Search Documents

By P. Chollet, A Constant

THE RESULTS of a previous investigation ( 1) on the work-softening of some heat-treated steels have led to the conclusion that the occurrence and intensity of the phenomenon is possibly governed by the work-hardening capacity of the material, and the relative amount of retained austenite. The first assumption is compatible with Polakowski's theory (2) that the absence of work-softening, in steels quenched and tempered at relatively low temperatures, may be attributed to the high rate of work-hardening which compensates for, and even out-weighs, the loss of internal energy associated with the simultaneous rearrangement of the original system of internal stresses. Indeed, Polakowski first considered the work-softening as a manifestation of a partial release (by cold-working) of the latent strain energy stored in

Jan 1, 1962

By Z. G. Tao, Y. Y. Peng, W. L. Gong, M. C. He

"This paper presents an overview of the major landslide hazards in open pit mines in China, the currently used landslide control and monitoring techniques, and development of a new slope control technique incorporating the reinforcement, sliding force monitoring, remote sensing and forecasting in one system in order to constrain the displacement of the sliding blocks in the landslide to minimized the influenced area and provide precise warnings timely for the imminent landslides. For implementation of the new technique, a novel rock cable with large deformation and high resistance (also known as HE cable) was developed, which can elongate as long as 2m. At the same time, the necessary and sufficient condition for initiating a landslide and energy balance equations are formulated. Based on the proposed mathematical models and Beidou satellite system, the software and data transmission hardware for remote sensing and forecasting were developed the new landslide control technique has been applied successfully in 245 landslide sites in 12 provinces across China. In this article, two practical application cases in the open pit mines are reported.INTRODUCTIONChina is one of the countries in the world with the most widely distributed landslides and suffering the heaviest damage. According to the incomplete statistics, landslide hazards have caused death of hundreds of people and direct economic losses of several hundred million RMB each year. The landslide hazards have a great impact on the life and property safety of the people, safety of the infrastructure, as well as the social stability. Thus development of new techniques for forecasting and prediction of the landslides is imperative and of great importance. In general, the forecasting and prediction of the landslides consists of three major aspects, i.e. sliding time forecasting, landslide activity intensity forecasting and landslide hazard degree forecasting. Since a considerable part of the landslide-suspected area are adjacent to the residential areas or important infrastructures, development of the advanced landslide control and monitoring techniques to cope with the sliding time forecasting problem is more important.Over the past one hundred years, the most widely used slope monitoring techniques are based on displacement monitoring (Xu, et al. 2007; Toshitaka, 1998). In the early days owing to the limitation of the technology and equipment, the ground surface displacement and underground water level change were inspected mainly by man power for inferring the possibility of a landslide. In recent several decades, more and more ground surface displacement monitoring devices were brought to the market, such as the automatic total station, theodolite, digital level, borehole inclinometer and GPS based instruments, etc. Based on these modern techniques, some advanced instruments have been developed and applied to the landslide monitoring, for example, the “landslides early warning monitoring system” (Leonardo, et al. 2002), the “In-SAR” technique (Reevea, et al. 2000), the GPS and satellite geodetic survey based technique (Reevea, et al. 2000), and real-time telemetry technology (Xu, et al. 2007). These monitoring approaches have made significant contributions to the landslide disaster monitoring and forecasting. The major limitations for the ground surface displacement monitoring techniques are lie in the inconsistence between the displacement in ground surface and that in the sliding surface for the sliding mass, resulting in low degree of forecasting accuracy."

Jan 1, 2015

By D. R. Jolley

"The selection of equipment for open-pit mining is an important decision which results in a considerable capital expenditure by the operator. The decision is complicated by the wide product range on the market. Certainly, equipment performance is an important criterion to consider in making the decision. Equally important, however, is the operating inter-relationship among the equipment. A poor balance increases production costs and waiting time as queues form at the bottlenecks. This inter-relationship is dependent on equipment performance, but it is also affected by management decisions (i.e. scheduling techniques).The purpose of this paper is to show how the computer is used to decide which equipment and operating decisions achieve the required production objectives at least cost. Actual mining of the pit is simulated over a period of time using different equipment and scheduling decisions. Production, waiting time and costs are evaluated for each alternative until the operator is satisfied that he has achieved the best result."

