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By M. S. M. Aljuhani

In this paper, one of the human factors that affect productivity in an underground gold mine in Saudi Arabia was investigated and analysed for the purpose of improving productivity. The human factor that was investigated is labour utilization and labour productivity. In the selected mine, labourer?s performances were measured carefully. It was found that in this mine, workers spend only 65% of the shift time in a productive work, and they spend 35% of the shift time in non-productive activities. As a result, recommendations were presented to enhance productivity in the selected underground gold mine by enhancing labour utilization.

Jan 1, 2002

By C. Ware, R. Uken, G. Whitmore

The coastal dune cordon of northern KwaZulu-Natal is among the highest in the world reaching heights in excess of 180 m and up to 2 km in width. It comprises a complex system of Quaternary stacked dunes of various geomorphologies, types and ages (Sudan, 1999; Maud and Botha, 2002;Ware et al., 2001; Ware, 2003). The dunes contain economic heavy minerals that have been exploited for the last two and a half decades. Dune units have recently been defined based on sand composition and texture(Sudan, 1999; Ware, 2003). Despite this, little work has been undertaken on the clay-fraction (< 2 um). This work documents the weathering of dunes to form clays. From the documented clay assemblages and relative abundances, a simplified weathering sequence with increasing maturity can be summarized as follows: primary minerals ? illite + vermiculite ?illite +interstratifications ?illite + montmorillonite ?halloysite + interstratifications + kaolinite ?kaolinite. The dominant controlling factors in determining clay assemblages is pH and leaching conditions. The presence of carbonates results in an alkaline pH and high concentrations of Ca2+and Mg2+which favours the formation of montmorillonite and vermiculite. However, vermiculite tends to form under slightly acidic conditions and is indicative of palaeosols where organic acids produce localized acidic pH’s. In contrast to this, kaolinite will only form and concentrate when carbonates have been leached. Kaolinite dominated samples are considered very mature under current climatic conditions(Chamley, 1989). Halloysite represents a transitional phase between montmorillonite and kaolinite (Herbillon et al., 1981). Ion mobility and evacuation is also critical in determining clay assemblages. Past work and field studies indicate that the dune cordon acts as an open system, resulting in carbonates and mobile ions being readily leached and lost from the system. However, when prolonged weathering has caused an accumulation of fine-grained material, the permeability decreases substantially whereby mobile cations and silica cannot be readily evacuated. This results in the formation of montmorillonite rather than kaolinite, even when carbonates have been leached. Illite (sericite) is considered to alter directly from feldspars. However, dune stacking and geometries, vegetation, water fluxes, reworking and erosion complicates this sequence.

Jan 1, 2003

By P. J. Bhonde, R. D. Angal

Conventionally low carbon ferromanganese is manufactured globally by refining high carbon ferromanganese in liquid state. This process is an expensive and lengthy technique. Hence, the present work was undertaken with the objective of understanding the feasibility and kinetics of the solid state refining of ferromanganese. The process involved transformation of carbon rich carbides viz. Mn3C2, Mn7C3 into metal rich carbide i.e. Mn15C4, Mn23C6 by subjecting the alloy powder to a flowing stream of carbon dioxide. Effect of the process governing parameters such as time, temperature, particle size, pressure on the extent of decarburization was studied. Without any loss of manganese in the form of fumes or slag, it was observed that, there was substantial reduction, viz. 65 per cent in the total carbon content, by this technique. Subsequently, the process was investigated to find out the mechanism of carbon removal. Depending upon the temperature and the particle size, it was found that the rate controlling mechanism changes from chemical reaction control to product layer (ash) diffusion control. The activation energy for each of the aforesaid mechanism was computed. The values thus obtained substantiated the aforesaid mechanisms.

