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By N. Naudé, J. de Villiers, C. P. Bergmann

It is proposed that the physical and chemical composition of individual mineral particles are an appropriate basis from which to model the performance of minerals processing equipment. Such a particle-based approach enables modelling across disciplines such as comminution, classification and flotation and automatically generates the traditional mass and chemistry balances. The general approach followed is to generate full grade-recovery curves for a separator by sampling product and tailings at varying mass yields. AutoSEM characterisation of each sample provides particle data that is used to reconcile mineral deportment and liberation to the measured size and assay data. In this way, partition surfaces can be generated and modelled. In this paper, an empirical model for the performance of a gravity spiral concentrator treating fine chromite ore is proposed. The model is based on the combination of two partition surfaces and is able to accommodate both forward and reverse gravity concentration effects per size fraction. The results show that this approach is well suited to represent spiral performance for the cases evaluated. The effect of two feed particle size distributions on the performance of the Multotec SC21 and SC25 spirals is demonstrated. Simulations are run in an Excel environment, linked to Python-enabled routines for enhanced data management and calculation speed. Keywords: Spiral concentrator, gravity separation, particle-based modelling

Jan 1, 2020

By H. L. Monro

Contribution by B. K. Martust I congratulate the author on his interesting paper. In my view, the establishment of the level at which South African gold output is at some kind of optimum is an interesting though somewhat academic exercise. Contribution by D. M. Hawkins* The thesis of the paper is a very interesting one, but, before it is used as the basis of any firm proposals to restructure the mining industry, which changes may be irreversible, one should be very sure that the basis of the calculations is sound. Contribution by P. J. Niewenhuizen* The hypothesis advanced by Mr Monro that the demonetization of gold in August 1971 introduced a major new policy variable, namely the supply-pricejdemand-price relationships, into the decision making process touches on a matter that has never really been given serious thought by the industry. Contribution by B. G. Kingsman* As a co-worker on the development of an econometric model for supply and demand in the world gold market with Mr H. L. Monro, it would perhaps be useful for me to make some comments on the various points raised in the discussions on his paper.

Jan 1, 1984

By D. M. Poulter, J. N. Brooke, P. H. Williams

"The complexity of the mining and metallurgical operations of Nchanga Consolidated Copper Mines, Limited, has made it necessary to use computer-assisted planning techniques in order to maximize copper production and marginal contribution to profit. The most successful of the Group Production Scheduling systems utilized linear programming to optimize the concentrate routing only. This third-generation system was commissioned in March, 1968.It bad become necessary by March, 1970, to expand the long-term planning activities and to take into account new mines and new concentrate treatment schemes. Technical difficulties and manpower limitations made it impossible to expand the third-generation system, and it was decided to construct a new Group Production Scheduling system using only linear programming.The plant models in the new fourth-generation system are based on data available from the monthly reports of the metallurgical plants. The models consist of mass balances and empirical relationships. Matrix coefficient assignment and management reports are produced using a Report Generator Language designed for linear programming data files. The development of this system is an example of a user application of a system package."

Jan 1, 2014

By Q. Liu, S. Liu, Y. Cui

To reduce the frequency of mining incidents and improve safety and production efficiency, it is important to develop technology for the autonomous positioning and navigation of mining equipment, without the assistance of satellite navigation signals. In this study we review the current technological environment for positioning and navigation underground and present several integrated navigation strategies. Existing underground positioning and navigation technology is described, and the performances of different methods based on this technology analysed and compared. The combination types and positioning effects of underground positioning and navigation strategies are discussed. Recent research directions for filtering methods and positioning estimation algorithms for underground positioning and navigation are reviewed. Finally, we summarize the future direction of underground positioning and navigation technology and related algorithms.

Jun 1, 2021

By A. F. Silva, J. M. G. Sotomayor, V. F. N. Torres

Geotechnical monitoring plays an important role in the detection of operational safety issues in the slopes of open pits. Currently, monitoring companies offer several solutions involving robust technologies that boast highly reliable data and the ability to control risky conditions. The monitoring data must be processed and analysed so as to allow the results to be used for several purposes, thereby providing information that can be used to manage operational actions and optimize mining plans or engineering projects. In this work we analysed monitoring data (pore pressure and displacement) and its correlation with the tension and displacement of the mass of an established failure slope calculated using the finite element method. To optimize the back-analysis, a Python language routine was developed using input data (point coordinates, parameter matrix, and critical section) to use software with the rock mass parameters (cohesion, friction angle, Young’s modulus, and Poisson’s ratio). For the back-analysis, the Mohr-Coulomb criterion was applied with the shear strength reduction technique to obtain the strength reduction factor. The results were consistent with both the measured displacements and the maximum deformation contours, revealing the possible failure mechanism, allowing the strength parameters to be calibrated according to the slope failure conditions, and providing information about the contribution of each variable (parameter) to the slope failure in the study area.