Jan 1, 1970

By V. Vakiloroaya

The paper aims at developing a hybrid solar-assisted air conditioner system for performance enhancement and energy efficiency improvement. To increase sub-cooling of the refrigerant at partial loads, we propose a new discharge bypass line together with an inline solenoid valve, installed after the compressor to regulate the mass flow rate of the refrigerant vapour passing through a hot water storage tank. For control design, a lumped parameter model is first developed to describe the dynamics of the system in an explicit form of input-output relationship. The system has been fully-instrumented to examine its performance under different operation conditions. The system model is then validated by extensive experimental tests. The predictions from the models exhibit a good coincidence with experimental results, judging by an RMS error less than 15%. Based on the obtained dynamic model, a linear quadratic regulator (LQR) is applied to optimize a cost function of the output errors and control efforts. The key challenge is to regulate the refrigerant temperature entering the condenser by controlling the valve opening. The design approach is then tested in a transient simulation tool to predict the system performance in transient conditions. The experimental results obtained from implementation with PLC demonstrate that the proposed system delivers higher system efficiency owing to the higher refrigeration effect in the direct expansion evaporator. Thus, the novel development is promising for improvement of energy efficiency, enhancement of the system performance while fulfilling the cooling demand. Consequently, between 25 and 43% of monthly electricity can be saved on average.

Aug 1, 2013

By R. A. May, P. J. Brooks, W. M. Smith

"Neill and Gunter Limited (NGL) has prepared a preliminary design and a cost estimate for a ferric chloride leach plant to recover copper, lead, zinc, and silver from a typical complex sulphide ore. This plant design is specifically intended to treat unconcentrated ground ore (flotation feed), but can be readily adapted to treat bulk concentrates. Samples of ground ore and bulk concentrate were obtained from Heath Steele Mines, Miramichi, New Brunswick, laboratory testing, and preliminary process flow sheet preparation was carried out by the Research and Productivity Council in Fredericton, New Brunswick. Approximately thirty drawings have been produced, including process and equipment flowsheets, process piping and instrumentation drawings, and preliminary general arrangements. Preliminary capital and operating cost estimates were prepared for a plant that would treat 1000 t/d of crushed and ground ore to produce about 30 000 tpy of zinc. Capital and operating cost estimates were also projected for plants up to 4000 t/d of processed ore. Recoveries of 99% for zinc, 98% for lead, and 96% for copper were achieved in laboratory tests on unconcentrated ore. These recoveries were higher than the overall recoveries obtained from bulk concentrate, yielding approximately 10% more revenue.A 1000 tonne per day plant was determined to have a low return on investment, however, depending on the size and type of mining operations employed and the FCL plant throughput. DCF-ROI projections of 20% to over 30% were calculated for 100% equity financed “green field” mine, mill and FCL plant operations of 2000 t/d and higher"

Jan 1, 1997

By A. O. Sfriso

"Numerical modelling is becoming universal in rock engineering practice. Most applications focus on the prediction of failure loads of 2D problems, where the numerical models are useful extensions to analytical methods and experience-based design criteria. For 3D problems and problems where the assessment of serviceability indicators – displacements, ground-structure response, etc. – are of importance, the selection of the constitutive models themselves and the implications of the selection of material parameters may have a very heavy impact on the reliability of the model outcome and its predictive capability.This paper overviews basic common aspects of constitutive equations used in practical rock engineering and summarizes some challenges that are frequently observed when reviewing numerical models performed for routine problems in rock engineering. INTRODUCTIONNumerical methodsFrom a philosophical perspective models, either analytical or numerical, are idealizations of a perceived reality. For us engineers, models are just tools we use to guide our judgement and understanding of the problem in hand. When dealing with problems in rock engineering, we resort to a wide range of techniques:1. Closed form solutions like confinement-convergence methods for circular tunnels: these methods satisfy equilibrium and compatibility requirements at the cost of a crude simplification of the material behavior and geometry;2. Limit analysis methods, like bearing capacity formulas: lower bound methods satisfy equilibrium but sacrifice compatibility, and upper bound methods do the opposite. Material behavior must be simple, geometry admits limited freedom;3. Limit equilibrium methods, like method of slices for slope stability: they satisfy restricted forms of equilibrium, do not satisfy compatibility requirements, require simple material behavior but have a much greater flexibility on geometry;4. Numerical methods, where a mesh is employed to discretize the problem geometry: when properly formulated, these methods satisfy equilibrium and compatibility requirements and give reasonable approximations to the behavior of very complex geometries and construction sequences. Very little restrictions remain on geometry and material behavior, but the cost of calibrating the material parameters can be very high."