Jan 1, 2004

By Elizma Ford, Vincent Sithole

"Two shortened test procedures for estimating the Bond ball work index are compared for suitability of use on Zambian/DRC-type copper–cobalt ores. The first procedure is based on a batch milling test while the second procedure is based on a limited locked-cycle test. Both procedures were conducted using a standard Bond test mill. INTRODUCTION The Bond ball work index is widely used in the field of minerals processing as an indicator of ore grindability. The work index is determined by means of a locked-cycle test procedure that typically requires seven to eight cycles to stabilise at a re-circulating load of 250%. A typical test requires between three to four kilogram of ore sample and around eight hours of operator time. For geometallurgical test work applications, where a large number of variability samples are to be tested, it would be highly beneficial to use a test procedure that requires less sample mass and operator time. Certain test work laboratories, for example SGS and JK Tech, are already offering various types of shortened test procedures for estimating the Bond ball work index. This paper discusses a comparison of two shortened test procedures that were evaluated for suitability of use on Zambian/DRC-type copper–cobalt ores. EXPERIMENTAL Test Procedure 1 – Batch Milling The first test procedure is derived from a batch milling approach proposed by the University of Hacettepe (Aksani, 2000). Some modifications were, however, made to the data analysis method from that originally proposed. During this test procedure, a 700 mL volume of sample is milled in a standard Bond test mill for a pre-determined number of revolutions. The feed and product particle size distributions are measured for each test. These results are then used to back-calculate a cumulative breakage rate parameter (k) for each particle size, according to the following formula:"

Jan 1, 2015

By S. K. Murphy, K. B. Le Bron, A. K. Ward, S. Hayes, T. Rangasamy

A process for evaluating different options for extraction of mining blocks is presented. The process is described and an example of the application of the process to a case study is presented. Un procédé pour évaluer différentes options pour l’extraction de blocs d’exploitation est présenté. Le procédé est décrit et un exemple de l’application du procédé à un cas particulier est présenté. Ein Prozeß für das Auswerten der unterschiedlichen Optionen für die Extraktion von Abbaublöcken wird dargestellt. Der Prozeß wird beschrieben und ein Beispiel der Anwendung des Prozesses zu einer Fallstudie wird dargestellt.

Jan 1, 2003

By S. E. Olsen, M. Tangstad

The main source of Mn in raw materials for SiMn production is Mn-ore and Mn-rich slag from the high carbon FeMn production. The amount of slag per tonne of SiMn metal is mainly determined by the ore/slag ratio. Increasing share of FeMn slag at expense of Mn-ore will lead to larger slag/metal ratio in the SiMn process. High volume of slag leads to an increased consumption of energy and probably to higher losses of metal inclusions in the final slag. Excavation of a SiMn furnace has shown that only modest pre-reduction of Mn-ore with CO gas seems to be obtained. Nearly all reduction of MnO was finished at the top of the cokebed. Dissolution and reduction of quartz obviously takes place in the cokebed zone after the main reduction of manganese oxide is finished. Probably the ?pick up? of Si in the metal is quite fast and takes place as the metal trickles down through the cokebed towards the metal bath. The distribution of Si between SiMn alloys and multicomponent MnO-SiO2-CaO-Al2O3-MgO slags is mainly determined by the process temperature, the silica content of the slag and its R-ratio = (CaO+MgO)/Al2O3. As an example, the equilibrium content of Si in the alloy will increase by about 6 % if the R-ratio is reduced from 2 to 1, provided constant temperature and silica content. The effect of temperature is also considerable. The equilibrium content of silicon will increase by approximately 6 % per 50°C in the temperature range 1550°C to 1700°C. The equilibrium content of MnO in SiMn slags depends first of all on the temperature and secondly on the silica content of the slag. At 1600°C the MnO content decreases from about 9 % at silica saturation to a minimum of about 3-4% when the silica content is reduced to about 40-45%.

Jan 1, 2004

By J. Griesel, P. H. F. Bouwer, K. Bisaka

Transalloys produces 160 000 tons of SiMn per annum from five AC submerged-arc furnaces. The lime-ore melt from two AC open-arc furnaces is contacted with SiMn to produce 50 000 tons of medium carbon FeMn per annum. Metallics in the slag are reclaimed in a jigging plant, which has been in operation since 1999. The flow of materials between the jigging plant and furnaces has been optimised. The amount of recycle slag in the feed of the SiMn furnaces has been decreased by more than 30% which still provides satisfactory stability of the furnace operation. The jigging plant has absorbed all the additional slag generated, to recover SiMn metal. A review of the raw materials used and operating parameters for SiMn production was also undertaken. Slag to metal ratios were decreased by more than 30% by reducing the slag recycle, removing magnesite from the recipe and introducing high-grade ore. Electrode penetration was improved by reducing coke levels and by utilising more reactive coal. The pitch circle diameter (PCD) was reduced to get a better operating stability on furnace no 5 using the MINSTRAL Control System. Energy consumption on the furnaces improved by more than 15% while SiMn production increased as a result by more than 18%.

