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By B. W. Wallace

Permitted explosives in South Africa are those explosives approved by the relevant State authority for use in fiery coal mines. The main tests that an explosive must pass for this approval are the gallery tests derived from the Buxton (U.K.) classification. These tests are described briefly. In addition, the safety of permitted explosives is affected by their ability to deflagrate, and to produce a naked flame after blasting, rather than to detonate fully. Tests done on this phenomenon are discussed. A further potential hazard of explosives is after-blast fume. The testing and behaviour of several permitted explosives in this respect are covered, both in the laboratory and in the field. Performance testing of permitted explosives, specifically the double-pipe, underwater, and ballistic mortar tests, and their relationship to field use, are considered in some detail. The application of traditional and new tests to permitted explosives leads to guidelines for the safe and efficient formulation and use of these products.

Jan 1, 1986

By M. Görnerup, M. Hayashi, S. Seetharaman, C. -Å Däcker

The mould flux plays a crucial role in the continuous casting operation of steel due to its multi-functional assignment as lubricator and heat flux controller. In reality, the commercial fluxes can fall short of the expectations of the operator. In such cases, the performance of the mould flux reduces production throughput in the casting machine. This paper presents the results of a study of two different commercial mould fluxes in continuous casting of steels. The results of online sampling during casting, as well as off-line measurements in the laboratory, are presented. Mould flux powder and slag samples from the caster have been characterized with respect to melting behaviour, interfacial tension and thermal diffusivity, using various measuring techniques. An experimental technique has been developed in order to simulate the melting behaviour of a flux in the mould, which has been found to be useful for qualitative studies. A cross-sectional view of different powders reveals that up to four different material layers may exist in the bed: a loosely packed powder layer, sintered layer, semi-solid layer and liquid slag layer. It is found that the melting rate of the mould flux is dependent on the liquid slag layer thickness. Thus, in a continuous casting operation the melting rate is likely to be non-uniform with position in mould due to the difference in liquid slag layer thickness. Mould slag composition is found to be influenced by the starting powder for as long as 30 min, representing a large part of the first heat casting time. Observations of gas formation indicate that interfacial reactions between the steel and slag take place. Keywords: continuous sacting, mould flux, mould slag, properties

Jan 1, 2004

By S. Okubo, K. Fukui

Empirical equations established for estimating the rock strength of the working face based on the cutting forces of a tunnel boring machines (TBM) are further examined and discussed with respect to the dominant factors affecting TBM performance. Constants in the equations are related to TBM-specific parameters such as excavation (tunnel) diameter, cutter diameter, and cutter distance. The relationship between the constants and the TBM specifications is examined in this study on the basis of data collected at ten tunnels, and it is found that the constants are most strongly influenced by the cutter diameter and tunnel diameter. Zur Schätzung der Gesteinsfestigkeit an der Arbeitsfläche ermittelte empirische Gleichungen, die auf den Schneidekräften von Tunnelbohrmaschinen (TBM) beruhen, wurden weiter im Hinblick auf die vorherrschenden, die Leistung der TBM beeinflussenden Faktoren hin untersucht und diskutiert. In der Gleichung enthaltene Konstanten werden zu den TBM-spezifischen Parametern wie Auschachtungs- (Tunnel) Durchmesser, Schneidendurchmesser und Schachtlänge in Beziehung gesetzt. Die Beziehung zwischen diesen Konstanten und den technischen Daten der TBM wird in dieser Studie auf der Basis der bei 10 Tunnelbauten gesammelten Daten untersucht. Dabei wurde gefunden, dass diese Konstanten am stärksten von den Durchmessern der Schneiden und der Tunnel beeinflusst werden. Cette étude examine et discute les équations empiriques permettant d'estimer la résistance de la roche attaquée aux forces de coupe des tunneliers dans le cadre de l'étude des facteurs dominants affectant les performances des tunneliers. Les constantes de ces équations concernent les paramètres spécifiques des tunneliers comme le diamètre d'excavation (du tunnel), le diamètre du couteau et la distance de coupe. Cette étude examine le rapport entre ces constantes et les caractéristiques techniques des tunneliers d'après des données collectées dans dix tunnels et elle conclut que ces constantes sont principalement influencées par le diamètre du couteau et le diamètre du tunnel.

