Search Documents

By K. Muchima, C. Siame, L. Little, B. Kaputula, Q. Mclennan

"The variability of copper mineralization at Kansanshi mine significantly affects the efficiencies of the processes used to recover copper. Quantifying this variability is therefore essential for monitoring and optimizing the performance of the concentrator, which comprises three different flotation circuits (sulphide, mixed, and oxide) and an atmospheric leach circuit. Onsite automated scanning electron microscopy with energy-dispersive X-ray spectrometry (Auto-SEM-EDS) is used to analyse routine weekly composite samples for each circuit, providing detailed analyses of bulk mineralogy, copper deportment to different minerals, mineral liberation, and associations. Weekly mineralogical trends are used to assess changes in process performance, and characterization of the copper losses has inspired a number of projects to target the specific particle types responsible for the main losses. In this paper we describe the relationship between mineralogy and plant performance at Kansanshi, and discus IntroductionKansanshi is a copper and gold mine located in the Northwestern Province of Zambia, with an annual production in the region of 250 000 t of copper and 160 000 ounces of gold. Ore mined from the epigenetic vein-hosted deposit is classified into three ore types based on the extent of oxidation and supergene enrichment. Sulphide, oxide, and mixed ore are fed to separate mineral processing circuits tailored for recovery of the dominant copper minerals in each. After comminution to a target grind size of 80% passing 150 µm, each ore type is subjected to flotation to recover the copper sulphide minerals (chalcopyrite, bornite, chalcocite, covellite). The oxide float tails and a large proportion of the mixed float tails are then treated by atmospheric leaching to extract copper from the remaining copper-hosting minerals, which include cuprite, malachite, chrysocolla, and delafossite. Some native copper is recovered by flotation and some of it is recovered by leaching. A small portion of the combined concentrate from all circuits is subjected to high-pressure leaching and the rest is sent to the smelter. Sulphuric acid produced during smelting is used for the atmospheric leach."

Nov 1, 2018

By C. Aldı, O. Yaral

For the more economical excavation of tunnels in underground mining activities, the selection of mechanised excavation machines (such as roadheaders, electro-hydraulic drills, etc.) and the analysis of performance prediction that can be used in estimating machine energy consumption have been subjects of research from past to present. One of the parameters to be considered in studies examining these methods, is the grinding process. The success of increasing efficiency in grinding is expressed by a reduction in energy consumption. The goal of a grinding process is to maximise the grinding amount at the appropriate grinding size while minimising the energy consumption per tonne of the fragmented material. Today, the depletion of high-grade ore deposits has largely directed the mining industry towards low-grade but large reserve ore deposits. This shift has particularly increased the importance of the grinding process, as it is dependent on particle liberation. Grinding is a critical step in reducing the mineral to the appropriate size, and energy consumption poses a significant challenge in this process. As a result, researchers have conducted various studies focusing on energy efficiency and cost optimisation in this field. In this study, the grindability of 7 different coal environment rocks (sandstone, siltstone) from the Zonguldak Basin, Uzulmez Region was investigated. For this, Hardgrove Grindability Index and Bond Work Index tests were conducted. While determining the relationships between grindability and other parameters, the results obtained from the Hardgrove Grindability Index (HGI) test were used. The energy values found in the Bond Work Index (BWI) test were used to evaluate the excavatability of the rocks. Additionally, tests for strength, hardness, drillability, and abrasiveness were conducted to observe the impact of other parameters on grindability. Considering the results obtained from the experiments, significant relationships were found between the grindability of the rocks and other parameters.

Mar 30, 2026

By A. Chuma, K. J. Nyembwe, H. Simonsen, J. H. Potgieter

Different concentration techniques were evaluated for preconcentration of a mineral ore at a coarser size to avoid energy and resource wastage. Specifically, the aim was to reduce milling costs and energy required in the beneficiation of tin. In this study, cassiterite (0.17% Sn) was the mineral of interest in a pegmatite ore body associated with quartz (SiO₂ > 60%) and alumina (Al₂O3 > 20%). Three concentration techniques, namely dense media, shaking table, and flotation, coupled with characterization analysis, were used to assess the concentration response. The results confirmed that particle size and mineral liberation impact the separation process. High recovery and grade were obtained with gravity concentration methods (dense media and shaking table) for coarser (+300 to +212 μm) and intermediate (+150 to +53 μm) particle sizes. Lower recovery and grade were identified for much finer sizes (−53 to −38 μm). Flotation produced a high-grade product at a relatively low recovery and appeared to be only applicable to finer grains. Separation efficiency based on Schulz’s equation measured a segregation performance of 74.8% for dense medium separation and 60.7% for the shaking table for the coarse and intermediate particle sizes. Flotation only achieved a separation of 30%–40%. The results suggest that use of dense media separation as a rough preconcentration method prior to further grinding, and the utilization of a more advanced concentration technique for mineral recovery and upgrade, constitute a successful approach to improve process economics.

