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It is indeed an honour to address the perth branch of the australian institute of mining and metallurgy and to have the opportunity to talk to you about the future role of upgraded ilmenite on t102 feedstock supply and demand. There have been many papers written on upgraded ilmenite supply and demand and now I would like to share with you QIT's view of the situation first, a word about demand, although I will be talking principally on the supply issue. The principal use of t102 is in the manufacture of pigments which, in turn, are used in paints, plastics, and the paper industry together with a few miscellaneous uses, while a further b% or so of t102 minerals are consumed for the manufacture of titanium metal and for the manufacture of welding electrodes. the total demand for contained t102 is of the order-of 3 million tons per annum, and the general consensus in the industry is that growth rates should be of the order of 2% annually- it is against this backdrop that suppliers must compete with one another and produce least cost materials for the pigment industry. At the moment, supplies are relatively tight, but the generally slow growth in demand coupled with the abundance of titanium bearing minerals should ensure that long term the reverse is generally true. Now, let us examine the supply situation. Titanium is the 9th most abundant element in the earth's crust, so the problem from the producers` point of view is not one of scarcity of titanium minerals, but of how to extract most economically t102 feedstocks from a wide variety of choices- up to the present, all titanium feedstocks are being derived from either rutile or ilmenite rutile, at about 95% t102 content, is indeed a premier raw material which does suffer from potential scarcity and rutile supplies will likely be a diminishing factor in future decades- whereas ilmenite, a combination of iron and titanium oxides found in varying ratios, may be found in huge quantities all over the world.

Jan 1, 1986

By A Baensch, E Grimsley

Eloise Copper Mine is situated 56 km east-southeast of Cloncurry, Queensland, Australia. The deposit was discovered by BHP Minerals in 1986 during follow up diamond drilling of EM anomalies associated with major aeromagnetic anomalies. The deposit is overlain by 60 m of Mesozoic cover. Amalg Resources NL commenced mining during 1995 by means of decline access and long hole-stoping. The total mineral resource comprised 1.77 million tonnes at 4.10 per cent Cu as at the end of June 2003. Proved and probable reserves are 930 000 tonnes at 3.97 per cent Cu. Mineralisation is hosted within a strongly foliated Proterozoic meta-sedimentary sequence comprising arenites and schists. The metasediment sequence also contains a coarse-grained amphibolite body possibly representing an early intrusion of gabbroic composition. Economic mineralisation characteristically occurs as a number of steeply plunging lenticular bodies with strike lengths of between 100 and 200 m and maximum widths approaching 25 m. The principal orebody, the Levuka (B) Lode, displays a down plunge extension exceeding 1000 m and is open at depth. Ore mineralogy is almost exclusively chalcopyrite with the principal gangue phases consisting of pyrrhotite + quartz + carbonate. A biotite + hornblende + magnetite assemblage represents locally intense mafic alteration of the metasedimentary host sequence. Magnetite is present in variable amounts and may be locally significant in some of the smaller satellite orebodies. Within the orebodies the sulfides display a range of textures from massive through to vein like. Sulfides commonly display brecciated textures at a range of scales. Post-mineralisation faulting has severely dislocated the orebodies, resulting in a complex arrangement of fault bounded ore blocks. These faults display considerable variability in regard to strike, dip and amount and direction of throw. A recent review of the fault system by means of large-scale structure underground mapping, re-interpretation of drill core and 3D modelling has led to a significant improvement in the understanding of these structures. A significant upgrade of the geological database has accompanied the structural review. The overall improved understanding has aided the mine design processes with particular regard to decline and access development and pillar location. This has also impacted on the design of drilling programs and exploration for additional satellite ore zones.