Jan 1, 2003

By J. Gholamnejad

In open pit mine planning and design, push back mine sequencing is widely used for long-term production planning. In push back design, a series of nested pits is generated and then considered as possible push backs with regard to the minimum push back width requirements. These nested pits are produced by parameterizing on one economic parameter like commodity price, mining or processing cost, stripping ratio, etc. The most important characterization of these push backs is that the innermost push back has the highest value per ton, the second innermost push back has the second highest value per ton, and so on. These nested pits are generated based on the best estimates of grade within a representation of the orebody in a three-dimensional matrix form. Therefore, the inherent uncertainty associated with reserve estimation (for our discussion, grade uncertainty) is not taken into account when push backs are designed. These methods do not attempt to establish which part of the deposit is likely to be worth most. This paper introduces a new algorithm that incorporates ore grade uncertainty during the pushback design process. The suggested strategy tries to seek to schedule risky blocks later in the extraction sequence. Keywords: open pit mine, push back, ore grade uncertainty.

Jan 1, 2007

By C. S. Northcote, I. F. Buchan, L. F. Baars

In 1969 the Coal Division of the Anglo American Corporation was awarded the tender to supply coal to the new 3000 MW power station to be erected at Kriel, which is situated midway between the towns of Ogies and Bethal in the eastern Transvaal. The coal was to be supplied from the No. 4 Seam in the Kriel Area of the Witbank Coalfield. The No. 4 Seam in this area varies in depth of overburden from 75 m to 6 m, with an average of 55 m. Initially, the mine was planned as an underground mine incorporating a three-shaft system for transporting some 8 million tons of coal per annum to the power station. As the result of negotiations between Anglo and Escom to improve the volumetric extraction of coal from the new mine, the Kriel Division of Anglo Power Collieries was finally planned to produce 4,1 million tons of coal from an underground mine and 4,5 million tons from an opencast mine, with a resultant increase in volumetric extraction. This paper describes the opencast operation at Kriel, with particular reference to the water problems encountered and to the operation of the draglines on sloping ground to a depth of 40 m to the top of the coal seam.

Jan 1, 1980

By P. J. Foster

A common theme running through recently introduced mining health and safety legislation in many parts of the world is risk assessment. Most recently, risk assessment legislation has been introduced across the mining industry of South Africa and the view that the introduction of risk assessment based legislation provides an ideal opportunity to improve on past health and safety performance is presented. Risk assessment techniques range from highly complex safety system techniques that are used in high technology process industries, to subjective techniques based on simple judgements that are finding use in many other industries. The objective of this paper is to shed some light on risk assessment, not by detailing the risk assessment process but by identifying the crucial elements that need to be considered if risk assessments are to be successful in changing health and safety performance. A case study is presented illustrating the introduction of risk assessment into the Ingwe Coal Corporation, one of South Africa?s largest mining houses, to indicate how the system was developed and how it is being used.

Jan 1, 1998

By V. V. Nazimko, A. I. Hohotva, S. N. Alexandrov, V. P. Sazhnev, V. S. Zaharov

Ground behaviour in the vicinity of a roadway has been investigated using a physical model and in situ tests during a roof fall. It was discovered that behaviour of the ground is governed by irreversible displacements of adjacent rock clusters. The cluster is a short-living sector of a rock mass that moves as a solid body. For the lack of degree of freedom, the rock mass must be divided into clusters that are forced to move one after another in space and in time. These clusters permanently rearrange and reform during irreversible (inelastic) ground deformation. The crowded clusters have to yield to each other and alter their velocity and direction of movement to accommodate their motion into the excavation. Such behaviour involves uneven and irregular vertical deflection and the movement of adjacent rock blocks in the roof, sides and floor of an opening. Such movement destroys the symmetry of horizontal displacements with respect to the centre line of the opening. A set of indicators that a roof fall is imminent has been identified. Horizontal displacements and dilation must be controlled in order to maintain the stability of an underground opening. Such a state retains the self-supporting effect of the roof and contributes to rock bolts bearing capacity.

