermediate types having a mildly tholeiitic character. A few samples from the southern end of Lower Waddy lake display komatiitic to basaltic-komatiitic afl'injties. The relatively immobile minor and trace elements (e.g. Ti , Zr, Nb, Y, Cr) provide reliable characterization of the metavolcanics, particularly of the basalts, which have highly distinctive trace element properties. Geochemical patterns for the basalts are similar to those for modem volcanic arc basalts. Low initial 87Sr/86Sr ratios (0.7017 - 0.7019) are consistent with a subduction-related origin for the volcanics. The major plutons have chemical properties typical of volcanic arc granites and are largely calc-alkaline in character, showing little chemical variation from the volcanics.

Jan 1, 1986

By Jae-Chun Lee, Rajiv Ranjan Srivastava, Min-seuk Kim, Byung-Su Kim

Recycling of spent hydrotreating catalysts (HTC) can potentially contribute towards the sustainable extraction of metal values. Treating such materials by hydrometallurgical methods to separate metals from the leach liquor of either acid/alkali media is a major step. In the present study, separation of molybdenum from HCl leach liquor of spent NiMo type HTC has been investigated by applying solvent extraction using Cyanex-923. For this, the chloride solution containing 973 mg/L Mo, 254 mg/L Ni and 1634 mg/L Al was taken as the aqueous feed. The parameters including contact time, concentration of the extractant, acid and chloride, and phase ratio were varied to investigate their effect on the extraction efficiency. The McCabe-Thiele plot suggests that > 99% Mo-loading using a 2-stage extraction process. From the molybdenum depleted solution, nickel was selectively extracted by Cyanex-301 leaving Al in the raffinate.

Jan 1, 2014

By David L. Anderson

This paper explores the financial impact of the initial version of the Saskatchewan Potash Reserve Tax; first, a one; and second, in conjunction with the other taxes affecting the industry's profitability. A though the introduction of the Reserve Tax is shown to lead to a substantia increase in a hypothetical firm's effective tax burden, the more unusual outcomes frequently attributed to this levy on y occur after the imposition of other non-provincial tax rulings. Despite this qualification, the results obtained suggest that the Reserve Tax undoubted y acted as a catalyst in the polarization of attitudes during the ear y period of industry/government confrontation

Jan 1, 1979

By R. E. Eyre, L. P. Landucci

C URRENT practice in the zinc concentrate roasting plant of The Consolidated Mining arid Smelting Company of Canada Limited, at Trail, B.C., involves passing the furnace effluent gases through an electrostatic precipitator for the recovery of dust. After removal of the dust the gas is treated for recovery of sulphur dioxide by conversion into sulphuric acid ( 1). However. as roasting techniques improved, and furnace productivity in-creased, the rated capacity of the precipitator was exceeded and it was necessary to consider various means of improving the dust recovery. A study of methods indicated that a baghouse using silicone-treated glass fabric, might be suitable for this particular application. Glass fabric was chosen because the temperature of the roaster effluent gases would range from 450°F to 500°F and tempering air was undesirable to avoid dilution of the sulphur dioxide gas.

Jan 1, 1962

By W. Rostoker

Packing Experiments The porosity and most of the other physical properties of a coherent mass of any material built up by the packing together of discrete particles will obviously vary with, and be governed by, the manner of association of the particles. The relation of packing to powder metallurgy has been discussed in some detail by at least two authors. Packing Theory Theories of particle packing have been put forward by C. C. Furnas and A. E. R. Westman. Although their approach to the problem is not the same, their conclusions are similar. In the process of packing, they visualize the voids of a uniformly sized material becoming filled with particles of a smaller size, and the voids between these being filled in turn with still finer particles. Obviously, if this process is carried ad infinitum, the resultant mass will have the same density as the constituent particles. In practice, of course, such a density of packing is never attained. In addition, the premise is made that successive particle sizes must fit into the voids left by the immediately larger particles- an assumption requiring definite size gradations and also particle shapes. It remained, then, for theory to correlate relative diameter ratios, and proportions and numbers of sizes of particles, for requisite packed densities. Briefly, the following principles were postulated: (a) For an infinite diameter ratio between largest and smallest sizes, an infinite number of particle sizes in proper proportion is required to give natural density. (b) For a given diameter ratio, there is a maximum number of permissible particle sizes for maximum packed density (Furnas). (c) Provided the particle shape is spherical, or approximately so, the proportions o particle sizes can be calculated. (d) The ratios of successive diameters of particles are in geometric progression.