Apr 14, 2024

By J. M. Descour, K. Aoki, S. Shirasagi

This paper describes the tunnel seismic reflective survey, which has been developed by the authors in order to detect the geological condition ahead of the tunnel face three-dimensionally using reflected seismic waves. In addition, the applicability and the accuracy of the result of this system has been validated by comparing with the geological observation results at the tunnel face and the result of the drill logging system, which was conducted simultaneously with this survey in order to predict the rock properties using the data acquired during drilling from the tunnel face by rotary percussion drilling. In dieser Arbeit werden Reflektionsseismische Tunneluntersuchtungen beschrieben, die von den Autoren entwickelt wurde, um die geologischen Eigenschaften am Tunnelstirnende dreidimensional an Hand reflektierter seismischer Wellen bei minimaler Unterbrechung der Arbeit zu untersuchen. Darüber hinaus wurde die Anwendbarkeit und Genauigkeit der mit diesem System erhaltenen Ergebnisse durch Vergleiche mit den Ergebnissen geologischer Beobachtungen am Tunnelstirnende sowie den Ergebnissen des Bohrlogsystems bewiesen. Das letztgenannte System wurde gleichzeitig mit dem hier genannten System eingesetzt, um die Gesteinseigenschaften mit Hilfe der Daten vorherzusagen, die beim Bohren von Probelöchern im Tunnelstirnende mit einer Drehschlagbohrmaschine erhalten wurden. Cet article décrit une méthode de prospection sismique de tunnel, développée par les auteurs, pour déterminer en 3 dimensions les conditions géologiques existant derrière le front de taille, au moyen d’étude et de mesure des ondes sismiques réfléchies dans le sous sol, et ce, avec un minimum d’arrêt des travaux d’excavation. En outre, l'applicabilité et l'exactitude des résultats de ce système ont été vérifiées, en comparant les résultats des observations géologiques effectuées au front de taille, avec ceux du log de forage qui a été effectué parallèlement à ce système, en vue de prévoir les propriétés de la roche, grâce aux données collectées au cours du forage d’un trou de sonde depuis le front de taille à l’aide d’une foreuse rotative à percussion.

Jan 1, 2003

By J. Du, V. Shukla, C. R. Kumar, U. Shivangi, D. P. Chakraborty

During the processing of iron ores, a large quantity of low-grade tailings containing abundant iron values in fine particle size range is produced. Due to the increasing demand in the high-grade ores for metallurgical operations and the stringent environmental conditions imposed on mining activity, it is essential to utilise the waste tailing pond slimes. Recovery of iron values from these tailing ponds not only enhances the life of the existing operating mines, but also enables achievement of a sustainable process. Iron ore tailing/slime (-150 μm) is produced after scrubbing and wet screening of a low-grade iron ore. Tailing beneficiation of iron ore has been addressed either by flotation or wet high intensity high gradient separation. The present paper aims to recover iron values from discarded slime containing assay ~56% Fe, ~6.5% SiO2, and ~7.0% Al2O3 from the Noamundi processing plant by using a high gradient magnetic separator (HGMS). In this process, tailings are effectively processed with a vertical pulsating high gradient magnetic separator to produce a relatively high-grade iron concentrate. The results of investigation indicate that this novel process is capable of producing an iron concentrate assaying ~ 60% Fe and ~3.25% alumina with a yield of ~55 % on weight basis and recover > 65 % iron bearing particles from the tailings. More importantly, the corresponding tailing contained ~45% Fe. It was concluded that this novel process may be effectively used to recover iron values from low-grade hematite tailings. Keywords: Iron ore slime, Fe recovery, HGMS, yield, Noamundi