Oct 1, 2021

By R. J. Durrheim, B. Manzunzu, V. Midzi

Selecting ground motion prediction models (GMPM) is crucial in assessing seismic hazard levels in a specific region. This study investigates the influence of ground motion model (GMM) selection on seismic hazard assessment in Johannesburg, South Africa. Most seismic events affecting Johannesburg are related to mining activities and water ingress into the underground mine voids. The most seismically active regions in South Africa include areas around Klerksdorp, Welkom, and Carletonville. These regions experience a significant number of earthquakes, with mining activities being a major factor contributing to seismic events. Ten ground motion prediction equations were selected from regions of similar tectonics setting and were assessed to see if they correspond to the available local data. Six of these were also compared to the ground motions produced by the earthquake of 14 August 2014, which occurred in the Orkney area, one of the mining areas in South Africa. Sensitivity analyses were also carried out to assess the influence of ground motion prediction equations (GMPE) on the seismic hazard of Johannesburg. The results indicate that the choice of GMPM significantly affects the estimation of seismic hazard levels in Johannesburg. Different GMM can lead to varying ground shaking intensity predictions, impacting risk assessments and engineering design considerations. The findings highlight the importance of carefully selecting appropriate GMM tailored to Johannesburg’s specific geological and tectonic characteristics. Understanding how different models perform in this region is essential for accurate seismic risk mitigation strategies.

Jan 12, 2025

By John W. Harbaugh, Alfredo Prelate

The goal of the study described here is to develop objective. quantitative methods for estimating the outcome probabilities of exploratory oil wells. The study employs the 're-experience' approach, in which historical data are used in a manner which attempts to recreate the past. Our past experience, of course, is the principal guide to the future. To appraise present-day oil prospects, however, we must analyze prospects that have been drilled in terms of how these former prospects were interpreted before they were drilled. An analysis of how they are interpreted after they were drilled is an inadequate guide to the future because our hindsight knowledge is superior to our foresight knowledge. Objective calculation of future outcome probabilities, then, requires that we attempt to treat past information in a manner analogous to that in which we must treat present information in forecasting future outcomes.

Jan 1, 2014

By E. R. Leeman

INTRODUCTION The first references in the literature to the so-called C.S.I.R. 'doorstopper' strain cell were made in 1964 1,2,3,4. These were the climax of nearly two years of experimental and developmental work with the instruments and the operating techniques involved. Since that time numerous field measurements have been made with 'doorstoppers' and they have been developed to a stage where they are in commercial production and are being supplied to users throughout the world. No detailed description of the latest 'doorstopper' equipment has, however, appeared in print and this paper is written to bring the literature up to date in this respect. The triaxial strain cell was developed three years ago 5, 6, 7 and was first described at the First Congress of the International Society for Rock Mechanics in Lisbon in 1966 8. Since that date laboratory tests and-particularly important-field tests 7' 9 have demonstrated the validity and practicality of the instruments and techniques. These instruments have also been developed to a stage where they have been released for commercial production. In this form they are very different from those described two years ago and a full description of them at this stage seems to be justified. THE INFORMATION SUPPLIED BY 'DOORSTOPPER' AND TRIAXIAL STRAIN CELLS Both the 'doorstopper' and triaxial strain cells were designed specifically to determine the absolute stress in rock using an overcoring stress relieving technique. They were not designed to measure changes in stress. They may, however, be used for the latter purpose provided the glue which is used to stick the strain gauges to the rock is known to possess sufficiently stable strain-time characteristics as not to affect the accuracy of the results during the time the measurements are made. The 'doorstopper' was designed primarily to measure the major principal stress in situations where its direction and those of the two other principal stresses were either known or could be assumed. For example, at great depth in undisturbed virgin ground, it is reasonable to assume that the maximum principal stress is vertical and that the other two lie in a horizontal plane. The borehole in which the 'doorstopper' is installed would thus be drilled in the horizontal plane parallel to one of the minor principal stresses, the direction of which would either have to be assumed or determined as described later. The stresses measured would be the vertical major principal stress and the principal stress acting in a horizontal plane normal to the borehole axis. It is possible, as will be shown later, to obtained the complete state of stress using 'doorstoppers'. In this event, it is necessary to make measurements in three boreholes drilled in any three known directions to each other and relative to a system of three orthogonal axes. The triaxial strain cell was designed to determine the complete state of stress in a single borehole drilled in any direction in any stress field. At first glance it would appear to supersede the 'doorstopper'. This is not necessarily true since there are