Jan 1, 1947

By Edgar A. Manker

"Today's market for columbium has only developed in the last two decades, and in this sense it is ""newer"" than molybdenum, vanadium and most other steel alloying elements. In this short period, it has assumed a very important role in steel alloying and in superalloys. From a few hundred thousand pounds of columbium in 1960, consumption has grown to nearly 30 million pounds per year, with a market value approaching two hundred million dollars.To assess the outlook for columbium, we will first consider the historical development of consumption and supply, particularly noting that all of today's major mines were developed during the last two decades. From current production, we will attempt to reasonably project the future. This future may well include new producers, particularly some producing columbium as a co-product with tantalum.The growth of current applications, and emerging new applications, will be considered with regard to future consumption and in relation to future trends in pricing.IntroductionThe nineteenth century was a busy time for the discovery and naming of new elements. Among those discovered were columbium in 1801 and niobium in 1844. Although it was later shown that columbium and niobium are the same element, the two names are still used today. Niobium has been pronounced the ""official"" name by the International Union of Pure and Applied Chemistry, but columbium is still widely used in commercial practice, and we have chosen to use columbium in this paper."

Jan 1, 1981

By A. Proulx

Durant les années 1955 à 1961, plusieurs campagnes d?exploration ont été menées sur la zone Bond dans la partie sud-ouest de l?anneau nord de la carbonatite d?Oka (propriété de Niocan, figure 1). Les zones minéralisées HWM1 et HWM2 sont découvertes à l?ouest de la propriété. Un des forages, le S-60, avait intercepté 80 mètres de minéralisation à 0.71% Nb2O5 à l?est des zones HWM1 et HWM2 mais aucun autres travaux d?exploration n?avaient été réalisés sur cette interception minéralisée. En 1995, Niocan réalise une campagne de forage pour mieux définir la zone minéralisée recoupée par le forage S-60. En 1997, une seconde campagne de forage détermine un tonnage de 14.37 Mt avec une teneur de 0.66 % Nb2O5 pour la zone S-60 (Marcotte et Gagnon, 1997). Le complexe carbonatitique d'Oka se situe à environ 35 km à l?ouest de Montréal sur la rive nord du lac des Deux-Montagnes. Sa formation remonte au Crétacé précoce (entre 117 à 123 Ma). La carbonatite d?Oka fait partie de la suite d'intrusions alcalines que constituent les collines Montérégiennes. Le complexe a une forme allongée (7.2 km par 2.4 km) orientée NO-SE (figure 1). Il est intrusif dans des roches précambriennes constituées d?anorthosites au nord et de gneiss charnokitique au sud (Gold, 1963) appartenant à la Formation de la colline d?Oka. Les gneiss au contact du complexe sont fénitisés sur une épaisseur qui peut atteindre jusqu?à 60 mètres. Les roches carbonatitiques forment la série dominante du complexe et elles sont composées principalement de calcite (> 50 %) à gros grain et parfois rubanées. Les minéraux accessoires les plus communs sont la biotite, le pyroxène, la monticellite, la magnétite, l?apatite, la forstérite, la mélilite, le pyrochlore, la pérovskite, la niocalite, la pyrite et la pyrrhotite (Gold, 1963).

May 1, 2003

By J. W. Rogers, S. K. Schwartz

"The Cape Breton Development Corporation (CBDC) is a federal Crown corporation which operates two coal mines (Phalen and Prince Collieries), a coal preparation plant, a railway, a central workshop and a deep water shipping facility.The Sydney coal field consists of 11 major seams, which range from 0.8 m to over 3.7 m in thickness. Of the 2.4 billion tonnes of known coal resources in the field, approximately 550 million tonnes can be mined with present mining technology. These parameters define reserves which extend more than 8 km beneath the ocean to a depth of 1200 m. With today’s design and present high production faces, the colliery life is projected at approximately 20 years."