Jan 1, 2003

By Jerry Gagnon, Matt Burr, Dave Evans, Timothy Ellis, Davies Kakengela, Abbas Mirza, Larry Webb, François Leclercq, Andrew Johnston

Lead-based alloys are the primary anodes used in electrowinning from sulphate-based aqueous systems. Lead anode technology has evolved over the years, migrating from pure lead and lead-antimonial alloys to the present day lead-calcium-tin alloys for copper electrowinning and lead-silver alloys for zinc electrowinning. 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 alloys and production processes, the industry still has unresolved issues related to untimely corrosion which limits anode life and may lead to higher contaminant levels in the metal being produced. Lead anodes corrode because of the difference in the chemical/electrochemical potential across the microstructural features of an anode. Given a very high purity material, we find that the grain boundary areas corrode significantly faster than the rest of the grain. The desire to minimize grain boundary corrosion by a balance of alloying element selection and microstructural design allows the grain boundary area to be engineered. However, operational issues can lead to unexpected corrosion behaviours which we will discuss moving forward. The comments in this work, though directed toward copper electrowinning, can be extended to similar phenomena in other metals electrowon from sulphate media (i.e., zinc, nickel, cobalt, manganese). The lifecycle of electrowinning anodes is dependent upon electrowinning tankhouse operating conditions and maintenance of the anodes, including cleaning and straightening. This paper will focus on the operational aspects of maximizing the utilization of lead electrowinning anodes.

Jan 1, 2015

By B Vorster

Falls of Ground is one of the highest causes of incidents, accidents and fatal injuries in our mines today. These falls of ground may occur as soon as the face is exposed after blasting or after machine cutting. The falls of ground can also occur after support has been installed. There are many reasons why these falls occur before and after supporting of the face. It is therefore important to support the exposed face as soon as possible to prevent the falls of ground. It is also very important to support the face with the correct support products and to support the face as designed and required by the mining engineers. The possible reasons for falls of ground, possible support methods and the products available will be discussed in this presentation. In typical conventional narrow vein stoping operations, the use of conventional temporary support components to offer some support to workers, whilst the permanent and generally more elaborate support system gets installed or constructed, still results in injuries to people. The author wishes to discuss the following items in this paper:- ? Introduction ? Basic face behaviour after exposure ? Controllable Parameters ? Mining Engineers support designs ? Primary and Secondary Support ? Products available for prevention of falls of ground

Jan 1, 2008

By R. Butcher

Mud rushes are hazardous occurrences that have occurred frequently in mines in South Africa, and have been the cause of numerous fatalities in the past. Mud rush incidents not associated with accidents are believed to be common occurrences that are not generally reported. Many such incidents are probably associated with the operation of chutes and box fronts. This paper describes the conditions necessary for mud rush occurrences, postulated mud rush mechanisms, and methods of combating the mud rush hazard.

Jan 1, 2005

[Consider the situation where we wish to estimate the value of a block of ore W from the values of n samples wt (i = 1, 2.... n). The samples can be located anywhere inside or outside W. The blocks and the samples can have any size or shape (Fig. 8.1). We define ws as the set of all the samples wi: WS = Iw1; W2; W3.. . wn and we wish to estimate the block W using the samples ws. Let xi be the value of the ith sample and µw the unknown average value of the block. We can estimate µw from the average value of all the samples. Let µw be the estimator of µw. As the samples need not be of equal size, the sample average is: µw = wi xi/~ wi. (8.1) The mean squared error made when estimating µw by µw is known as the variance of estimation of W by ws. It is the error made when giving the value of the sample set ws to the block W and is written o2E (WS to W). By definition: o2E (ws to W) = E [(µw - µw)2]. (8.2) If n = 1, this error is known as the extension variance. Since the sum of the weights given to the sample values is equal to 1,0, the estimator µw is unbiased (the question of the absence of bias is studied in more detail in Chapter 9): E [( µw - µw)1 = 0. (8.3) The error (µw - µw) has zero mean and a variance o2E = E (W8 to W). If we assume that this error is normally distributed, we can define confidence limits for µw. Let tP be the value of the standardized normal variance t such that the probability that t is less than tP is p: (t,) = .\/27T f exp (- t2/2) dt = p (8.4) The probability that µw is larger than µw + t1-P oE is p. The probability that µw is smaller than µw- t1-P oE is p. The following approximation formulae are often used to calculate 2p central confidence limits for the block value: 68% central confidence limits (p = 16%): µw - o2E, and µw + o2E. 95 % central confidence limits (p = 2,5 %): µw - 2 oE, and µw + 2 oE. Tables of the function 0 can be found in any textbook on statistics (for example, Fraser, 1958, p. 388) (see Table 7.2). [ ] The last line of Table 2.2, corresponding to f = 00, also contains the value of tP for p = 80, 90, 95 and 97,5 %.]