Jan 1, 2020

Advances in extractive metallurgy, 1977. Proceedings of the third symposium organised by the Institution of Mining and Metallurgy held from 18-20th April 1977. London, the Institution of Mining and Metallurgy, 1977. 244 pp. £18,50. Coal preparation A meeting of the Organising Committee of the Eighth International Coal Preparation Congress took place in Moscow on 24th and 25th May, 1977. Representatives NIM reports Report no. 1906 An automated instrument for measuring the effects of impurities on cathodic-current efficiency during the electrowinning of zinc. (2nd Sep., 1977). Report no. 1908 An analysis of the replies to a questionnaire on materials of construction for ore hoppers. (16th Sep., 1977). Report no. 1913 The mechanism and rate of reduction of Mamatwan manganese-ore fines by carbon. (2nd Sep., 1977). Report no. 1914 The thermodynamics of the formation of sulphate complexes of iron (111), cobalt (11), iron (11), manganese (11), and copper (11) in perchlorate medium. (15th Sep., 1977). Report no. 1924 The composition of chromite grains from varwUB Witwatersrand reefs. (23rd Sep., 1977). Atomic absorption The Perkin-Elmer Corporation of South Africa is planning to hold an Atomic Absorption Autumn School in Cape Town from 10th to 13th April, 1978. Travel bursaries Two Atlas Cop co travel bursaries for study tours of Swedish mines may be awarded annually to young mining graduates. Stability in coal mining The First International Symposium on the above subject is to be held in Vancouver (Canada) on 5th to 7th April, 1978.

Jan 1, 1978

By J. R. Percival, L. Ip, M. D. Piggott, S. J. Neethling

Component wear due to particle-laden flow is a significant challenge in the minerals processing industry in the handling and transportation of abrasive mineral slurries. Studying wear through experimentation is time-consuming and expensive; therefore possessing the ability to accurately simulate, understand and predict wear in these complex environments is highly desirable. The ability to predict wear is important in both the design of equipment in order to maximise the performance over the wear life of the components, as well in minimising potentially costly and dangerous failures and unscheduled maintenance.. Particle-induced wear is a complex problem, requring an understanding of coupled fluid-solid motion, geometry deformation in response to fluid-solid behaviour, moving geometries and wear modelling. Although the literature demonstrates that rebounding particles and changes to surface profiles can have a significant effect on subsequent wear rates and patterns, the challenge of implementing a model to account for this effect in complex geometries has been addressed by only a few authors in the literature. This paper describes a new wear simulator, leveraging fluidity, an open-source, massively parallel, finite element based CFD simulator capable of unstructured adaptive meshing. The wear simulator includes the ability to model particle-laden flow using representative Lagrangian particles and dynamic remeshing of geometry in response to wear and component movement. These capabilities are demonstrated using wear and the associated dynamically deforming boundaries within a Coriolis tester arm, with the results comparing favourably with the experimentally observed wear patterns. Keywords: CFD, wear, two-phase flows, anisotropic mesh adaptivity, boundary deformation

Jan 1, 2020

By G. Sommer, R. P. Chaix, G. T. W. Ormrod

Recent developments in the instrumentation and automation of uranium-processing plants by G. SOMMER, Ing. (Grad.) (Visitor), G. T. W. ORMROD (Visitor), and R. P. CHAIX, B.Sc. (Visitor) The paper discusses work at the National Institute for Metallurgy on the evaluation of measuring techniques for the automatic control of free acid in leaching. of the ratio of ferric to ferrous ion in leaching, of pH in liquid-liquid extraction. and of uranium in loaded solvent. Commercially available instruments. and the modifications that have been made to adapt them to South African uranium plants, are also described.

By S. Zhang, Z. Hua, D. Feng, X. Tong, X. Xie

The separation and beneficiation of low grade collophanite has long been a technical challenge in phosphorous production. It requires the joint efforts of process design, reagents optimisation and operational control. In this study, the statistical response surface method was applied for determining the optimum reagent dosing in the flocculate flotation of a low grade (18.59%) collophanite ore. The dosage of three reagents, including a pH regulator (Na2CO3), depressant (Na2SiO3) and flocculant (modified starch), were input parameters of the modelling design. Two quadratic mathematical models were derived for prediction of grade and recovery based on the statistical design. Statistical analysis of the experimental results validates the reliability of the models. Through further calculation, the optimum dosage of the three reagents were found to be 3,020g/t Na2CO3, 1,990g/t Na2SiO3 and 880g/t modified starch, with which a maximum recovery of 75.81% and P2O5 grade of 30.08% was obtained from flocculate flotation test. Keywords: Process optimisation, modelling, froth flotation, collophanite ore, response surface methodology