Jan 1, 2003

By G R. Hancock, D Verdon-Kidd, M J. Saynor, J B. C Lowry, T J. Coulthard

The ability to simulate the stability of post-mining landscapes over time scales ranging from decades to millennia is a critical element in the assessment of closure designs for uranium mines. Landscape Evolution Modelling (LEM) technologies provide a means to simulate and assess the long-term geomorphic stability of a conceptual rehabilitated landform for periods of thousands of years. However, a major issue with simulations derived from long-term modelling are the limitations associated with the data inputs. Specifically, simulations which utilise historic rainfall data only represent the variability of rainfall events that have occurred over a relatively short period. Consequently, these simulations run the risk of not accounting for the full range of rainfall variability that might be expected over an extended period of up to 10 000 years. Therefore, for this study a probabilistic approach was adopted to generate a stochastic synthetic rainfall data set to produce a series of unique rainfall scenarios, each representing a simulated period of 100 years. Importantly, utilising such an approach allows uncertainty in predictions to be better accounted for and provides a range or probability of likely outcomes.In this study, the effect of ten individual rainfall scenarios are assessed in terms of their impact on the predicted erosion and denudations rates produced by the CAESAR-Lisflood LEM for a conceptual rehabilitated landform of the Ranger Uranium Mine (RUM) in the Northern Territory of Australia, focusing on the Corridor Creek catchment (Figure 1). While legislation requires this site to be erosionally stable for at least 10 000 years (Commonwealth of Australia, 1987), here the focus is on the first one hundred years of landscape evolution, as this is the period in which erosion is expected to be higher, with limited vegetation cover or pedogenic development in the initial decades after rehabilitation. It is also the period where the drainage pattern is set.CITATION:Lowry, J B C, Verdon-Kidd, D, Hancock, G R, Saynor, M J and Coulthard, T J, 2016. Application of synthetic rainfall data to long-term modelling of a rehabilitated landform, in Proceedings Life-of-Mine 2016 Conference , pp 75–79 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jun 28, 2016

By C van Wyk, I Reeves, J Webber, G B. Gnoinski

The minerals industry has been given an opportunity to grow and continue to advance again in an environment where there is the potential to reap big rewards for efficiency improvements due to buoyant metal prices and the growing demand of markets in Asia. Improving efficiency may also provide a better return compared to risks of expansions and bringing new projects online due to limited human and financial capital.An opportunity for improvement presents itself in the area of mine-mill reconciliation, which entails the quantification of the variance between measurement points along the mining value chain. Reconciliation factors are calculated from the variance between respective sections within the mining sequence. These factors are commonly used as key performance indicators to provide a check on the performance of the operations. Over parts of the mining value chain, there is a fair understanding of the reconciliation between the Resource and Reserve estimates and the measured metallurgical plant inputs and product outputs through understanding of the mine-mill interface. The quality of reconciliation data gathered across the mine and plant is generally not well established due to practices employed in generating the data. The reconciliation variances are often a function of data accuracy and quality used in the comparison. In general, the sources and magnitude of measurement and sampling errors and their impact on reconciliation are not that well understood. Examples of the current practices of mass measurement, sampling, sample preparation, chemical analysis and quality assurance for broken ore and across the metallurgical process stream are considered. Guidelines are given for those reconciliation elements that are identified as requiring a high degree of confidence for Mineral Resource/Reserve and metal accounting reporting. These guidelines are presented and practices are demonstrated to improve mine to mill reconciliation and support increased resource to product efficiency and value.CITATION:Gnoinski, G B, van Wyk, C, Webber, J and Reeves, I, 2012. Guidelines and practical applications for continuous improvement in mine to mill reconciliation, in Proceedings 11th AusIMM Mill OperatorsÆ Conference, pp 309-316 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Oct 29, 2012

By R Moller

Reconciliation at large iron ore operations is a complex and time- consuming process. Often the volume of data and the large range of different stakeholders makes the process almost impossible. Up until recently geologists and engineers at these operations would spend hours cutting and pasting data in and out of monster spreadsheets, diligently comparing how resource/reserve models, grade control and survey pick-ups compare to what was actually produced. In 2003 the Sishen Iron Ore Mine in South Africa broke this cycle by implementing SnowdenÆs Reconcilor software. The implementation of a dedicated reconciliation system required a number of existing practices to be changed, with the involvement of stakeholders right across the mine. Data sources had to be clarified and validated, terminology had to be standardised, processes needed to be documented and some methodologies needed to be updated. This was a task that required significant effort by Kumba personnel so that the system could be successfully implemented. This paper provides a case study of the reconciliation system implementation at Sishen. It is a story of an operation that evolved from using a number of fragmented reconciliation processes to using a unified automated system. This paper outlines the key estimates and measurements that are used for reconciliation, details the characteristics of an automated web-based information management system to facilitate the process and provides some insights about the benefits that have been gained though the use of a rigorous reconciliation process.