Jan 1, 2004

By Ch. Schroeder, F. Collin, R. Charlier, Y. J. Cui

The paper proposes two numerical models ot the mechanical behaviour of chalk. First, an elasto-plastic constitutive law reproduces the different plastic mechanisms of the chalk and the influence of pore fluids by introducing the concept of suction. Secondly, a model able to reproduce time dependence behaviour. Eventually, the paper gives a simulation of an academic reservoir during depletion and waterflooding phase. Der Artikel stellt zwei numerische Modelle des mechanischen Verhaltens der Kreide vor. Das erste ist ein elasto-plastisches Modell, das verschiedene plastische Mechanismen der Kreide und den Einfluss von Porenflüssigkeit, unter dem Begriff der Suktion, reproduziert. Das zweite Modell berücksichtigt darüberhinaus das zeitabhängige Verhalten. Schliesslich zeigt die Veröffentlichung eine Simulation einer theoretischen Lagerstätte während der Entleerung und der Wasserinjektion. L&apos;article propose deux modèles numériques du comportement mécanique de la craie. Le premier est une loi élasto-plastique qui reproduit les différents mécanismes plastiques de la craie et l&apos;influence du fluide interstitiel par l&apos;introduction de la notion de succion. Le second est un modèle prenant en compte les effets différés. Enfin, l&apos;article présente une simulation d&apos;un réservoir académique durant les phases de déplétion et d&apos;injection d&apos;eau.

Jan 1, 2003

By I. V. Lunkin, E. B. Rakishev, B. R. Rakishev

In mining the method of statistical tests is used by solving of problems, exposing to influence of random factors. Such problems are: rational selection of equipment set; co-ordination in time of different processes; interaction between some processes and kinds of works. Usually it is considered that Monte Carlo method proves its value in the first place in that problems, which allow theoretical-probabilistic description. Analysis of numerical solution of mining-economic problems shows that the method of statistical tests may be used successfully by solving of determinate problems, which are solved usually analytically or by the methods of mathematical programming. We are talking about the problems of optimal use of resources, expedient placing of equipment, effective use of investments, rational planning of stripping and extracting works, groups of mining enterprises and about different variants of transport problem. In the report possibility of the method use is studied at an example of typical technical-economic problems solving. By solving of these problems the variant of the method with uniform distribution of random quantity had been applied and built-in random number generator of visual modelling system VisSim had been used. By algorithms elaboration it seems very perspective to use combination of the Monte Carlo method with traditional methods of numerical solving of the problems (methods of linear, nonlinear and dynamic programming and so on). Keywords: method of statistical tests, mining-technical problems, diapason of random number sample, efficiency function and its extremum.