Jan 1, 2015

By F. Melo, M. Pawlik

Fine coal aggregation in concentrated coal-water suspensions was studied through steady-state rheological measurements. The wettability of coal particles was modified by dry oxidation of a bituminous coal. The degree of hydrophobicity was monitored using film flotation. The rheological measurements revealed that hydrophobic coal particles aggregate in aqueous suspensions, over a wide pH range, and produce slurries with high yield stresses. As the degree of coal oxidation increases, the coal particles become more hydrophilic and such suspensions exhibit lower yield stresses values. The yield stress values for suspensions prepared from oxidized/hydrophilic coal become a strong function of pH and correlate well with the surface charge as determined through electroacoustic measurements. These results indicate that the yield stress of aqueous suspensions of coal, and hence coal particles aggregation, is strongly affected by the wettability of coal particles.

Jan 1, 2004

By W. G. Hubler

It has been within only the last two or three years that enough progress has been made in preferential flotation to warrant metallurgists in recommending the installation of commercial-sized plants for the treatment of copper-zinc-iron ores. Until the new processes had been worked out successfully, the treatment of this type of ore had proved a stumbling block in the path of metallurgical progress. Separation of lead-zinc ore is comparatively simple. A lead-zinc ore low in iron may be separated and concentrated by gravity con-centration, provided it is not necessary to grind too fine. Owing to the specific gravity of chalcopyrite and sphalerite being so nearly the same, however, their separation by gravity concentration is out of the question. Complex lead-zinc-iron ores in which the several minerals are intimately associated, requiring fine grinding to free them, have been successfully treated by flotation for the past fifteen years. Galena is easily floated, and its flotation, unlike that of chal¬copyrite, is not affected by the reagents used to inhibit the flotation of sphalerite and iron sulphides. When an attempt was made to use the methods of lead-zinc se-paration on copper-zinc ores, it was found that the depressant re-agents added to inhibit the flotation of the iron and zinc minerals would, under certain conditions, depress a large part of the copper. It was also recognized that, in the grinding of copper-zinc ore, soluble salts were generated which were detrimental to flotation unless properly controlled. The main part of this paper will be a discussion of solutions in the grinding circuit in relation to the pro¬duction of soluble salts and their effect on flotation.

Jan 1, 1931

By Edward Sampson

Bases of National Power At a time when the economy of the world is in a particularly troubled state it is appropriate to examine some problems of the distribution of natural resources. I should like particularly to call attention to the remarkable increasing demand for natural resources, to give an analysis of the demand for certain mineral resources, and to direct attention to some problems in satisfying this demand. All industrial power is based on natural resources and the most basic of these are soils, energy resources, and mineral resources. There is a strong interrelation of these resources, more than is obvious, and I shall take up certain aspects from the point of view of a geologist. Few nations are well endowed with all three of the kinds of natural resources I have mentioned and much has been done by some small countries whose peoples are industrious and enterprising and where conditions for free world trade have been favourable. However, major industrial power is dependent on a substantial endowment of all three classes.

Jan 1, 1949

By Alan E. Cameron

WE assemble again today in this comfortable, hospitable Inn to begin this, the 58th, Meeting of our Society. It is just a year ago when last we met but that year was, probably, the most portentious year in the whole history of mankind. In that year, the German 'Atlantic Wall' was broached, the Rhine was crossed, and Germany, as a Nation, has ceased to be. The agony of Europe is over; convalescence may be, probably will be, slow. But blood no longer flows in Europe. Time will heal the sores, cover the scars, regenerate the industries, rebuild the cities, and re-establish the people. True, the war of all wars is not yet over. True, a bloody conflict remains . But, the power of the United Nations now converges on one target. The rain of blood will be heavy. We can hope the storm will be short. The sun is on the horizon. The light of peace 1s in the sky. What of that Peace? Are we ready for it? Have we a 'sure foundation ' for our future world? Are the footings under that foundation broad and substantial? Can we look forward with confidence to a lasting peace and a fruitful life? The United Nations, even as this is being written, are in conference in San Francisco, placing the footings, rearing the foundations for a world edifice. There are bickerings; there are jealousies. The world is tired, and a tired family always squabbles. We can, we must, believe that the decisions they make, the edifices they rear, will be better than anything we each could effect separately. It will be a compromise, probably; it will carry things that will hurt us, just as it will carry things that will hurt others. We can, we must, believe that the good of the whole is a greater good than the good of the part. Each Nation within the United Nations must sacrifice something, each part of each Nation must sacrifice something, each individual within each part of each nation must contribute something, if the whole is to be wholesome. Sacrifice and contribution must be the order of the day if the New World we are about to build is to be worth while. What of Nova Scotia? The world has travelled far in the last year; how far has Nova Scotia gone? Canada has preparations for the Peace under way; what has Nova Scotia done? Is Nova Scotia preparing counter measures for the sacrifices it must make? Is each of us ready to contribute his share?