Jan 1, 2005

By A Penney, M J. Pascoe, R M. Stephenson

The empirical McCracken and Stacey stability and risk assessment method has been in use for more than 20 years to assess geotechnical stability issues for raise bored shafts. The methodology has been applied with various levels of success. Increasingly, trends in mining and civil tunnelling have been towards larger diameter, single pass, raise bored shafts to rapidly provide means of ventilation, material movement (ore passes), or emergency egress. Identifying and assessing potentially problematic zones before raise boring commences can allow for appropriate risk-based decisions on construction, or to investigate alternative solutions. The implementation of a proactive solution to raising through an identified weak zone is preferred to the application of an engineered solution to an area subjected to substantial instability or failure. Methods for investigating potentially problematic areas are discussed in this paper based on AMC’s benchmarking data. Proactive investigation programmes resulting from these investigations are also discussed. Previous publications discussing the benchmarking data have concentrated on Australian case studies. Increased efforts and recent updates have been made to expand the database to include international case studies. This has provided further refinement of lower bound ‘raise bore rock quality index’ (QR) values, and various rock mass parameters for stability assessments. CITATION:Penney, A, Stephenson, R M and Pascoe, M J, 2018. Raise bore stability and risk assessment empirical database update, in Proceedings The Fourth Australasian Ground Control in Mining Conference (AusRock), pp 434–445 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Nov 30, 2018

RME has a vision for a new mill operational paradigm made possible by RMEÆs fast, safe Mill Relining System. This vision can be moved forward into reality at any time with or without guidance from recent development in measurement and predictive modelling tools.Some new liner designs can degrade SAG mill performance because of mill volume loss, ball strike (rotational speed limitations) and other issues often brought about by optimising liners for life and without a backward glance at metallurgical consequences. Freshly relined mills can initially produce as little as 80 per cent of their maximum throughput, that maximum occurring toward the end of the linersÆ wear life. RMEÆs proposition is to design new liners for maximum commercial performance. This may mean more frequent changes of liners but with liners designed to yield optimum grinding, metallurgical and profitability performance. In other words, mill liner profiles and mill relining speed become key operational controls and not simply æmust doÆ maintenance functions. Taken to the extreme, liner profiles may prove capable of ætuningÆ a grinding plant for maximum profitability in any metal price environment. This paper provides an update regarding RMEÆs fast, safe Mill Relining System technologies and outlines RMEÆs vision of a æliner profile versus profitabilityÆ model as a function of metal price, developed intuitively or by using a combination of new measurement and modelling technologies. These new measurement and modelling tools provide the opportunity to predict the optimum commercial outcome, off-line in the virtual world, before committing to an expensive liner experiment.

Jan 1, 2006

The Newcrest Mining Limited Telfer Gold Mine consists of an underground sublevel cave (SLC) operation located 734 m directly below active open pit operations. Open pit and underground current production rates are 50 million and 5.7 million tonnes per anum (Mt/a) respectively. The SLC was initiated in late 2006 with breakthrough planned to occur on the 5484 bench of the west wall in late 2009. Risk to the south ramp was identified during this time, resulting in the construction of the north ramp. The SLC was continually tracked from initiation with a suite of monitoring systems and managed with a Major Hazard Management Plan (MHMP) and associated Trigger Action and Response Plans (TARP). At breakthrough the eastern limb of the cave was located within a 70 m horizontal distance from the south ramp. The south ramp was closed in October 2009 due to significant slope deformation, extensive cracking in the berms and batters between the ramp and breakthrough bench and a major failure 250 m to the north of the cave breakthrough. Wall response was first identified from slope deformation measurements taken by the wall monitoring radar in May 2009, at which point the SLC was 160 m from breakthrough. The impact of the SLC on the slope is a unique case with the monitoring systems in place able to provide data on the slope reaction to the SLC progression. This paper will discuss the management of the south ramp such as the early interpretation of risk associated with cave breakthrough, monitoring systems implemented to track the cave progression and wall deformation, data integration and interpretation and risk management. Following the closure of the south ramp further instrumentation programs and risk assessments were conducted to determine the risk of re-opening this haulage route. The outcomes of this program will also be presented.