By R. Minnitt , D. Fourie, P. le Roux

This study proposes that the moving search neighbourhood used in ordinary kriging selects a subset of data surrounding each estimation block, and that this subset represents a local subpopulation of which the distributional parameters can be used to determine local, spatially-adaptive outlier capping values. This paper introduces a distance-weighted capping method applied within the kriging search ellipse after kriging weight calculation, transitioning from one-dimensional point estimation to two-dimensional block estimation for Witwatersrand-type gold deposits. Accurate ore grade estimation is essential for mine planning and economic evaluation, particularly in deep-level gold mines where extreme grade values (outliers) may distort resource assessments. Traditional capping methods, which apply a uniform threshold to outliers, often fail to account for spatial and geological variability, leading to biased estimates. A high-resolution simulation generates a synthetic ‘ground truth’ orebody, subsampled to mimic real-world data scarcity. A two-parameter lognormal distribution models grade variability, with capping values optimised by minimising the mean squared error between estimated and simulated block grades. Comparative analyses against traditional capping techniques demonstrate that the dynamic method improves regression fit, reduces conditional bias, and aligns more closely with production reconciliation data. Validation using swath plots, QQ-plots, and mine call factor comparisons confirms that the spatially adaptive capping technique mitigates over- and under-estimation, particularly in high-grade zones. Results indicate superior performance over conventional domain capping, with higher R² values and better alignment with actual production metrics. This approach offers a reproducible, scientifically rigorous framework for resource estimation, reducing reliance on rigid sub-domaining while enhancing decision-making in complex ore bodies. The study underscores the importance of integrating geological information with advanced geostatistics to optimise grade estimation and mine planning.

Jul 3, 2026

By M. Kumral, Y. A. Sari

Underground mining operations tend to have higher operating costs than surface mines. When metal prices decrease, profitability is jeopardized due to the high costs. Therefore, mining management harnesses new practices that increase operational efficiency. One way to manage this challenge is to invest in new mine planning practices. Stope layout optimization as a part of underground mine planning aims to identify a portion of the orebody in the form of production volumes (stopes) to maximize profit under roadway and stope dimension constraints. In this paper we propose a novel approach based on identifying ore-rich areas of the deposit and prioritizing their extraction through an iterative heuristic clustering approach. The proposed approach is compared with and validated by an exact method through a small mining example. The heuristics produced nearly identical results in a very short time. Finally, a case study was carried out using a larger data-set. The cluster-based iterative approach generated nearoptimal stope layouts in a computationally effective manner.

Mar 1, 2021

By J. E. Dickinson, R. Campbell, M. J. Cole, K. P. Galvin, M. C. Cole

It is common practice in the beneficiation of iron ore ultrafines to apply reverse flotation, and hence float the gangue minerals, leaving behind a high-grade iron ore product. Given the difficulty in floating particles finer than 20 μm, especially those finer than 10 μm, it is necessary to subject the feed to desliming ahead of flotation. There are two problems with this approach. Firstly, given the known inefficiencies of cyclones, desliming needs to be aggressively applied to particle sizes upwards of 45 μm to ensure all the offending ultrafine gangue is removed. Secondly, desliming also removes a significant portion of the valuable iron ore. Thus, a significant portion of the ultrafines, including the iron ore, is lost to the tailings. This paper examines the direct flotation of iron ore fines using the Reflux Flotation Cell. The RFC operates using a concentrated bubbly zone, in the absence of a conventional froth zone, for delivering strong counter current washing through an inverted fluidised bed of bubbles ahead of the product discharge. A system of parallel inclined channels in the lower part of the cell provides enhanced segregation of the bubbles from the tailings, preventing the loss of air bubbles into the tailings. Experiments conducted under semi-batch conditions produced encouraging results with concentrates of ~65% Fe grade in a single flotation stage. Comparatively, up to five successive batch flotation stages were required when using a laboratory scale batch mechanical flotation cell to achieve similar Fe grades. For a given grade, lower Fe recoveries were typically achieved by the RFC. This was attributed to the effective prevention of ultrafine particles succumbing to hydraulic entrainment under a positive bias flux, as well as an increasing feed volume involved in the semi-batch operation using inverted fluidisation water for cleaning. Overall, similar grade-recovery curves were produced, however, significantly higher grades were obtained by the RFC and with fewer separation stages. Keywords: Desliming flotation, iron ore, modified release analysis, reflux flotation cell