Jan 1, 2020

By B. Genc, C. Gous

Spontaneous combustion during coal mining operations is a major problem that affects the health and safety of workers and causes environmental problems. The phenomenon is associated with the presence of coal, coal shale, and pyrite. In 2020, a premature detonation incident occurred at an iron ore mine where the waste material contains black carbonaceous shale units known to be associated with pyrite. The spontaneous combustion propensity and properties of samples of the black carbonaceous shales from the mine were examined and compared with samples from the Witbank Coalfield. The spontaneous combustion liability indexes of these samples were correlated with X-ray fluorescence (XRF) and proximate and ultimate analyses using linear regression. The Wits-Ehac Index classification results show that the samples were between medium and high risk. The linear regression analysis showed very poor correlations between the Wits-Ehac Index results and the XRF and proximate and ultimate results. The most valuable relationship found is between the presence of relatively high sulphur (greater than 3%) and ground reactivity with nitrate-bearing explosive emulsion.

Jun 5, 2023

Rock mass classification systems are extensively used in rock engineering design work, and mine design is no exception. Among the systems most widely used for mining-related design work are the NGI 0-system (Barton et al., 1974), the RMR system (Bieniawski, 1976), the MRMR system (Laubscher and Taylor, 1976) and, more recently, the GSI system (Hoek et al., 1998). Classifying the rock mass is widely seen as being the fieldwork required to characterize the rock mass and enable the application of empirical design methods associated with the different classification systems. This paper argues that it is fundamentally important to recognize the distinction between rock mass characterization and rock mass classification. These two processes should, in most cases, be separated from each other. Rock mass characterization should be used to determine the intrinsic properties of the rock mass independently of the application; i.e. independent from the infrastructure to be designed, the size, shape, and orientation of the excavation(s) or pillar(s), etc. Rock mass characterization should also be compatible with most classification systems and empirical design methods to be used. Rock mass characterization is the background fieldwork required to perform rock mass classification and/or engineering design work. Rock mass classification is the subsequent step to the characterization, and an integral part of the design process. Parameters that vary according to the design, such as the relative orientation of geological structures compared to the opening or the mine-induced stresses, should be calculated as part of the rock mass classification and design process, rather than during the rock mass characterization process. The failure to distinguish between rock mass characterization and rock mass classification can lead to major design errors and poor results.

Jan 1, 2012

By M. Smit, N. C. J. Dempers, S. Lunkov, C. Saguru, J. Nel

A common method for the recovery of copper is by heap leaching, solvent extraction, and electrowinning. During solvent extraction, the solution is continuously recycled, and it is necessary to remove impurities that build up in the raffinate. For the process investigated in this study, the main impurities include Fe, Co, As, and Zn. Recovery of these impurities can provide economic benefits while adhering to legal and environmental constraints. Such impurities are often removed by precipitation utilizing a neutralizing agent, such as limestone or lime, but it is also possible to remove the impurities by sulfide precipitation. Sodium hydrosulfide (NaHS) is used to selectively precipitate copper, arsenic, and zinc from a solvent-extraction raffinate stream. The resulting sulfide precipitate is bagged and sent to a roaster for further treatment. The design of the sulfide precipitation was investigated to optimize the processing conditions (including temperature, pressure, and residence time), the materials of construction, and the toxicity and explosive nature of the hydrogen sulfide gas produced

Jan 1, 2023

The following corrections should be made to pages 346 and 347 of the December 1981 issue (vol. 81, no. 12) in the paper by O. L. Papendorf entitled 'A note on rapid determinations of present values in the presence of growth and inflation'. (1) Equation (2) on page 346 should read as follows:

Jan 1, 1982

By P. Lenegan, R. Masethe, R. I. L. Ferreira

Underground mining in high rock-stress environments can induce unanticipated dynamic rockmass deformation, posing a serious risk to the workforce. Data collected by seismic networks are imperative for the design-as-you-mine process. Often an inappropriate assessment of the seismic hazard is done when unnecessary data are included in analytical techniques, particularly short-term time frames. Depending on the methodology or application of data analysis and interpretation, some of the information may not be relevant and even detract from the objective. By using the spatial event clusters associated with active workplaces to define the shape and size of the polygons for data selection for subsequent analysis, a problematic subjective component can be eliminated. The mining of tabular reefs in South Africa, be they gold- or platinum group metals, is very extensive, and underground workplaces are often widespread. Production stoppages are very costly, especially for marginal mines, so there is just cause not to evacuate an entire operation’s workforce following the occurrence of a large mining-induced seismic event. A rationale based on the damaging peak particle velocities (PPV) of the past seismicity can exclude the unaffected underground personnel and allow a quick orderly withdrawal where required. Micro-deformation may precede rockbursting, which can occur on-shift close to the workface. A mine-wide array of geophones suitable for the accurate location and analysis of seismicity may not be able to detect these higher-frequency emissions. Inexpensive but fit-for-purpose accelerometers, providing real-time, continuous measurement of acoustic rockmass deformation near the workplace, integrated through underground and surface communications networks, are shown to record ‘rock-talk’, clearly distinguishable from the instrument background noise, which can be in the order of hours leading up to an imminent damaging seismic event.

Jan 12, 2025

By F. T. Cawood, M. N. M. Cudjoe

The ability to conduct real-time material tracking in mines has been a long-standing challenge. Technological innovations such as radio frequency identification technology (RFID) have over the years contributed to the effective tracking of material flow and reporting of metal content. This paper outlines the laboratory procedures and results from testing the suitability of microdot technology as a viable technique for real-time material tracking in mining. The paper clarifies the reasons for conducting the test and presents the material safety data sheet (MSDS) from a South African and Canadian perspective. Microdots from three aerosol systems were immersed in water, heated to 100°C, and crushed into coarse and fine material. These tests were used to ascertain if the technology could withstand mining conditions. A strength, weakness, opportunity, and threat (SWOT) analysis was used to evaluate and compare microdot technology with RFID. It was shown that microdot technology has some potential to track ore parcels because data integrity was retained after exposure to post-blast mining conditions. However, more improvement is required to digitally detect microdots before the technology can be implemented at scale in the mining industry.

Apr 2, 2022

By J. P. Gous, M. Tangstad, J. D. Steenkamp

In April of 2013 a 48 MVA submerged arc furnace producing silicomanganese was excavated in South Africa. One of the areas excavated systematically was the furnace taphole. The aim was to obtain a refractory wear profile of the tap-hole area, together with affected hearth and sidewall refractory. Subsequently, thermodynamic modelling was applied to quantify the potential for chemical reaction between refractory and slag and refractory and metal in the tap-hole area.

Jan 1, 2014

By P. J. K Leeuw, E. Uludag, M. J. Nong

Efficient drill-and-blast performance is pivotal to the profitability of deep-level mines, where high operating costs and declining grades demand maximum throughput. This study investigated persistent fragmentation problems at a longhole stoping operation that suffered from simultaneous oversized rock blockages in 300 mm × 300 mm grizzlies and excessive fines. Fifty-one muckpile images from five blasted stopes were analysed with Split-Desktop. Although the overall F₈₀ was 287 mm, nominally suitable for the grizzly aperture, the Rosin- Rammler uniformity index of 0.80 revealed a highly inconsistent size distribution containing both boulders and fines. Existing drill patterns were then evaluated with the Aegis underground software, which showed negligible crack overlap at the toe owing to inadequate spacing and burden. Insufficient energy overlap between blastholes, particularly at the toe, was found to contribute to the coarse fragmentation, while excessive fines were attributed to the crushing and severely fractured zones of blastholes. Optimisation simulations demonstrated that an 89 mm blasthole diameter on a 2 m × 2 m pattern would overlap, aligning with Aegis requirements of balancing powder factor, break angle, and energy distribution. Implementing this revised pattern is expected to reduce secondary breaking, prevent ore-pass blockages, lower fines, and ultimately improve overall production efficiency. The methodology illustrates how integrated image analysis and modelling software can effectively diagnose and address fragmentation issues, particularly in underground longhole mining, where challenging blasting conditions require a balance between achieving optimal fragmentation and maintaining stope stability. This approach offers a cost-effective pathway to improving comminution performance in deeplevel mines.

