Pit Walls Research Articles

Real-time prediction and assessment of hydrogeological conditions in pit wall rock mass using advanced computer technologies

For the feasibility study of preventive drainage, it is often required to evaluate groundwater inflows in specific pit areas, to identify seepage height in pit wall, and to determine hydrodynamic parameters of flow in the existing geological and hydrogeological conditions. The authors have identified methodological approaches, technological methods and schemes, and combinations of software tools that allow automation of evaluating and predictive studies of hydrogeological conditions in certain areas of open pits using 3D models and finite element methodbased calculations. To solve these tasks, we have tested the dynamic geological simulation software system Leapfrog Geo (Seequent) in combination with the dedicated calculation module Slide2 (Rocscience Inc.). A promising area of joint application of Leapfrog Geo and Slide software is real-time permeation calculations in areas of complex geological and hydrogeological conditions, where grapho-analytical methods provide very approximate and rough results, whereas 3D software products (like MODFLOW or FEFLOW) require too much time and labor input, or even are inapplicable due to lack of modeling source data. The water inflow estimation procedure included determination of specific water inflow in the profile which passed through the center of the flow path, and multiplication of the result by the width of the pit wall intake area with regard to nonuniform permeability of rocks.

Gravity bypass of ore down weakened pit wall in upland quarries

There are many currently known studies and methods concerned with gravity rock flow down the slopes of upland quarries to the receiving sites or into ore chutes. At the same time, the gravity flow of rocks down the highwall of a quarry, which is weakened and is subjected to cumulative load applied by tectonic faults and natural slope above the upper edge of the pit wall, needs extra investigation. The operating experience of upland quarries shows that higwalls often contain eroded areas and tectonic faults. The latter, given certain conditions, can cause large shears, deformations and rock falls in highwalls. Particular hazards can arise when highwall intersects and shears off faults composed of clayey rock layers and dipping toward the mined-out void of the pit. This article offers a brief analysis of the common methods available for gravity rock flows down ore passes in upland quarries in the world. The authors propose a new safe and efficient approach including construction of a support pillar shaped as a truncated pyramid in the weakened pit wall. This engineering solution enables overburden haulage by motor roads made at the top of the support pillar shaped as a truncated pyramid, which allows smooth movement of dump trucks along such roads. Depending on the complexity of geotechnical conditions and cumulative load applied by tectonic faulting and natural slope above the upper edge of the quarry, it is possible to make a number of the support pillars in the weakened pit wall.

Обоснование условий применения автоматизированных систем управления открытыми горными работами строительства комплекса циклично-поточной геотехнологии в карьере с помощью имитационного моделирования

The simulation modeling approach described in the article is intended to assess the efficiency of geo-technologies and can be applied: 1) to evaluate the implementation of smart geotechnologies with digital transformation of the mining systems; 2) to select the mining and transportation management system as well as the preferred logistic scheme of the mine. This approach makes it possible to make more reasonable investment decisions based on an objective quantitative assessment. Simulation modeling should be based on the results of geotechnical justification of structural parameters of the pit walls and benches in operating and limit states. Transition to automated systems to control smart geotechnologies in programmable mode and timely inclusion of the In Pit Crushing and Conveying (IPCC) technology into the transport scheme helps to: 1) remove people from the working zones inside the open pit; 2) significantly reduce the ore mining costs; 3) advance to a higher level of technology in developing the deposits; 4) process ores that were previously considered substandard. As an example, the assessment results are provided of the implementation of new rock mass transportation technologies at the Codelco copper mine in Chile in the Radomiro Tomic open pit.