Nov 25, 2010

By G Fahey, S Rose

"Mining geology as a defined profession is only about 100 years old. The successful modern mine geologist needs to be a multidisciplinarian, but also needs to maintain a focus on the key outputs of the role. The technical skills needed in the role have increased as mining methods move to increasingly mechanised techniques. As well as being the guardian of the orebody and ensuring minimal dilution to expected ore grades, the mine geologist should be competent in the 12-point mine geology process. The mine geology process should include:a statement of purpose (a ‘mission statement’)geological mapping/logging system that supports consistent and regular geological data collection, storage, and interpretationsampling system that can produce representative samples and fits in with the mining scheduleassay database with relevant controls to ensure only ‘clean’ data is loadedsimple quality assurance / quality control (QA/QC) system for samples and assays, with a response process to react to out of specification resultsconsistent method of exporting, visualising, processing and interpreting assay data to create mining blocksdevelopment sign-off system so that all development and stoping is controlledproduction tracking system to monitoring and reporting what ore and waste volumes have been moved from the face, to any intermediate stockpiles, the run-of-mine (ROM) pad and into the crusherreporting system for daily, weekly and monthly reporting of tonnes and gradesdocumentation so that the grade control system has simple, but effective descriptions of how it works, who has responsibilities, and authorities, and be easily maintainedreconciliation system to compare resource and reserve to grade control and to mined and milledtraining system so that the geology team can quickly become competent.In this paper, the authors discuss the requirements of each point, and comment on common shortfalls observed by them over several years’ experience on producing mines worldwide.CITATION:Rose, S and Fahey, G, 2014. Modern mining geology, in Proceedings Ninth International Mining Geology Conference 2014 , pp 461–466 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

Aug 18, 2014

By N Elith

The explosives demolition of a post-stressed, steel reinforced, concrete road bridge in Australia’s capital city, Canberra. The bridge was 50 m from the new replacement bridge, 320 m from community structures and within five kilometres of the national parliament buildings. The job required multiple overlays of risk assessment, public relations, safe work procedures, specialised blast design, environmental predictions and flyrock controls. Project stakeholders included Worksafe, Roads ACT, bridge owners, consulting structural engineers, community groups and road users. The bridge precincts, including a major road underneath, had to remain operational to peak traffic in the days leading up to the demolition. The break-up and removal of debris had to be executed in just two days from Friday to have the road beneath re-opened for Monday morning city-bound traffic.In Canberra, all explosives demolitions are now viewed with particular caution after a demolition in 1997, during which a young girl was killed. Any approval requires that Explosives Regulations, AS2187 2006 and Worksafe processes are satisfied, and a convincing case presented for blasting as a safe and viable option.Our design used specialised shaped cutting and blasting charges to sever in situ concrete beams and tendons and to shatter components of the stressed concrete bridge assembly. We include comments on structural engineering reports dealing with pre-weakening mechanisms. The benefit of pre-weakening is that it reduces the amount of explosives needed to safely complete the job and facilitates quick removal of debris after the shot. The complementary skills of the team, each one an expert in his field, resulted in a highly successful demolition, praised by authorities as an outstanding example of controlled use of explosives.

Nov 8, 2011

By O Handayani, R Barr, E Isaaks

The mining industry has focused a great deal of attention recently on the impact of blast movement on grade control. Although the problem of blast movement and its contribution to dilution and ore loss is well known, solutions to the problem are less than satisfactory. Perhaps the most recent innovation is the application of blast movement monitoring (BMM) devices to quantify blast movement. These devices emit an electronic signal and are planted at surveyed locations within the preblast material. Following the blast, their new locations are found using an electronic scanner. The magnitude and direction of the blast movement is given by the vectors between the pre- and post-blast BMM locations. However, it’s not clear how the BMM vector data can be best used to minimise dilution and ore loss. One common solution is to displace preblast dig line polygons by distances indicated by the BMM vectors. However, studies of BMM vectors show that blast movement not only displaces material laterally but also mixes material internally within the bench (Thornton, 2009a).This paper presents a method for modelling the post-blast muck pile that accounts for displacement and internal dilution using simulated annealing. The preblast ore control block model is re-blocked to 1?×?1?×?1?m sub-blocks. Each sub-block is displaced by simulated BMM vectors conditional to post-blast surface topography and blast initiation sequence data in addition to BMM vector data. The displaced sub-blocks are aggregated into new ore control model blocks whose grades are calculated from the contained sub-blocks. New dig lines are then designed on the post-blast muck pile model using the new ore control block model grades. A case study based on actual data is provided.CITATION:Isaaks, E, Barr, R and Handayani, O, 2014. Modelling blast movement for grade control, in Proceedings Ninth International Mining Geology Conference 2014 , pp 433–440 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Aug 18, 2014