Jan 1, 1978

By L. G. Stolarczyk, J. Duncan

"SynopsisLong before the environmental movement, coal miners were suffering from occupational diseases that became apparent in the later years of service, and especially during the retirement years. Chronic exposure to micro-fine dust in the respirable range (‘float’ dust) causes various lung diseases, referred to as coal mine dust lung disease. In the USA alone, 76 000 miners have died of coal mine dust lung disease since early legislation recognized the issue in 1969. Researchers believe that reducing float dust exposure limits alone will not reverse the increasing incidence of coal mine dust lung disease seen in the current generation of miners. Trace and radioactive metals are concentrated in the thin boundary layers of the coal seam (Roberts, 2013), and hence float dust includes silica and toxic trace metals. The production and quality of coal is also significantly impacted by the presence of these contaminants in the coal. In the combustion process, the trace metals are oxidized and become incorporated in the fly ash and flue gas. Since they are extremely water-soluble, they represent a significant danger to health and the environment. Coal preparation plants and power stations need to mitigate these contaminants as far as is practical, but the simple fact is that most contaminants should have been left un-mined.This paper describes an innovative coal-cutting solution to the longstanding technology gap in mining – the ability to measure uncut coal layer thickness to the boundary rock layer. Because of constant changes in geology, seam thickness, and seam undulation, the horizon sensor must be located in the bit-block of the rotating cutter drum of the mining machine. Contaminants in ROM coal must be minimized at the source – that is, at the rock/coal crushing cone directly under the bit-tips of the cutting drum. Bittip distances to the rock boundary layer must be automatically controlled in real time when mining in a complex and undulating coal bed. Horizon sensing (HS) technology enables the mining machine’s cutting picks to stop at a specified distance from undulating horizons of the boundary rock. The thin contaminated coal layer can be left in situ, significantly reducing the toxicity of the float dust. Preventing the metal picks from striking quartz-containing boundary rock also reduces the occurrence of methane ignitions. HS technology equipped with pick force vector sensing can allow optimization of the cutting pick lacing pattern for minimum coal and rock crushing, thereby reducing float dust. This technology may enable the mining industry to convert from automated machine control to autonomous during coal cutting and loading."

Jan 1, 2015

By Y. I. Yang, Y. -B. Tang, D. -J. Ma

Chlorine-containing minerals are commonly present in coal. Associated minerals such as pyrite can undergo exothermic reactions. Consequently, it is of great significance to study the effect of inorganic chloride on the spontaneous combustion of coal. In this study, the effects of five inorganic chlorides (sodium chloride, magnesium chloride, potassium chloride, calcium chloride, and zinc chloride) on the spontaneous oxidation of coal were investigated. Analysis of the gaseous products of coal oxidization at low temperatures (323K to 453K) showed that the presence of inorganic chlorine in coal markedly decreases O2 consumption and the generation of CO and CO2. Samples of raw coal and chlorine-loaded coal were oxidized for 36 hours under the same experimental conditions. Infrared diffuse reflectance spectroscopy results showed that inorganic chloride can inhibit the oxidative decomposition of some functional structure components (methyl, methylene, methine, and hydroxy) in the coal. The influence of inorganic chloride on the oxidation characteristics of the functional groups in coal during spontaneous combustion was investigated using benzyl alcohol and 1-phenylpropanol as model compounds, which were tested under the same experimental conditions as the coal samples. The oxygen consumption of model compounds with and without the addition of inorganic chloride further suggested that inorganic chloride may hinder the oxygenolysis of these structures during low-temperature oxidation. This phenomenon can be attributed to the radical reaction from the perspective of radical chemistry. It can therefore be concluded that inorganic chlorides play an inhibitory role in the spontaneous combustion of coal.