Analysis for design optimization of high thrust liquid engine hot test facility

A high thrust liquid oxygen-kerosene fuelled engine is being developed for future launch vehicle applications. Comprehensive hot testing of engine at sea level conditions is required for qualification and acceptance of flight engine and launch vehicle stage. The engine and stage will be tested in a specialized rocket engine and stage hot test facility which deflects the flame safely to avoid any hazard to engine and adjoining mechanical structures. The facility is equipped with water jets to sufficiently cool the rocket plume before impinging on deflector pit walls. The high temperature and high-pressure rocket exhaust jet is cooled with sufficient quantity of water to maintain the impingement wall temperature within safe working limits.In this study, a multi-phase computational fluid dynamics (CFD) methodology is developed for design of water-cooling jet configuration of deflector facility. Multi-phase model validation study using full phase treatment and droplet assumption for water injection is performed prior to water jet optimization analysis of high thrust LOX-kerosene test facility. Validation studies based on simulation and analysis of existing test stand is developed. A discrete particle (DPM) based two phase methodology is chosen to model water injection in RANS framework. The optimum cooling configuration is determined iteratively through numerous multi-phase simulations. The multi-phase analysis showed ineffectiveness of initial water injection scheme which results in facility wall temperature above safe limit. A multi-plane water injection scheme is devised there on with provision of water injection at two axial locations from the nozzle exit. A detailed parametric multi-phase analysis is carried out for design optimization of multi-plane water injection scheme and to determine thermal condition of the test facility. Analysis showed effective rocket plume cooling and lower facility wall temperature with two plane water injection schemes in comparison to initial single plane design configuration. The study highlights the role of CFD based methodology to formulate an engineering solution for design optimization of LOX-kerosene engine hot test facility.

Geomechanical substantiation of the Oleniy Ruchey deposit underground mining in a protective pillar of the Niorkpakhk open pit

The location of significant volumes of the lower level reserves close to an open pit which produces the adjacent Niorkpakhk deposit considerably complicates underground mining of the Oleniy Ruchey rockburst-hazardous deposit. The progress of underground excavations into the under-pit space is permitted if the undermined rock thickness and open pit walls remain stable. 3D numerical studies of stress-strain state have indicated particularities in deformation such as increase in undermined thickness stability under high tectonic stresses. The parameters of safe mining of temporary inactive reserves were scientifically substantiated. The boundaries of maximal development of underground mining were determined. The stability of overlying rocks and open pit walls is maintained by forming an advance of overlying sublevels relative underlying ones under 45° angle and providing the monitoring for the undermined rock mass. The mining method in a protective pillar the authors propose allows increasing reserves of the first mining stage by 76.9% and avoiding decrease in production volumes when mining operations terminate.

Engineering formulas for dimensioning of deformation and damage zones in jointed rock mass under impact of blasting in quarries in Transbaikalia

Currently, there are five characteristic zones of blast-induced impact in quarries: crushed zone, radial cracking zone, severely fractured zone, blast-induced residual stress zone, and blast-induced load zone. Knowledge about the size of the zones is very important in the technological processes of mining. The size of the crushed zone governs the amount of ore over-grinding and loss. The size of the radial cracking zone is reflective of the spacing of blastholes. The size of the severe fracturing zone is characteristic of the geometry of an unstable pit wall area. The zone of blast-induced residual stresses in rock mass and its size affects the slope stability of pit wall. The purpose of this study is to develop engineering formulas for calculating the sizes of deformation and damage zones in jointed rock mass during short-delay blasting in quarries. The mathematical and numerical analyses of the complex theoretical expression provided engineering formulas for dimensioning of the blasting-induced impact zones in quarries. The reliability of the formulas is proved by the comparison with the full-scale testing data obtained in quarries in Transbaikalia.

Predictive assessment of the stability of quarry sides

The composition of the rocks composing the quarry sides and the approximate slope angles in accordance with the mining and geological conditions are described. The issues of creating observation stations are considered taking into account seasonal temperature fluctuations of the benchmarks. Observation materials are generalized, the degree of danger of deformations is established on the basis of observations of deformation speed. The mining safety control methods are described. The disadvantages of the approach to data processing and analysis are identified. A criterion for mine surveying prediction of the pit wall stability based on the comparison of critical and actual relative deformations is proposed. The purpose of the local forecast of wall deformation is to control the stability of non-working and working slopes of the sides, and to confirm the efficiency of the method used. The predictive assessment was carried out on the shift of working benchmarks on one of the open pits of Transbaikalia. It is suggested monitoring the stability of rocks using oscillograms obtained by seismic equipment.