By D Reid, J McKibben, M Noppe

International mineral disclosure standards and guidelines aligned with the CRIRSCO (Committee for Mineral Reserves International Reporting Standards) template were developed to inform stakeholders about the relative accuracy and confidence levels of publicly reported information and to support investment decisions, particularly when advancing projects through different development stages. The traditional stages range from early to advanced exploration, through pre-development (with Mineral Resources and pre-feasibility and/or feasibility levels of study) before the final development stages, where a decision to proceed with construction or production (or both) is made. The traditional definition of Mineral Resource and Ore/Mineral Reserve classification categories and techno-economic study levels (including Preliminary Economic Assessment (PEA), Scoping Study (SS), Pre-Feasibility Study (PFS) and Feasibility Study (FS)) were defined with pre-development project assessment in mind. As such, these definitions are not necessarily well aligned to the reporting structures required by operating mines which need to consider a range of timelines spanning short to long-term operating conditions. However, the same terminology and definitions are used, or expected to be used, by both project developers and mine operators when reporting resources, reserves and techno-economic study outcomes. This paper discusses how various stakeholders in the minerals industry (including competent/qualified persons, mining company leaders, investors, lenders and regulators), generally interpret the definitions of Mineral Resource and Ore Reserve categories in terms of the relative accuracy of the estimates, their link to techno-economic study levels and their contribution to life-of-mine (LOM) schedules. The paper examines the degree to which mining companies recognise, and apply, enhanced operational knowledge to reflect short-term views of the relative accuracy and confidence levels associated with publicly reported Mineral Resource and Ore Reserve estimates and forecasts. Furthermore, this paper explores how this knowledge is applied to support ongoing Mineral Resource, and particularly Ore Reserve, generation and reporting. This paper is informed by public data and responses to an internal survey prepared by the authors and completed in 2021 by several mining companies.

Mar 22, 2022

By G Danckert

The key technical theme of ‘orebody knowledge’ has been applied by Rio Tinto in the Pilbara iron ore precinct from 1966, when operations first started there. It forms the basis of present day application, as well as planning for the future.This paper will review how the early towns and mines commenced and how they formed the basis of Rio Tinto’s early operations, on which the Pilbara precinct has been based. A profile of the last decade of Pilbara growth will be highlighted, together with the current integrated network of mines, rail and ports and the next generation of expansions.The paper will specifically describe the Rio Tinto process of significant resource evaluation, including comprehensive drilling programs and the conversion from resource to reserves. It will also describe the overall mine planning process, both from the strategic view, as well as for short-term mine plans.The ability to innovate in resource development will be discussed. This will include not only the technical dimension of changing cut off grades, use of low-grade ores and managing low-grade stockpiling and beneficiation, but also the broader application of new technology and innovation in the iron ore business.

Jul 11, 2011

By K Zhao, H Gong, B Li

Health and safety are the first priority for Australian minerals sector. Australia has a global reputation in the mining industry. However, accidents occur every year. Legislation and regulation are important to prevent the accident from occurring, so do the new technologies. It is sad to witness the collision incident persisting and the long called collision avoidance system (CAS) is still not widely used in underground mines. The main reason is that the existing systems are still not advanced enough. The current CASs utilise GPS, infrared, ultrasonic, RFID, Radar, electromagnetic etc have their limitations and disadvantages. For instance, GPS is widely used in a surface mine, but it cannot be applied in underground mine; Infrared and electromagnetic have the false positive problem.