Jan 1, 2003

By H. Willenberg, J. S. Coggan

ABSTRACT: Although individually both continuum and discontinuum numerical analyses provide useful means to analyze rock slope stability problems, complex failures typically involve mechanisms related to both existing discontinuities (i.e. discontinuum) and deformation and brittle fracture of intact rock (i.e. continuum). One such example is the 1991 Randa rockslide in the southwestern Swiss Alps, where failure involved several complex mechanisms, which require the consideration of progressive failure and rock mass strength degradation. This paper presents results from a series of hybrid finite-/discrete-element models directed towards the explicit modelling of brittle fracturing in natural rock slopes, enabling the modelling of progressive failure, from initiation, through to the development of catastrophic failure, transport and deposition. RÉSUMÉ: Si les modélisations numériques de type continu ou discontinu fournissent des outils utiles pour l’analyse de problèmes de stabilité de pentes rocheuses, elles montrent de sérieuses limitations lorsque des mécanismes de rupture complexes impliquent des processus liés autant aux discontinuités préexistantes qu’au développement progressif de nouvelles fractures. Ceci se retrouve typiquement dans l’exemple de l’éboulement de 1991 à Randa dans les Alpes suisses du sud-ouest, où la rupture a impliqué plusieurs mécanismes complexes nécessitant la prise en considération de la fracturation progressive ainsi que de la dégradation de la résistance des masses rocheuses. Cet article présente des résultats provisoires d&apos;une série de modèles hybrides orientés vers la modélisation explicite de la fracturation de pentes naturelles, permettant la modélisation de fractures progressive de leur initiation jusqu’à leur développement, leur rupture catastrophique, leur transport et leur déposition. ZUSAMMENFASSUNG: Obwohl numerische Kontinuum- und Diskontinuum-Berechnungen einzeln nützliche Ergebnisse zur Stabilitätsanalyse von Felshängen liefern, sind komplexe Felsrutschungen typischerweise mit Mechanismen verbunden, die sowohl durch bestehende Trennflächen (s.a. Diskontinuum-Ansatz) als auch durch die Deformation und das Versagen intakter Felsbereiche (s.a. Kontinuum-Ansatz) bedingt werden. Ein Beispiel für einen solchen Sachverhalt ist der Bergsturz von Randa 1991 im südwestlichen Teil der Schweizer Alpen, bei dem die Rutschung mehrere komplexe Mechanismen umfasste, so dass “progressive failure” und Verminderung der Gebirgsfestigkeit in Betracht gezogen werden müssen. Dieser Artikel beschreibt vorläufige Ergebnisse einer Reihe von hybriden Modellrechnungen (Finite-/Diskrete-Elemente). Diese haben zum Ziel, explizit das bruchhafte Versagen natürlicher Felshänge zu modellieren, wobei das progressives Versagen im ganzen modelliert wird, von der Anfangsphase über die Entwicklung zum katastrophalen Versagen und den Transport und die Ablagerung der Rutschmassen.

Jan 1, 2003

By K. Cybulski

In 2002 a coal dust explosions occurred in the Polish collieries “Jas-Mos” and “Rydultowy” in the Upper Silesia coal basin. In the “Jas-Mos” colliery the coal dust explosion was initiated in the face of gallery by explosives and causing ten death. The stone dust barrier extinguished the flame, stopped the explosion development and saved forty nine miners working in that area. In the “Rydultowy” colliery methane inflammation caused three deaths and seven serious burns and ignited the coal dust explosion. The coal dust explosion was stopped by stone dust barrier and did not cause any victims itself. This paper presents the investigation carried out by the Central Mining Institute Experimental Mine “Barbara” and shows that the stone dust barriers remain still a basic mean for suppression of coal dust explosion in mines. The investigation were aimed at determining the cause of explosion and circumstances that led to their propagation. The evaluation of the state of dust explosion hazard in the areas of accidents have been performed, and the range of flame estimated.

Jan 1, 2003

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 Durell Denysschen, Rafael Abela

The recovery of gold from old mine dumps has been carried out over the last two decades. The gold value and price together with recovery methods, determine whether it is economical to process a dump. Pre-concentration with cyclones and spiral concentrators may offer a method to process dumps considered currently uneconomical to treat.

Jan 1, 2006

By Andrew Jones

This paper discusses the worldwide market and cost environments for the bulk ferroalloys namely manganese alloys (ferromanganese, silicomanganese), ferrosilicon and ferrochrome (high-carbon ferrochrome, charge chrome). Annual average market prices since 1993 are presented graphically and analysed, and the main supply and demand trends for manganese, ferrosilicon and ferrochrome are summarized. The paper shows carbon and stainless steel output data for 1995, 2000 and 2005, mainly to demonstrate the rising importance of China as a ferroalloys market. Developments in ferroalloys capacity worldwide from 1991 to 2007 are discussed (plant start-ups and closures, ownership changes). Finally, the paper examines developments in the main cost factors for the bulk ferroalloys, i.e., chrome and manganese ore, electricity, carbon reductants and labour. Note that data for 2006 are estimated based on information available in November 2006.