Stabilization of sand pit wall permeability using Ranney wells

Safety of operating conditions is the paramount objective in any mine design, planning, construction and performance. In the Kursk Magnetic Anomaly, the emphasis is laid on the integrated and efficient protection of surface and underground mines from groundwater inflows. Stoilensky iron ore field hydrogeologically adjoins the northeast of Dnepr–Donets artesian basin which is contiguous to the southwest slope of Voronezh crystalline massif. The field mostly occurs in the zone of damaged groundwater dynamics under the impact of drainage facilities at opencasts of Lebedinsky and Stoilensky GOKs (Mining and Processing Plants) and at Gubkin Mine, hydraulic fills and tailings ponds of operating processing factories, and Stary Oskol water storage basin. The adversities of groundwater catchment inside sand pit wall rock mass are analyzed. The capabilities of a pit wall drainage system in stabilization of sand permeability are discussed. The experience gained in design and construction of a local drainage system based on Ranney-type well within the limits of Novaya station of an operating opencast is summarized.

Geomechanical substantiation of the northeastern pit wall stability in Kurzhunkul mine

Kurzhunkul magnetite deposit is located in the Kostanai Region of Kazakhstan and is an open pit mining project of Sokolovsko–Sarbay Mining and Production Association (SSGPO) since 1983. The current depth of the open pit is 240 m (Level -28 m). It is expected that Kurzhunkul pit reaches the depth of 290 m. The deformation determinant in Kurzhunkul mine is its geological structure represented by complex faulting. Special care and attention should be paid to the northeastern pit wall which is a zone of large and closely spaced tectonic faults essentially extended along the strike and dip of the deposit, and depthward the pit. Unfavorable bedding conditions in combination with weak physical and mechanical properties of fracture fillers can induce movement of rock blocks during extraction of mineral reserves from the weak zone of the northeastern pit wall. This study offers the geomechanical substantiation of stability of NE Kurzhunkul pit wall which is most heavily intersected by tectonic faults and has low strength characteristics. The study was carried out with grant financing in framework of Project No. AR08053358 Rock Mass Control Based on the Integrated Geomechanical Model toward Mining Safety.

Uncertainty consideration in rock mass blastability assessment in open pit mines using Monte Carlo simulation

Blastability is defined as the resistance of rock mass to fragmentation due to the dynamic stress of blasting. Comprehensive study and understanding of geomechanical conditions of the in-situ rock mass are necessary to analyze the blastability along with optimal blasting design. Blastability Index (BI) is one of the most widely applied methods for the classification of rock mass and predicting the specific charge of blasting in open pit mines. Regarding the existence of uncertainty in the geomechanical characteristics of in-situ rock masses, accurate BI assessment requires a wide range of field studies. It could lead designers to a wrong decision about rock mass classification. Simulation is one of the reliable and applicable approaches to overcome the geomechanical uncertainties in rock mass studies. Therefore, in this paper, the Monte Carlo simulation method has been applied to blastability assessment in Sungun Copper Mine, Iran. For this purpose, the geological factors, including rock mass description, joint plane spacing, joint plane orientation, specific gravity influence, and hardness, were measured and implemented in 46 points of the pit wall. Statistical analysis was carried out to find out the best fit-distribution functions of all mentioned parameters. After that, the Monte Carlo simulation program was developed and carried out in MATLAB software. The overall results of the simulation reveal that the Monte Carlo method could provide a better vision of any possible combination of geological factors. It is also found out that less than two percent of the rock masses do have challenging blastability conditions, and the average blastability of rock masses in the studied mine is 18, which is close to an average score of blastability classification as well.

Evaluation of the Influence of In Situ Stress on the Stability of Mine Pit Walls: A Case Study of Songwe Mine

The investigation of the influence of in situ stress in Open Pit Mine (OPM) projects has not been accorded a deserved attention despite being a fundamental concern in the design of underground excavations. Hence, its long-term potential adverse impacts on pit slope performance are overly undermined. Nevertheless, in mines located in tectonically active settings with a potential high horizontal stress regime like the Songwe mine, the impact could be considerable. Thus, Using FLAC3D 5.0 software, based on Finite Difference Method (FDM) code, we assessed the role of stress regimes as a potential triggering factor for slope instability in Songwe mine. The results of the evaluated shearing contours and quantified strain rate and displacement values reveal that high horizontal stress can reduce the stability performance of the pit-wall in spite of the minimal change in Factor of Safety (FoS). Since mining projects have a long life span, it would be recommendable to consider “in situ stress-stability analyses” for OPM operations that would be planned to extend to greater depths and those located in tectonically active regions.