Jan 1, 2015

By C. Sahyoun

The influence of microwave treatment on copper flotation has been investigated. Comparative batch flotation tests carried out on ore treated at 5?12 kW for 0.1?0.5 s showed that improvements in copper recovery of between 6?15 % could be achieved compared with untreated ore. Both recovery and cumulative grade increased with increasing treatment time and power. A preliminary economic analysis showed that microwave treatment will be economically viable if recoveries similar to those determined on laboratory scale can be achieved on a plant. Keywords: microwave treatment, copper ore, flotation, liberation, recovery

Jan 1, 2005

By C. Wade, A. Swart, M. Dworzanowski

AngloGold Ashanti operate a pyrite flotation plant at their East Gold Plant, Acid Plant and Flotation Plant (EGAF) metallurgical complex within their Vaal River operations in the North West province in South Africa. The flotation plant feed is reclaimed pyrite rich tailings and the concentrate produced is used as the source of sulphur for the EGAF acid plant. The sulphuric acid produced is in turn used for the recovery of uranium at the Vaal River South uranium plant. The original flotation plant built in 1960 was based on the use of many small volume flotation cells and was becoming very expensive to operate and its age severely limited further operation. A decision was taken in 2005 to replace this plant with a new one based on fewer, larger volume flotation cells. This paper describes the benefits of using larger volume flotation cells in this new flotation plant when compared to the smaller volume flotation cells in the old plant. The benefits of the new plant include a smaller plant footprint, fewer flotation cells, fewer pumps, no distribution boxes, simpler piping, a greater flotation volume and a reduction in installed power. The saving in capital cost could not be quantified because of the age of the old plant. The savings in operating cost will arise from fewer operators, less maintenance and reduced power consumption. The new plant has not been in operation long enough to quantify the benefits in operating cost and metallurgical performance. However, recovery improvements can be expected given the greater flotation volume (increased residence time) and the installation of larger, more efficient flotation cells.

Jan 1, 2007

By P. J. van Staden, T. W. Walker

The Minfurn is a novel carbon-regeneration furnace developed at Mintek. It combines the advantages of direct resistive heating in a vertical-tube furnace with those of continuous operation, in a furnace whose capital, operating, and maintenance costs compare favourably with those of conventional rotary kilns. After successful tests under experimental conditions on carbons containing different contaminants, a 3 kg/h unit was installed on the carbon-in-pulp (CIP) plant at the Klipwal Gold Mine near Piet Retief, where it has been operating at, on average, 123 per cent of its design capacity. Since the installation of the Minfurn, monthly average losses of dissolved gold of less than 0,02 p.p.m. have been maintained for several successive months for the first time since January 1989. It is also possible that the monthly average residue values have been reduced. Further improvements to the carbon circuit are possible, and the possibility of making further savings by a reduction in the carbon-throughput rate still needs to be investigated. The mathematical modeling of the furnace has progressed to the stage where the future scale-up and design of the Minfurn can be carried out by simulation of the performance of different designs, and choosing the design that yields the desired performance.

Jan 1, 1993

By J. W. van der Merwe

Technology is advancing at a rate that makes it extremely difficult for the mining industry to keep pace. Many advances occur within a given piece of technology and often this is missed by the disciplines that could have gained advantage by its implementation. Often this may have been simply an aspect of cost exceeding benefit. However, there are some technologies that potentially have such a far-reaching impact on the mining industry that the benefits simply outweigh the cost. The application of 3D laser scanning in the mining industry has the potential of taking the concept of 'Google maps?' underground. This presents an opportunity where the virtual world of underground can be traversed with relative ease and many aspects of measurements could be obtained without having to visit the working place again, potentially saving countless man-hours and still delivering precision work with significant savings in downtime, stoppages, and exposure to safety incidents. Anglo American Platinum maintains its competitive advantage though the review and application of appropriate technology. This paper describes the 3D laser scanning trial at one of Anglo American Platinum's new shafts, and goes on to show the benefits encountered through the application and the involvement of the various MRM disciplines.