Jan 1, 2007

Dr R. E. Robinson, Pr. Eng., obtained a B.sc. (Chem. Eng.) cum laude from the University of the Witwatersrand in 1950 and a Ph.D. (Eng.) from the same University in 1953, where he was awarded the Haikes Memorial Medal for Industrial Chemistry. Professor G. G. Garrett was appointed Professor of Physical and :Fabrication Metallurgy in the Department of Metallurgy at the University of the Witwatersrand in June 1980, and in January 1984 he became Head of the Department. Mr P. A. van Wielligh, Pr. Eng., climbed the mining ladder in the hard way, starting as a Mine Surveyor in 1936 and working his way up as Chief Surveyor, Underground Manager, Mine Manager, and Consulting Engineer, to Executive Director, including the intermediate steps. Mr H. E. James, Pr. Eng., is a graduate in Chemical Engineering from the University of the Witwatersrand. Both his B.sc. degree (1961) and his M.sc. degree (1964) were obtained on bursaries, the former from Gold Fields of South Africa and the latter from the Atomic Energy Board. Mr G. Pienaar, Pr. Eng., obtained a B.Eng. (Met) in 1967 and an M.Eng. in 1973, both from the University of Pretoria. Dr A. K. Haines, Pr. Eng., obtained all his degrees from the University of Natal, finishing with a. Ph.D. in 1971. Mr B. C. Alberts, Pr. Eng., obtained his academic training at the University of Pretoria, where he was awarded B.sc. degrees in both agricultural engineering (1963) and mining engineering (1965). Mr H. C. van Zyl, Pr. Eng., holds B.sc. degrees in mining engineering (1968) and civil engineering (1972), both from the University of Pretoria.

Jan 1, 1984

By J. F. Papp

In the United States, chromium has been consumed in three major markets: chemical, metallurgical, and refractory. The predominant end use for chromium in the United States is in the metallurgical market as an alloying element in the production of stainless steel. In addition to being a major stainless steel-producing country, the United States is a major world producer of chromium-containing chemicals and has used substantial amounts of chromite ore for refractory applications. Chromium use is not easily further subdivided within the chemical and refractory industries because there is insufficient publicly available information to do so; however, chromium use can be subdivided among metallurgical industry uses based on the American Iron and Steel Institute (AISI) reported shipments of stainless steel by market classification (agricultural, aircraft, automotive, etc.). It is the goal of this study to determine the distribution of U.S. chromium apparent consumption among major markets in the United States. The distribution is expressed in the form of dimensionless fractions that are computed based on documented chromium consumption by major market. The distribution of chromium among markets within the metallurgical market is computed in a similar manner. Distribution factors are first computed for the major markets, then for markets that are subdivisions of the metallurgical market. The distribution of chromium among major markets has changed substantially over the time period of analysis. The fraction of chromium consumed by the metallurgical market has increased while that of the chemical and refractory markets has declined. Within the metallurgical market, the service industry market accounts for the greatest fraction of chromium consumption followed by transportation. Electrical, machinery, and fabricated products markets account for a substantial share of the metallurgical chromium consumption.

Jan 1, 2004

By N. Sasto, E. Bondi, G. R. Lane

Cyest Corporation has been involved in economic modelling and optimisation with various mining clients within South Africa, and internationally, for the past 5 years. In the mining industry in particular, the relationships between variables that are controllable, and those that are not, and the physical and economic outcomes are complex and often non-linear. These relationships constitute an economic system. In the mining context, although many of the relationships can be accurately quantified on a ?single variable to single variable? basis, such simplistic relationships will not suffice in order to understand the dynamics of an entire mine. One has to specify and quantify the relationships between hundreds, if not thousands, of variables. Furthermore, in reality, these relationships change over time. This is the role of an economic model where all the relevant cause-effect relationships, within pertinent constraints, are accurately represented. Models that are used for optimisation must therefore capture the dynamics of the economic system in question as well as anticipate changes to the relationships between these variables. An accurate economic model is a prerequisite for successful optimisation. Optimisation entails the allocation or configuration of resources, within control of management, which will maximise (or minimise) a desired objective function. An optimal configuration (implying trade-off) of controllable variables therefore exists for a given set of assumptions that will yield a maximised objective function. Due to the multi-variant trade-offs required for optimisation, the concept of the ?Economic Surface? or ?Hill of Value? has been used to represent these optimisation outcomes and to discern the route to an optimal configuration. A good example of this is the volume versus cut-off grade trade-off that yields an optimal value for a particular shaft with its unique geological and economic assumptions. More recently, Cyest has extended these economic models to incorporate risk associated with variance in assumptions and inputs. This is termed DFA (dynamic financial analysis) and incorporates stochastic modelling and some of the latest actuarial techniques around modelling global assumptions (such as pricing and exchange rate). This paper will cover the theory around mine optimisation through some example case studies, and also explain the latest thinking regarding incorporating DFA.