The influence of bottom-up anchors pre-tension optimization on the prediction of pit walls rockfall displacements

Introduction. Currently in Russia, innovations in urban subsoil facilities construction are among the key factors of economic development. To improve the efficiency of holding a pit wall in restraint urban conditions and prevent soil loosening around the pit, it is proposed to optimize the pre-tension forces of the bottom-up anchors. It has been determined that the pre-tension forces of the active anchors create extra retention forces in the sliding wedge and, in some specified sense, reinforce the walled soil. Research methodology. When modeling the complex calculation of a pit wall, 4 main stages of the pit excavation and 3 stages of preliminary level tensions of anchor ties were preset. The numerical solution of the beam bending problem is the basic method of calculating the walling strength; the beam laying on the elastoplastic base and retained by the anchors as bonds. The bottom-up anchor structure is modeled in the operating environment of GeoWall software. The values of bottom-up anchors pre-tension are set following the ordinates of forces in the anchors, obtained from the walling stability calculation by the deterministic approach. Experimental research was carried out of the impact made by pit opening stages on the walling stress strained state. Results. Analysis and discussion. The efficiency of bottom-up anchors optimal pre-tension, according to the research results, is obtained by constructing the diagrams reflecting the correlation dependence between the anchors loading and the walling displacement. An obvious advantage of the software is the opportunity to calculate walling and retaining structures stage by stage ignoring their construction technologies. Experimental calculation in GeoWall has shown a high bearing capacity of the bottom-up anchor support. Summary. The nature of the obtained dependence between the anchor longitudinal forces and the pit walling horizontal displacement reflects the actual situation. Thus, for a quiet expectable value of horizontal displacement, it is required to correct the optimal value of pre-tension using the empiricalformula dependences.

Impact of blasting on pit wall rock mass

The paper presents the research findings obtained by the Institute of Mining in drilling and blasting in Dzhetygara open pit mass. The research was aimed at enhanced stability of stationary benches and at cost minimization of drilling and blasting. The research met two objectives. First, in terms of Dzhetygara deposit, perimeter blasting designs were developed, which ensured reduced impact of blasting on adjacent rock mass. Second, the blast-induced PPV measurement procedure was refined and introduced, and the blasting technology was improved for blasting operations at ultimate pit limit. The special technology for ultimate pit perimeter blasting includes: analysis of blast effects on pit wall rock mass; finding of mechanisms of wave processes in rock mass; interaction of perimeter blasts depending on strength characteristics of rock mass; field trial of cutback methods; determination of sequence of blasts when approaching a guarded sites; determination of efficiency criteria of drilling and blasting.

Features of seismic wave travel along a coal pit wall

Triple gain of the maximum amplitudes or massif vibrations in a final phase of the consecutive blasting of groups of borehole charges during the propagation of a seismic blast wave outside the mined block in the Quarternary deposits of a coal mine slope has been experimentally established. The effect of “rocking” the massif occurs stepwise, and it is synchronized according to the selected delay intervals at detonation.

Determination of bench, dump and road sliding wedge technological parameters

Mine surveying in mining operations is of particular importance, since all technological processes of the full life cycle of a mining enterprise and, ultimately, its competitiveness depend on the surveying quality, efficiency and reliability. Organizations independently determine the structure of mine surveying services, taking into account the methods applied and the scale of mining. To ensure safe open-pit mining of minerals, it is necessary to permanently assess and monitor the pit bench and wall rock mass condition. Misjudgement of rock physical and mechanical properties, non-observance of the minerals mining and transportation process cycle, changes in climatic conditions and other problems lead to loss of stability of rocks in all parts of an open pit, including in the areas of ore production and mining and transport equipment operation. The existing practice shows that the effectiveness of an open pit wall and bench stability calculation can be achieved using a technique that should take into account the slope deformation and failure mechanism, as well as the nature of the stress-strain state of the open pit rock mass. The studies presented in the paper are based on comparative analysis of the sliding wedge parameters for benches, dumps and roads at open pits using analytical and graphical software packages, and taking into account the static load produced by dump trucks. The study findings allow to establish that: determination of the bench slope stability and the sliding wedge width, performed by the analytical method, gives higher accuracy results than those obtained by the graphical method; the bench slope stability and the sliding wedge width depend not only on the rock physical and mechanical condition, but also on the bench height, the dump truck (plus its freight load) weight per 1 linear meter of the placement area, the distance from the slope edge and other factors; the rock mass is stable and not subject to landslide phenomena for as long as the sum of the holding forces is greater than or equal to the sum of the shearing forces; when using large-sized transport equipment of nonstandard weight in open-pit mining, it is necessary to calculate the safe width of the sliding wedges, taking into account the loads on them (per 1 linear meter), the values of which can be 1.5–2.0 times higher than those calculated for the circular-cylindrical sliding surface.