Jan 1, 2020

By N. Morris

In South Africa, diamonds are mined predominantly in rural areas. Kimberlitic diamonds dominate in Limpopo and the Northern Cape Provinces whereas alluvial diamonds are mainly sourced from the North West and Northern Cape Provinces. There are a few large and medium sized diamond companies (De Beers, Petra Diamonds, Trans Hex, Rockwell and Alexkor). There are many smaller companies involved in diamond mining, mostly alluvial diamond mines. The nature of alluvial diamond deposits is that they are aerially more extensive and thus their surface impacts are more pervasive: The recent downturn in diamond prices has resulted in the sudden cessation of mining at many small and medium diamond operations. The South African Mining Charter requires all mines, including diamond mines, to subscribe' to .the following empowerment objectives:

Jan 1, 2010

By L. A. Cornish, J. W. van der Merwe

"The hydrofluoric acid (HF) industry in South Africa uses normalized mild steel (SA 516 Gr 70) for the storage and distribution of its technical-grade product (70% HF). The technical-grade acid is split from the anhydrous hydrogen fluoride (AHF) product during distillation just after HF is produced, in a stainless-steel-lined kiln, from the reaction of calcium fluoride (CaF2) with sulphuric acid (H2SO4). Uniform corrosion of the storage tanks is mitigated during commissioning by contacting the steel with 70% HF. A corrosive reaction takes place (2H+ + 2F- + Fe - H2 + FeF2) to form scale inside the tank which diminishes the attack of the steel by fresh HF, thus prolonging the service life expectancy of the vessels. This iron fluoride scale in the vessel grows continually, resulting in corrosion of the vessels continuing at a predictable rate (approx.0.5 mm/a) since the first commissioning of the tanks at Necsa in 1993. In early 2012, an increase in the average corrosion rate of the tanks to 3 mm/a measured at and below the liquid band in the storage vessels was noted. Three months later the corrosion rate had increased to 30 mm/a, just before the first leak from the tank was detected. The tanks were decommissioned shortly afterwards and an investigation revealed that the rapid corrosion was due to the presence of increased levels (>50 ppm) of nitric acid (HNO3) in the tanks, which attacked the fluoride layer protecting the steel.The oxidation characteristics of high concentrations of HNO3 with low concentrations of HF on stainless steel surface treatment are well documented. The effects of low levels of nitric acid on the corrosion of steels in sulphuric acid are also known, but no suitable published data currently exists on corrosion by high HF concentrations with low HNO3 concentrations. Establishing the rate and mechanism of corrosion by HNO3 (0.1 to 1%) in 70% HF is currently a high priority for the HF industry in South Africa and will become increasingly important in the near future due to depleting fluorite reserves and cheaper, but less efficient, processes producing H2SO4 with higher impurity levels, which were not anticipated in the original plant design. The aim of this study is to simulate the corrosion conditions in the plant on a laboratory scale in order to establish the corrosion characteristics of the steels used in the HF plant, which are increasingly exposed to the HNO3 impurities that tend to concentrate in the final technical-grade HF acid product."