Jan 1, 1945

By Eurípides do Amaral Vargas Jr., J. A. de Mello Franco

"It is frequently necessary to excavate a tunnel for Civil Engineering purposes, or wells for petroleum exploitation, in laminated rock mass like schists or phyllites or in highly foliated gneisses. The determination of the pre-existing in situ stresses is essential, in order to assure the stability of these excavations. In most cases, the pre-existing triaxial stress field is arbitrary in relation to the tunnel or well axis. For these rock masses the concept of Generalised Plane Strain can be correctly utilized.There are closed form solutions for the calculation of stresses in anisotropic rock masses under Generalised Plane Strain conditions (Lehknitskii, 1981 and Hong , 1994). Based on these analytical solutions, established for the cases of Generalised Plane Strain, a synthetic problem will be formulated: the theoretical in situ stress tensor acting on this rock mass will be determined, with the aid of Bayesian Inverse Problem Techniques, as developed by de Mello Franco (2009). Additionally, the reliability of results obtained will be evaluated, in accordance with the research performed by this author. INTRODUCTIONThe Inverse Problem Technique, as developed in the paper, is based on the definitions and concepts obtained from the current literature and used for the solution of Inverse Problems, but the innovation to be presented is the utilisation of Bayesian Techniques and the determination of the reliability of the results obtained. This will be shown in a synthetic example where the determination of the in situ stress tensor, from strain measurements in a drill hole is supposedly performed. It is assumed that this drill has its axis arbitrarily placed in relation to the rock mass. Generalised Plane Strain conditions will hold for use with problem. The equations of Beltrami – Mitchel, in agreement to Lekhnitskii (1981) and Ong (1994), will be used in this synthetic case, for calculating strains, hypothetically measured in the hole before the final excavations. Finally a synthetic example for the determination of the in situ stress in a fully anisotropic rock mass, based on Bayesian Techniques and its reliability, developed in de Mello Franco (2009) is presented."

Jan 1, 2015

By Jerry Gagnon, Matt Burr, Timothy Ellis, Abbas Mirza, Larry Webb

"The mechanical properties of RSR anode alloys (lead-calcium-tin, 009+ and lead-strontium-tin) were investigated as a function of time with an objective of developing lead anodes for use in high temperature electrolytic processes such as in copper liberator cells and in cobalt and nickel electrowinning. At a temperature of 70 oC, the mechanical properties of rolled RSR lead-calcium-tin (PbCaSn) alloy currently used in copper electrowinning decreased gradually while the mechanical properties of rolled RSR lead-strontium-tin (PbSrSn) decreased relatively quickly and stabilized at low strength levels. Cast PbSrSn started off as the weakest alloy but its properties remained stable with time. Rolled RSR 009+ anode alloy showed improvement in ageing properties over the other alloys tested. However, its mechanical properties did not stabilize in the study timeframe of 284 days. Further investigations are planned to study the effect of alloying elements on mechanical properties of RSR 009+ anode alloy over several years as a function of time at 70 oC. The mechanical properties will be evaluated to determine the time at which they stabilize. Comparative plant trials with rolled RSR PbCaSn and RSR 009+ will also be performed in copper liberator cells and in cobalt and nickel electrowinning tankhouses to determine their mechanical and electrochemical performance at temperatures of 65-75 oC.INTRODUCTIONLead-based alloys are the primary anodes used in the electrowinning of copper, zinc, nickel, cobalt and manganese from sulfate-based aqueous systems. Lead anode technology has evolved over the years migrating from pure lead and lead-antimonial alloys to the present day PbCaSn alloys for copper and PbAg and PbCaAg alloys for zinc electrowinning (Prengaman, Ellis and Mirza, 2010). It has also migrated from cast to rolled microstructures in search of improved mechanical properties and higher corrosion resistance. Although great strides have been made in the development of new lead anode alloys and production processes for lead anodes to be used in copper electrowinning, the industry still has some unresolved issues. These relate to the necessity of having higher mechanical properties especially for the lead anodes in liberator cells in copper electrorefining and for cobalt and nickel electrowinning as these tankhouses operate at temperatures of 65-75 oC compared to 40-45 oC in case of copper electrowinning."