Sep 1, 2024

By M Tayebi-Khorami

There is an increasing trend in the extraction and development of copper resources from complex deposits. The complex deposits pose mineral processing challenges, as they often contain low grade copper ore, relatively large quantity of clay minerals, complex texture, very fine disseminated ore, high amount of pyrite, and high level of impurity elements such as arsenic. With the amount of arsenic in concentrates increasing and with environment, occupational health and safety regulations becoming more restrict, there is a need for a processing method that results in no arsenic emissions and captures all arsenic while immobilizing it in a compound that is stable under a wide range of conditions, so it is suitable for long-term disposal. Some development work has been undertaken to examine the most effective arsenic treatment option for complex orebodies that contain arsenic, but a technically robust and economically viable option has not yet been developed. Previous research has demonstrated the possibility of separating arsenic-copper sulphides from other copper minerals by controlling the potential of the flotation pulp in the single mineral systems. The selective flotation of enargite from copper sulphides in a real complex ore system was studied by Tayebi-Khorami (2016), which is summarised in this paper. CITATION: Tayebi-Khorami, M, 2018. Arsenic in complex orebodies, in Proceedings Complex Orebodies Conference 2018, pp 132–134 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Nov 21, 2018

By I Mason, M van de Werken, B Zhou, J Hargreaves, W Stasinowsky

A critical step in open cut coal mining is clean removal of the overburden. This is usually achieved by drilling, blasting and digging. A key part of this process being successful is to stop drilling at the correct blast ‘stand-off distance’. The stand-off distance is the distance between the base of the drilled blasthole and the top of the coal horizon to be mined. Having this correct provides a protective cap of rock above the coal horizon so that the blast will fracture all the overburden without damaging the coal horizon or mixing it with the overburden. Drilling beyond the correct stand-off distance causes the blast to continue into the coal horizon, damaging it and mixing it with the overburden, leading to significant losses of coal product. Conversely, drilling short of the correct stand-off distance results in additional work to remove the intact overburden.

Sep 1, 2024

By J Lainé, M Badawi, A C. de Araujo, Y Foucaud, C Veloso

Flotation is the one of the most used techniques for the mineral separation of non-ferrous ores worldwide. However, the increase of the complexness along with the decrease of ores liberation sizes ought to become important challenges for mineral processing, including flotation. It now appears necessary to better understand the fundamentals of the flotation process, particularly the adsorption of flotation reagents at the liquid/mineral interfaces, to propose further improvements. Flotation relies on different phenomena: surfactants adsorption, on one hand, and collision, adhesion, and transport of particles with bubbles, on the other hand. For acknowledging the reagents adsorption mechanisms, molecular modelling tools borrowed from chemical and material sciences, are increasingly used. Atomistic simulations were successfully applied to study the flotation reagents interaction with various mineral surfaces, eg of two common minerals from iron ores, kaolinite, and magnetite surfaces, or with fluorite surface, a tungsten ores common gangue mineral.

Aug 24, 2022

By D François-Bongarçon

The link between geostatistics and Theory of Sampling (TOS) is examined again in view of new findings made while trying to compare predicted sampling variances and estimated grades (using geostatistics) on the same material, and this provides an important consistency requirement whenever calculations are made that involve both theories in a comparative way. It also briefly explores the relationship to De Wijs fractal model of mineralisation and eventually provides new support for the use of consistency theory for calibrating TOS variance formulas.CITATION:François-Bongarçon, D, 2017. Theory of Sampling and geostatistics – the ultimate link, in Proceedings Eighth World Conference on Sampling and Blending , pp 391–394 (The Australasian Institute of Mining and Metallurgy: Melbourne).

May 9, 2017

By S H. Hyun, J W. Cho

Jun 19, 2024

By J A. M Luz, A T. Bernardes

HukkiÆs law is an empirical law, which does not take into account several events of energy loss during the fragmentation processes. Since experimental results are very difficult to obtain, for a large range of fragment sizes, the verification of the law is very difficult. The relation between fractures and fragmentation processes with fractal geometry was proposed some decades ago. Empirical laws known in this context show basic features of fractal geometry, mainly self-affinity and power law behaviour. Thus, in this work a model was developed to simulate the fragmentation process and to check the relation between energy consumption and fragment sizes. The model is represented on a regular lattice. Links can represent pathways for fracture processes. The events of fragmentation have energy given by a probability distribution function. In the model there is no mass loss. Propagation of fractures occurs as self-avoiding random walks on the regular lattice.

Sep 26, 2011