Jan 1, 2016

By I. B. Fernandes, M. A. Reuter, A. Abadias Llamas

Metallurgical simulation and evaluation of the resource efficiency of whole production processes are of key importance for impact assessment, in terms of environment and resources. Exergy is a measure of resource consumption, taking into account energy, raw materials, water, and chemicals; which allows for the evaluation of different technologies to find the most resource efficient and environmentally friendly process. This paper compares the sustainability for production of rare earth magnets from primary and secondary resources through an exergetic evaluation of the production process, in addition to traditional life cycle assessment (LCA). The methodology makes use of simulation tools for tracking material flow and resources used, based on thermodynamic laws, from ore exploitation to magnet production and recycling. It highlights areas with the greatest potential for improvements in terms of resource consumption and environmental impact generation, having a thermodynamic-validated flowsheet for primary and secondary production of NdFeB magnets, present in several low-carbon technologies, such as wind turbines, electric vehicles, and cooling systems. It demonstrates the minimum exergy destruction for magnet production, through an irreversibility breakdown chart, showing where irreversible material and energy losses occur. Results show that CO2-equivalent emissions for producing NdFeB permanent magnets from primary resources could be twice as high when compared to magnets produced from recycling technologies. The theoretical maximum exergetic efficiency for primary production is 57.61%, whereas for permanent magnets produced from secondary resources, the exergetic efficiency reaches up to 82.89%. Two magnet recycling technologies were evaluated, i.e. in acidic medium and via hydrogen decrepitation, and it was observed that their exergetic efficiency and environmental impact performed better than production from primary resources. Keywords: Resource efficiency, exergy analysis, permanent magnet recycling, process simulation, system design

Jan 1, 2020

By M. Mpofu, M. van Schoor, T. Kgarume, H. Grobler

The South African mining industry has committed to achieving a state of zero harm for its workforce, with a strong emphasis on worker health and safety. Among the major safety concerns are falls of ground, a leading cause of injuries and fatalities. Ground-penetrating radar, a non-destructive geophysical method, is recognised for its ability to image structures, fractures, and geological features within the rock mass. However, ground penetrating radar data is often acquired in local coordinates, posing challenges for visualisation in mine computer-aided design or three-dimensional visualisation software. This study explores the pivotal role of light detection and ranging data in transforming ground penetrating radar data from local survey coordinates to absolute mine coordinates. A comprehensive georeferencing methodology is presented, providing the stepwise progression from the initial georeferencing of ground penetrating radar data to the ultimate integration of ground penetrating radar and light detection and ranging datasets, resulting in the creation of a ground penetrating radar-light detection and ranging three-dimensional model. The proposed approach not only facilitates the integration of but also offers a practical means of visualising the integrated datasets within commonly used computer-aided design or three-dimensional visualisation software. An essential aspect of this integration is the adoption of non-proprietary data formats, specifically American Standard Code for Information Interchange text files, ensuring broader accessibility and compatibility. The potential for integrating diverse datasets to construct insightful models of the underground mining environment is illustrated. Integration of different datasets has the potential to offer a holistic understanding of the mining environment, providing essential information to decision-makers.

Jul 23, 2025

By M. Tangstad, J. D. Steenkamp

In April 2013 a 48 MVA submerged arc furnace producing silicomanganese was excavated in South Africa. Since the high shell temperatures recorded in the tap-hole area resulted in the furnace being switched out for relining, the tap-hole area was excavated systematically. A refractory wear profile of the tap-hole area with affected hearth and sidewall refractory was obtained in elevation. The carbon ramming paste in front of, above, andbelow the tap-hole was worn, as was the SiC with which the tap-hole was built. A clay mushroom formed but was detached from the refractories. Thermodynamic and mass-transfer calculations were conducted to quantify the potential for wear by chemical reaction between refractory and slag and refractory and metal in the tap-hole area. It was found that chemical reaction between refractory and slag or metal could offer only a partial explanation for the wear observed; erosion is expected to contribute significantly to wear.

Jan 1, 2015

By I. A. Mwamba

Titanium aluminide of composition Ti-47.5 at.% Al was prepared by melting titanium and aluminium of commercial purity with additions of precious metals of 0, 0.2, 1, 1.5 and 2 at.% content. The microstructure, hardness and oxidation properties were assessed. It was found that at 47.5 at.% Al, the microstructure of plain TiAl alloys was duplex, consisting of duplex lamellar grains and ? grains. The lamellar grains consisted of alternating lamellae of ? (TiAl) and a2 (Ti3Al), with overall aluminium content in the range of 43?47 at.%. The ? grains had a aluminium content above 50 at.%. The addition of precious metals to the TiAl alloy resulted in the formation of a new phase, with a high precious metal content, occurring mostly in the ? phase, without any major change to the microstructure. Increasing the amount of precious metals resulted in an increase of the new phase amount, at the expense of the ? phase. The hardness of the different alloys was around 300HV10. Overall, the research has shown that addition of precious metals to TiAl resulted in a slight increase in hardness and a significant improvement of the oxidation resistance. This shows that alloying TiAl with precious metals, at the addition levels investigated, does not alter the mechanical properties very much, but improves oxidation resistance.