Jan 1, 2016

By Marc Boyer

Modern civilization, modern industry, and modern standards of living, bring into, sharp relief the present-day essentiality of metals .and minerals, and the wide and diversified use which is made of them. Any attempt, therefore, to appraise the international situation today must take into consideration the metal and mineral resources of the world. If, as some believe, the world is divided into two distinct ideologies of political belief, one unalterably opposed to the other, so that armed conflict is unavoidable, then the question of national strength in mineral resources becomes of paramount importance. If, however, it is possible to avoid war by raising the standard of living in the underdeveloped ?areas of the world, thus ensuring all peoples everywhere against the dread spectres of starvation and disease, then the development of the world's mineral resources assumes even greater importance. Today it is difficult to realize that, prior to the industrial revolution in Great Britain, only a few of the metals and minerals now in common use entered into the everyday life of the people. !iron and steel, copper, lead, tin, and zinc, usually in .their unalloyed forms, along with the more common industrial minerals, were those most widely used, and then only in limited amount. With the advance of technology in metallurgy and in fabricating skills, the list of commercial metals and minerals has expanded until today they number more than eighty.

Jan 1, 1951

By H. McLeod

Introduction In the period from 1939 to the present, Canada has experienced a remarkable industrial expansion, rising to probably seventh in rank amongst world countries. In the early part of this period, the desperate need for military supplies unloosed tremendous amounts of capital for building new factories and for expanding and converting existing facilities. Mines, factories, and other divisions of the industrial economy bent every energy toward greater and greater output. The result was an 80 per cent increase in the volume of the nation's production within a period of four years, a truly remarkable accomplishment and one in which the mining industry had a very vital part. After the critical year, 1944, the tempo of industry eased off a bit, dropping approximately 20 per cent by 1946. At this time the prospects or post-war industry were clouded by monetary and political chaos in overseas countries, by trade restrictions, and by market uncertainties. There was, of course, a pent-up demand, both at home and abroad, for civilian goods that had been curtailed during the war and for capital equipment that had been destroyed. In the midst of this world-wide uncertainty, if anyone had ventured to predict that by the end of 1950 Canada's industrial output would be back to the 1944 level and humming along at nearly twice the best pre-war pace, he would have been considered rash indeed. Yet this has been the case.

Jan 1, 1951

By G. R. Guillet

THE LATE Dr. D. F. Hewitt, Ontario's foremost authority on industrial minerals, was the first to point out the importance of urban minerals when he produced figures (Hewitt 1968) to prove that the Toronto-Hamilton area was Ontario's second largest mining camp in 1966 (Fig . 1). In that year, the value of mineral production within a 60-mile radius of downtown Toronto exceeded individually that of Steep Rock, Kirkland Lake, Timmins, Manitouwadge and Elliott Lake. Only the nickel and precious-metal production of Sudbury .surpassed in value that of Toronto's pits and quarries. Although that position was unchanged for some years during the early sixties, it was admittedly an unusual situation: gold was still pegged at an artificially low value; uranium was stagnant; and Texasgulf had not entered the scene. However, the point had dramatically been made. The combined value of production from hundreds of sand and gravel pits and dozens of limestone and shale quarries was of formidable proportions. The mining industry of the urban fringe could not be denied. Construction aggregates, cement, building stone and bricks were fueling an apparently insatiable appetite for urban expansion and redevelopment.