Jan 1, 2013

By J. -P. Tshibangu, A. Vervoort, A. Lavrov

Abstract: The aim of the research presented is to study the effect of complex loading schemes on the fracturing process during loading and/or unloading. A first set of experiments was done using a poly-axial cell. These experiments in combination with numerical simulations showed a difference in micro-fracturing (shear and tensile cracks), but not in macro-failure between various loading/ unloading schemes. The second set of experiments was based on the three-point bending test and several cycles with or without rotation between cycles were applied. If the specimen was rotated by 90° or 180° about its long axis between the first and second cycle, no Kaiser effect was observed. Résumé: Le but de la recherche présentée est d’étudier l’effet de schémas de charge complexe sur le processus de fracturation durant la phase de charge et de décharge. Une première série d’expériences était réalisée utilisant une cellule polyaxiale. Ces expériences combinées avec des simulations numériques ont montré une différence de micro-fracturation (fissures de cisaillements et de traction) pour les différents schémas de charge et décharge, mais en ce qui concerne la macro-fracturation ce n’est pas le cas. La deuxième série d’expériences était basée sur des essais de flexion trois points avec plusieurs cycles, avec ou sans rotation entre les cycles. Si l’échantillon est tourné de 90° ou 180° selon le grand axe entre le premier et le second cycle, l’effet Kaiser n’est pas observé. Zusammenfassung: Der Zweck der vorliegenden Forschung bestand darin, den Einfluß von komplizierten Beanspruchungsschemen auf den Bruchprozess im Laufe von Belastung und/oder Entlastung von Gesteinen zu untersuchen. Der erste hier beschriebene Satz von Experimenten wurde mit einer dreiaxialen Belastungsmaschine angestellt. Diese Experimenten zusammen mit dazugehörigen numerischen Simulationen zeigten Unterschiede zwischen Be- und Entlastungsbeanspruchungen in Bezug auf mikrobruchmechanische Mechanismen (d.h. Scher- oder Zugrisse) an, aber nicht in Bezug auf den Makrobruchprozess. Der zweite Satz von Experimenten umfasste Gesteinsbeanspruchung in mehreren Zyklen von Drei-Punkt-Biegung, indem die Gesteinsproben zwischen den Zyklen um einen angegebenen Winkel (0°, 90° oder 180°) gedreht wurden. Falls die Probe um 90° oder 180° gedreht wurde, wurde kein Kaiser-Effekt im zweiten Zyklus beobachtet.

Jan 1, 2003

By J. Danoczi

Specially designed X-ray machines are used extensively on diamond mines for the recovery of diamonds from ores. These machines are extremely expensive and, at present, there are no reliable methods of determining if the equipment is performing efficiently. The objective of this work was to manufacture translucent X-ray diamond simulants, which would emit varying but known luminescence signals when exposed to X-rays. These X-ray diamond simulants could then be used to determine the efficiency of diamond recovery operations.

Jan 1, 2008

By Harushige Kusumi, Yuzuru Ashida, Toshiki Watanabe, Toshifumi Matsuoka

ABSTRACT: The technique of various kinds of numerical analysis offered remarkable results to explication of many rock mechanical phenomena. These techniques regarded a rock stratum as a continuum body and solved the governing equation of continuum mechanics by using finite differ-ence method, finite element method and/or others. Using numerical analysis based on continuum mechanics, however, the simulations of destruction phenomena caused by elastic waves and on the other hand, the elastic wave propagation which generated by fracturing events are quite difficult. In this paper, we express a rock stratum by a granular body model and develop a simulation tech-nique can simulate both wave phenomena and destruction phenomena at once. The DEM (discrete element method) simulation results are compared with finite difference solutions of elastic wave equation. Furthermore, we simulate Hopkinson effect by this proposed method. Hopkinson effect is famous as a destruction phenomenon caused by elastic wave propagation. ABRISS: In dieser Studie drücken wird eine Felsschicht durch ein Granularkörpermodell aus und entwickeln eine Simulationstechnik, die sowohl Wellenphänomene als auch Zerstörungsphänomene simulieren kann. Die Ergebnisse der Simulation mit DEM (Diskrete-Elemente-Methode) werden mit denen der Finit-Differenz-Lösung von Gleichungen elastischer Wellen verglichen. Desweiteren simulierten wir den Hopkinson-Effekt mit dieser vorgeschlagenen Methode. Der Hopkinson-Effekt ist als Zerstörungsphänomen berühmt, verursacht durch Fortpflanzung elastischer Wellen. RESUME: Dans cette étude, nous exprimons un lit de roches par un modèle à corps granulaire et développons une technique, permettant de simuler d'un coup le phénomène des ondes et le phé-nomène de destruction. Les résultats de la simulation DEM (méthode d'éléments discrets) sont comparés aux solutions à différence finie de l'équation d'ondes élastiques. En outre, nous simulons l'effet d'Hopkinson par la méthode proposée. L'effet d'Hopkinson est connu comme phénomène de destruction, causé par la propagation d'ondes élastiques.

Jan 1, 2003