Oct 2, 2025

By L. Petzold

The demand for stainless steel is ever-increasing. As an essential element in stainless steel-making process, so is the demand of chromite concentrate. At the same time, the industry proven technologies for beneficiation of chromite are limited. Chromite is only crushed, screened and jigged to produce a concentrate. However, for ultrafine and low-grade material, no satisfactory beneficiation methods for the enrichment of chromite fines exist in industrial operation. This poses a clear challenge for the industry, which Primetals Technologies has addressed with the development of a new beneficiation process. The aim of this process was to enrich low grade chromite tailings to a quality suitable for the smelting process. Required concentrate grades are different over the world, concentrate grades of Cr2O3=40% and lower are found at the Bushveld Complex, South Africa. The target for the present study was a Cr2O3-grade in the area of 49%. Three different chromite tailings with Cr2O3 grades between 16 % and 29 % were part of a study, executed by Primetals Technologies. All three tailing materials were characterised by Mineral Liberation Analysis (MLA). Based on the physical, chemical and mineralogical findings, process flowsheets were developed. The process flowsheets included grinding to ensure a full liberation of the chromite. The liberated material was classified at a cut size of 63 μm to a coarse and fine fraction. Gravity separation and flotation processes were tested with the coarse particle fraction. Due to the limitations of gravity separation with fine particles, only the flotation process is suitable and was tested with the fine fraction < 63 μm. A Design of Experiment (DoE) with six factors, each three levels, was conducted to identify optimal parameters for the fine chromite flotation. Two different collectors were tested: a phosphoric acid ester and a fatty acid type collector. In small scale test work a chromite concentration suitable for the smelting process was achieved. On this basis Primetals Technologies will develop a pilot-scale test program to research recirculation effects and upscale potential of the process. Keywords: Mineral processing, tailings beneficiation, flotation, density separation, process development, chromite

Jan 1, 2020

By M. Z. Emad, Y. Majeed, G. Rehman

Massive deposits of rock salt are mined in the Salt Range area of Pakistan. The main export products of rock salt include salt lamps, blocks, and tiles, while local consumption includes the chemical industry and domestic use. The profitable production of salt for value addition depends on the quality, size, and shape of the block. Salt processing for value addition is easier when very few cracks are present in the blocks. The current salt mining practice involves drilling and blasting, which introduces undesired fractures in the material. This paper focuses on the extraction of rock salt blocks by applying conventional cuboidshaped block mining methods used in quarries. The techniques include wedges and feathers, expansion chemicals, and blasting with low-yield explosives. Experimental work involved both laboratory-scale and in-situ field testing. Laboratory experiments assisted with the determination of splitting force, loaddeformation curves, and other rock mechanics parameters. Regression analysis proposes a relationship for the estimation of radial strain from the load in the case of the wedges and feathers method. The splitting force obtained from the laboratory tests was used to confirm the accuracy of the already published empirical relationship. The results of the laboratory as well as in-situ tests showed that the wedges and feathers technique is the most suitable method for mining rock salt blocks of the desired size, shape, while minimizing cracking.

Mar 2, 2022

By A. McQuillan, N. Bar

Geotechnical models developed during the planning stages of open pit mines are three-dimensional so as to capture the spatial variation in lithological, structural, hydrogeological, and geomechanical conditions. Geological models that describe the lithological and structural (faulting and folding) characteristics of a deposit are always 3D. Likewise, boreholes and piezometers used to develop geomechanical properties and groundwater models are drilled at spatial offsets across the deposit to understand the lateral and vertical characteristics. Yet when geotechnical analysis is completed, often the three-dimensional geological, hydrogeological, and structural models as well as geometrically complex 3D mine designs for optimizing economic mineral recovery and overburden removal are simplified to two-dimensional sections. In this paper we demonstrate that this simplification can lead to the wrong failure mechanism being identified, analysed, and/or a conservative factor of safety being calculated and hence an over-estimation of slope stability. Through case studies we show how three-dimensional analysis methods are more suited to rock slopes, particularly those with anisotropic material strength, when singularities such as geological faults are present, and nonlinear slope geometry. When the same slopes are analysed in two dimensions, the failure mechanism calculated is often fundamentally incorrect. The case studies further reveal that the factor of safety calculated in three dimensions is not always higher than the two-dimensional factor of safety.

Feb 6, 2023