Jan 1, 1978

By Louis Cabot

A pilot plant of the Modular Gold Processing Unit (MGPU) was designed, installed and operated, over a 8 months period, by RSW-Béroma, at the Granada Mine located near Rouyn-Noranda, Quebec. A description of the project geology, plant set up as well as exploitation results, including productivity and profitability curves, are given for a small scale mining operation in comparison with larger ones. Copyright ã 2001 CIM

May 1, 2001

By P. G. Dunn, J. Fitzgerald

ABSTRACT The scheduling of underground mining activities is a complex task that must simultaneously satisfy a large number of constraints. A schedule optimization tool (SOT) for underground mine planning is described, and its use for investigating strategic decisions is illustrated through a case study. The maincomponents of the SOT include (a) a genetic algorithm that searches for optimal schedules, (b) guidance for the application of heuristic rules, and (c) sliding, which implements just-in-time development. Findings indicated that preliminary scheduling performed before invoking the SOT, intended to provide a good starting point for the search, did not ultimately lead to higher value schedules.

Jan 1, 2010

By Stanley Davidson

Introduction The ore deposit mined by Falconbridge Nickel Mines, Limited, is one of the numerous nickel-copper sulphide bodies marginal to the large oyster-shaped mass of differentiated norite in the Sudbury district, famous as the world's most important nickel producing field. The unique character of the ore deposits of the district has resulted in its intensive geological study over a period of more than fifty years. The results of these studies have given rise to a voluminous geological literature and to a great deal of controversy as to the genesis of the ores. This description of the structural geology at the Falconbridge mine is presented in the hope that it may form a small part of the chain of evidence leading to a reasonably satisfactory explanation of the ore genesis. The mine, named after Falconbridge township in which the deposit occurs, lies along the southeast margin of the norite mass which, however, is here concealed beneath a deep mantle of glacial sands and gravels averaging over 100 feet in thickness. As a consequence, the deposit was not discovered by the early prospectors, and it was not until 1916-17 that E. J. Longyear, of Minneapolis, located the ore by drilling. The discovery was foreshadowed in 1899 by the work of Thomas A. Edison, who found indications of the deposit by what is believed to have been a combination of magnetic and electrical geophysical surveys. He sank a prospect shaft over what has to date proven to be the largest and richest ore section in the mine. A wet quicksand layer at the rock surface proved impenetrable, however, and the "Edison' shaft never reached bed-rock.

Jan 1, 1946

By J. Jung, W. Keller, N. Rohn

In hydrometallurgical minerals processing slurries are often processed at very small grind sizes and high solids concentrations. This normally results in flow anomalies of such slurries. Due to flow limits or yield stress the slurry tends to stagnate close to the vessel bottom, the walls and at any internals. The main mixing task therefore generally is not suspending of the solids but the homogeneous blending of the entire vessel volume. If not considered during the agitator design only a fraction of the vessel contents will be mixed. Therefore the knowledge of the slurry rheology as well as the variations in process parameters is vital to design e.g. storage or surge tanks. The integral mixing solution considers the motor power, the choice of the impeller type and number, the impeller diameter as well as the design of the baffles and feed and discharge positions.

Jan 1, 2014

By Bai-ru Xia, Cang-qin Jia, Qi-wu Huang

Limit Analysis Theorems has revealed to be a powerful tool for the development of numerical models aiming the determination of the load bearing capacity of structures reached by plastic collapse. This work presents a numerical formulation for the computation of strict upper bounds of the collapse loads of rigid-perfectly plastic mechanical systems, derived within the kinematical theorem framework. A key advance of this present method is that the problem is described only in terms of nodes and discontinuities connecting those nodes rather than element or bodies. The alternative approximation procedure to the traditional finite element method might involve discretization of a given body using a suitably large number of nodes laid out on a grid, with the failure mechanism comprising the most critical subset of potential discontinuities interconnecting these nodes. Potential discontinuities which interlink nodes laid out across the problem domain are permitted to crossover one another, giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient interior point method solvers can be employed when certain popular failure criteria are specified (e.g. Mohr-Coulomb). By adopting this processing approach it is possible to solve very large problems which normally exceed the memory capacities of a single computer. The developed numerical tool reveals to be robust and versatile, able to solve a wide range of 2D problems. Velocity singularities are automatically identified and visual interpretation of the output is straightforward. Several numerical examples including rock slope are studied by the new method, and the results are very close to those calculated by using analytical method and FEM.

Jan 1, 2015