Jan 1, 2007

By B. W. Lee, P. O?Shaughnessy

The practice of manganese ferroalloy smelting has traditionally been based on utilising oxide ores which typically contain a high level of manganese. This preference for oxides has even been extended to the modification of natural carbonates into nodulized oxides. However smelting practices developed over the past 30 years have created a market for natural manganese carbonate ores, driven in part by the unique properties that this type of ore can offer. An understanding of the mineralogy of carbonate ore and its thermal properties has provided important information which enables furnace operators to take full advantage of the chemical differences. However changes to traditional operating practices have been necessary. Once furnace operations using natural and unmodified carbonate ore have been mastered, the unique chemical features of manganese carbonate ore are able to contribute, not only to new product development, but also to cost savings. The use of natural manganese carbonate ore is now a well-established aspect of the industry. The sustained increase in demand for carbonate ore worldwide over the past several years confirms acceptance of its quality. There are effectively few limits to its successful use.

Jan 1, 2004

By M. Tanaka, K. Aoki, T. Mori, H. Morioka, K. Iwano, T. Kanagawa

To estimate the detailed characteristics of the rock around the cavern during excavation, new monitoring technique for dynamic properties of the rock has been applied. In this paper, micro-seismic monitoring and AE monitoring technique are applied to the excavation of large underground rock cavern and the result was discussed to clarify the acutal behavior of EDZ around the cavern. Zur Einschätzung der Gesteinseigenschaften um die Ausschachtung herum haben die Autoren eine Technik eingesetzt, mit der die physikalischen und dynamischen Änderungen im Gestein um den Schacht während der Ausschachtung beobachtet werden. In der vorliegenden Studie wurde zur mikroseismischen Überwachung ein AE Überwachungsverfahren eingesetzt und die Autoren berichten über die Veränderungen in den Gesteinseigenschaften um die Ausschachtung herum. Dans le but d&apos;évaluer en détail les propriétés des roches qui forment les parois des cavernes creusées, les auteurs ont utilisé une technique de mesure permettant d’observer les modifications physico-dynamiques des roches aux alentours de la caverne pendant son excavation. Dans le cadre de cet article, une technique de surveillance de l’agitation et du bruit microséismiques a été mise en œuvre et les auteurs font état de la modification des propriétés de la roche environnante.

Jan 1, 2003

By Marco Barla, Mariacristina Bonini, Giovanni Barla

ABSTRACT: The paper describes the characterisation studies of Tectonised Clay Shales at laboratory and in situ scale. The interest relates to tunnelling under squeezing and swelling conditions, in Italy, along the Apennines. The results of monitoring during full face excavation are presented in conjunction with numerical modelling. RESUME: Cet article présente la caractérisation, à l&apos;échelle du laboratoire et in situ, des Argiles Chaotiques. L&apos;attention est portée sur le creusement, dans ces milieux gonflants, des tunnels, dans les zones montagneuses des Appennini, en Italie. Enfin, on présentera les résultats de la modélisation numérique et la comparaison de ces derniers avec les mesures effectuées in situ. KURZFASSUNG: Die Arbeit beschreibt die Charakterisierungsstudien von tektonisierten Schiefertonen, sowohl im Labor als auch vor Ort. Das Interesse gilt dem Tunnelbau unter Quetsch- und Schwellbedingungen in Italien entlang der Apenninen. Die Überwachungsergebnisse des ganzflächigen Ausbruchs werden mit numerischen Modellen präsentiert.

Jan 1, 2003