Jan 1, 1996

By T. W. Wlodek

In this paper the relative merits of shot peening, induction surface hardening, spiral-rolling, and the combination of these surface treatments, are evaluated on the basis of their capacity to increase the fatigue strength of drill steel. The S-N relations for plain car-bon steel (SAE 1080) and Ni-Cr-Mo drill steels in the as-rolled condition were determined previously, using the new Canadian method of testing drill steel introduced at the annual meeting of the Institute in Toronto in 1950 (19). S-N curves have now been determined by this method for these two drill steels in the following conditions: shot-peened and drawn, induction hardened, induction hardened and shot-peened, and spiral-rolled. ( S.R.) . The ratios of the fatigue strengths of these steels after surface treatment, to their fatigue strengths in the as-rolled condition, are compared and the most beneficial treatments are thereby pointed out. The expected range of stresses and their distribution during actual drilling operations are estimated from data available, and the mechanism of failure of drill steel in the as-rolled and surface-treated conditions is analyzed. The magnitude of the surface compression stresses and their effect on ?fatigue strength are discussed.

Jan 1, 1958

By P .. H. Grimley, N. Champigny

"Fourteen companies (Appendix) representing senior mining organizations in Canada were canvassed in order to assess: (1) the current usage and trends, and (2) the usefulness of computer applications in ore reserve estimation and grade control. The results of the questionnaire suggest that:• computers are unsurprisingly, predominant in the mining industry for calculating reserves and performing grade control;• time and cost savings are realized;• computer-based approaches are applicable to underground situations;• geological information is incorporated to the computerization process; and• computer usage does not hinder the collaboration of geologist and mining engineer.A clear need is identified for case histories comparing computer-calculated ore reserves and actual production data.IntroductionAmong the management and technical staff of some mining companies there is a perception that the application of computer based technology for the estimation of ore reserves and grade control, has as many drawbacks as benefits. Some of the objections raised against the utilization of computers for ore reserve estimation are that:• computer-based reserve models work for large open pit mines but not for underground situations;• computer-generated reserves ignore the geologist's knowledge base; they are strictly a number crunching exercise; and• the use of computers for ore reserves hinders collaboration between the geologist and mining engineer.In order to determine (I) the extent of current computer usage and future trends and (2) whether the objections noted above are borne out by experience, a number of senior Canadian mining companies were canvassed.The respondents were asked to provide:• an assessment of the importance of the computer in the ore reserve estimation and grade control process;• the level of involvement of individuals and staff groups with computer-based ore reserve estimation;• the advantages perceived and realized from the utilization of computer-based ore reserve approaches;• the current and future human resources requirements for the evaluation, implementation, maintenance and development of computer-based ore reserve systems;• the hardware and software resources presently used and planned; and• the developments needed to increase the use and acceptance of computer-based ore reserves."

Jan 1, 1990

By Gang Mei, Nengxiong Xu, Yanlin Zhang

After open-pit mining finishes, an iron mine with steeply inclined ore-bodies will generally transform to underground mining. Non-pillar sublevel caving method, with horizontal slice mining from up to down, is commonly used for mining deep ore-bodies under the open-pit bottom. As horizontal slice mining proceeds, a gradually enlarging goaf will be formed under the open-pit bottom, the rocks surrounding the handing and heading sides of the goaf will collapse continuously, and then these results in rock-mass failure with large deformation and displacement in the open-pit slope. Based on FLAC3D, a modeling approach to predict pit slope deformation and failure induced by transitioning open-pit to underground mining is proposed in this paper. This method mainly consists of three procedures of modeling, i.e., mining modeling, landslide modeling, and filling modeling, of which landslide modeling is the core of the proposed approach. In the procedures of modeling with FLAC3D, iteration non-convergence is taken as a local failure criterion of pit slope. When iteration calculation cannot converge, the sliding modeling will start by deleting some elements with large displacements, and finish until convergence. Before modeling landslide, several displacement contours of rock-masses in the pit slope are searched out, and each contour is an approximate possible sliding surface of the open-pit slope. From these contours, the most proper one is selected as the slope sliding surface by using the iteration calculation convergence and minimum element deletion as the judgment condition. Landslide modeling is then realized by removing the elements outside the slope sliding surface. Finally, to demonstrate the effectiveness, the proposed approach is used to simulate the process of open-pit to underground mining at Yanqianshan Iron Mine, and to predict the deformation and failure characteristics of open-pit slope during underground mining. The case study results show that: the prediction of the slope stability determined by using our method is consistent with that calculated by using the limit equilibrium methods.

Jan 1, 2015