Jan 1, 2012

By H. W. J. P. Neomagus, R. K. K. Mbaya, J. R. Bunt, N. T. Leokaoke, N. W. Makgobelele

Silicon Smelters consumes more than 80000 t/a of wood-derived charcoal as carbonaceous reductant in the production of silicon metal. More than 10% of this material is discarded as fines (<6 mm) generated due to abrasion during processing. Charcoal fine residues (<650 μm) and polyvinyl alcohol (PVA) binder were used in this study to produce mechanically strong charcoal briquettes for metallurgical application as carbonaceous reductant. The PVA binder was added in mass percentages of 1, 3, and 5 wt% to the charcoal fines. The compressive strength, abrasion resistance index (ARI), drop shatter resistance (SRI), and water resistance index (WRI) were measured as functions of curing for up to 7 days under atmospheric conditions, and the results compared with metallurgical grade coarse charcoal. The ash content of the produced briquettes was found to be high (6.6–8.0%) compared with the coarse charcoal (1–3%). The 3 and 5 wt% PVA-bound briquettes were found to be the strongest, with compressive strengths of 40 and 115 kg/cm2 respectively, with WRI values of 75 and 73% respectively. The produced briquettes were found to have lower ARI and SRI values compared to the coarse charcoal. Future work should include beneficiation of the fine charcoal discards prior to briquetting, and an increase in binder addition to above 6 wt% to improve the ARI and SRIn.

May 1, 2021

By C. C. Pretorius, S. Ramjee, R. J. Mostert

The study investigates the effect of prior corrosive exposure on crack growth resistance behaviour of thin sheet (3 mm thick) aluminium alloy 2024-T3 at slow strain rates. Compact tension specimens were exposed to standard corrosive environments that simulate accelerated atmospheric corrosion attack. Two corrosive environments were considered – an exfoliation corrosion (EXCO) solution and a 3.5 wt% sodium chloride solution. The unloading compliance R-curves of the two-hour EXCO-exposed specimens revealed a significant degradation of approximately 11% in the crack growth resistance behaviour (Kc_e values) compared to the baseline (air-exposed) values. Furthermore, secondary intergranular crack formation was also revealed in the plastic zone ahead of, and adjacent to, the crack tip of these specimens; which formed during the crack growth resistance loading. It is postulated that the observed degradation of the Kc_e values of the EXCO-exposed material is due to hydrogen embrittlement since the exposure times for the EXCO evaluation were limited to ensure that uniform corrosion dominated; that is, significant penetration of corrosion damage and pitting due to localized corrosive attack did not occur. The sodium chloride-exposed specimens revealed a similar degradation (13%) after 24 hours exposure. However, slight intergranular corrosive attack and isolated pitting were observed on the exposed surfaces prior to crack growth resistance loading, resulting in notch effects that could assist in crack growth. Pitting and intergranular corrosion were, however, not observed at the pre-crack tip. The relative contributions of the notch effects and the hydrogen embrittlement during the degradation of the KR performance are, therefore, unclear.

Apr 1, 2021

By C. I. Kim, I. C. Paek, I. K. Tae, P. J. Thak, U. C. Han, K. S. Jong

This paper analyses the energy consumption according to the type of dump scroll track during skip discharging in an inclined shaft hoist for an open pit mine. For the purpose of the project, it was necessary to set up an equation for a geometrical locus of a skip dump scroll track, and from the need for technical engineering and study purposes, to derive equations for two track types by using cam design theory (cosine track and linear accretion track). Skip discharging is analysed using discrete element method software, and dynamic simulation of its run is performed using Visual Nastran software. The energy consumption during skip discharging can be calculated from the rope tension obtained by dynamic simulation, and graphs obtained from the simulated results using discrete element method and Visual Nastran software. From this, the study demonstrates that the energy consumption at the cosine track is always lower than that at the linear accretion track, without regard to the property change of a payload depending on grain size distribution.

May 8, 2026