Engineering and geological zoning of the Malmyzhsky deposit weathering crusts (Svoboda area)

Introduction. Interest in the study of weathering crusts arose at a time when geological engineers faced the problem of developing open pits formed by eluvial soils. However, the exact and detailed division of the weathering crusts into engineering-geological zones, especially when studying mineral deposits, is not given due attention even today. Therefore, in the course of prospecting, it is important to correctly determine weathering crust type and profile, and establish the possibility of changing the engineering and geological conditions when opening the rock mass by mine workings for further slope stability prediction of the designed mining structures. Research aim is to determine vertical engineering-geological zoning of the Malmyzhsky deposit weathering crusts (Svoboda area) and identify patterns in alluvial deposits physical and mechanical properties change, which define the safety of mine development. Methodology. A significant number of Russian and foreign scientists have considered the formation of weathering crusts from different positions. They established the geochemical zoning and engineeringgeological zoning of the weathering crusts. Results. The article describes the Svoboda area at the Malmyzhsky gold-copper-porphyry deposit. Engineering and geological zoning of the weathering crust section was carried out according to a set of features, including structural and textural features, mineral composition, physical and mechanical properties of rocks. Within it, three zones are identified at the Malmyzhsky field, the Svoboda area: IV – dispersed, III – litomarge, and II – clastic. Physical and mechanical properties of rock building up the considered weathering crust have been analyzed proving that change in geological conditions within even one zone of the Malmyzhsky gold-copper-porphyry deposit (Svoboda area) entails a change in the choice of projected pit wall angles.

Мобильный локализатор для разрушения негабаритов

Research objective: Development and implementation of a mobile safety screen for secondary breaking. Research methodology: Analysis of secondary breaking of oversize boulders. Research results: blasting creates oversize chunks of rock (boulders) in the pit walls and floor, which affects the productivity of the pit and the mining operation as a whole. Open pit mines with large volumes of rock formations have to handle hundreds of cubic metres of boulders every day bearing significant labour and material costs of these activities. Various methods of boulder breaking are used in open pit mining, including electrical treatment, mechanical impact, blasting, etc. A common disadvantage of these techniques is their relatively low capacity. Out of all the applied methods, drilling and blasting of boulders is the most effective, but the use of this method is limited due to the use of various equipment, increased hazards and the presence of certain other disadvantages. The autonomous mobile safety screen has been developed to solve this bottleneck. The use of this safety screen enables breaking boulders using blasting techniques, reduces the size of the hazardous area, increases the efficiency of the air shock waves, prepares safety trenches in open pits and for road construction, prepares the rock mass for long-distance transport by road or railways. Conclusions: The use of this safety screen enables breaking boulders using blasting techniques, reduces the size of the hazardous area, increases the efficiency of the air shock waves, prepares safety trenches in open pits and, during road construction, prepares the rock mass for long-distance transport by motor and railroads.

A Numerical Investigation of the Deformation Mechanism of a Large Metro Station Foundation Pit under the Influence of Hydromechanical Processes

Considering the unique conditions of deep and large subway foundation pit excavation affected by heavy rainfall in soil-rock composite strata, this paper employs finite element numerical simulation methods to study foundation pit instability under the influence of heavy rainfall. According to the hydraulic coupling conditions caused by rainfall, a fluid-solid coupling numerical model for a deep and large subway foundation pit in soil-rock composite strata is established in this paper. By selecting the Anshan road station of Qingdao subway line 4 as the engineering background, various parameters related to foundation pit excavation affected by heavy rainfall at different excavation depths were analyzed. The study found that after the foundation pit was excavated, the surrounding pore water pressure decreased and the pore water pressure near the ground surface increased rapidly due to rainfall. As the horizontal distance from the foundation pit increased, the pore water pressure at the same depth also increased. The excavation of the foundation pit caused uplift of the bottom of the pit. After rainfall, the uplift value decreased compared with that before rainfall. With increasing excavation depth, the decreased value of the bottom uplift decreased and then increased. The rainfall caused the horizontal displacement of the pit walls on both sides of the pit to increase. When the excavation depth was 10 m, the horizontal displacements on both sides of the pit were equivalent. When the excavation depth was 20 m, the horizontal displacement was concentrated in the first 10 m; when the excavation depths were 30 m and 40 m, the horizontal displacement was concentrated in the first 13 m. This finding shows that when the foundation pit was affected by rainfall, the sidewall collapsed at a distance of 13 meters from the ground. As the excavation depth increased, the depth of excavation instability was closer to the bottom of the pit. The research in this paper can provide a reference for the construction of deep and large foundation pits in similar composite ground conditions that are affected by rainfall.

General concept of determining the parameters of non-mining walls of ultra-deep diamond deposits development open pits

A specific feature of open pit mining of diamond deposits in Western Yakutia is the construction of the open pits in the zone of negative ambient temperatures, which includes thick permafrost rock mass, and which is at the same time complicated by the influence of cryogenic processes on deformation of pit wall benches. The paper presents the comparative analysis of strength characteristics in frozen and thawed rocks, stability of benches during mining, the general geomechanical approach to the determination of parameters of non-mining walls of the ultra-deep open pit diamond mines, and the parameters of nonmining walls and benches. Optimization of open pit wall configuration should primarily be based on the maximum utilization of the strength properties of frozen rocks in combination with the development of new approaches, calculation schemes and methods for assessing stability of open pit walls and benches of unconventional design, including the non-mining vertical benches. The main design characteristic that determines the parameters of open pit walls is the structural tectonic relaxation coefficient, which specifies the calculated value of cohesion in rock mass. For the diamond deposits, the values of the structural relaxation coefficient were obtained in a series of field tests and back calculations. Full-scale tests were carried out both during exploration operations in underground mines and in open pits. The accuracy of determining the values of the structural relaxation coefficient in the range of 0.085–0.11 is confirmed by the parameters of non-mining walls in an open pit mine 385–640 m deep, with overall slope angles of 38–55° and a steeper H 0.35–0.5 lower part having the slope angle of up to 70° with average strength characteristics of 7.85–11.84 MPa and the internal friction angle of 28.1–37.4°. Using the natural load-bearing capacity of rock mass to the full advantage, which the values of the structural relaxation coefficient of deposits show, allows optimization of open pit wall slope design and minimization of stripping operations.

Assessing the impact made by groundwater processes and undermining on coal pit wall stability

Introduction. The reliability of geomechanical prediction depends on the level of detail of databases covering geological structure, geometry and physical properties of the rock mass under investigation. In order to improve the accuracy of coal pit wall stability prediction, following the generalization of databases containing geological survey, groundwater monitoring, geophysical sounding and mine surveying, it is advisable to construct three-dimensional geological-geophysical models accounting for the main adverse factors, and thereafter search for the most hazardous section. Research aim is to predict wall stability according to the developed algorithm based on the threedimensional geological-geophysical model. Research methodology includes a search for the most hazardous rock mass site section by the ratio between shear and retaining forces within the established zones with anomalous physical characteristics. Results. By generalizing databases containing geological studies, groundwater monitoring, geophysical sounding by the method of electrical resistivity tomography, and mine surveying, a three-dimensional geological- geophysical model has been constructed of a wall loaded with “heap of dry rock atop of the hydraulic dump” man-made structure and undermined by underground works. The trial site stability has been predicted for the true state of mining. Comparative analysis of the obtained data has been carried out. Summary. The combination of natural and man-made factors, including hydrogeological conditions of the territory, seasonal and climatic behavior, tectonic faulting of the deposit and shear zones connected with undermining result in the development of a rather complex geological structure of the wall which includes local deconsolidated and waterlogged zones significantly reducing the stability of the pit slope. At the trial site of Kedrovsky pit due to spatial and temporal alternation of properties and state of rock within the landslide hazardous zone, the variation range of the factor of safety in six typical sections amounts n = 1.06–2.39. For that reason the objective prediction of slope stability in similar conditions (in addition to geological survey and hydrogeological observations data analysis) should include geophysical monitoring of anomalous zones origination and development, hereupon creation of a treedimensional geological-physical model, and the automated calculation of the factor of safety including repeated selection of the most hazardous section.