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By William Gleason

"It is safe to say that the coal industry, in the United States and globally, is currently suffering through one of the hardest times in its history.A perfect storm of competition, changing energy demands, politics and public perceptions have collided, inflicting significant harm to the industry that many say is irreparable. This, in turn, has led to massive job losses in some regions, heavy cuts in production and even bankruptcy filings from two of the largest coal mining companies in the nation.Cheaper natural gas can certainly take a large share of the blame for the struggle of coal, as utility companies switch from coal to natural gas for power generation. According to the U.S. Energy Information Administration (EIA) the amount of coal used for electricity generation in the United States is at a 45-year low.November 2015 marked the fifth consecutive month that natural gas was the leading source of power generation in the United States. EIA said generators produced 101,866 thousand megawatt hours (MWh) of electricity with gas in November versus just 87,789 thousand MWh with coal, the lowest monthly level since May 1980 when monthly coal use was 84,884 thousand MWh.According to Robert Godby, director of the Center for Energy Economics and Public Policy at the University of Wyoming, there are a number of factors playing a role in the decline of coal, but he points to the advances in fracking as the tipping point.“A lot of people will argue that regulation is the cause of the decline, and it has played a part, for sure, but the story of the recent past is more about what competition has done to the energy market,” Godby told Mining Engineering. “The war on coal was originally declared by natural gas in 2008.”The price of natural gas, which was at $13 per million Btu before the gas fracking boom, has fallen to as low as $1.68 in December 2015. Likewise, Godby said the cost of wind generation is now lower than the cost of generation from coal and the cost of solar generation is coming down as well. In addition to that, the demand for energy has changed in the past five years with more efficiencies in everything from building design to lightbulbs."

Jan 1, 2015

By William Gleason

"Government support for Canada’s mineral industry was on full display during the Prospectors & Developers Association of Canada (PDAC) conference in Toronto, ON, Canada on March 3-6. First, there was the announcement of the five-year extension of Canada’s Mineral Exploration Tax Credit (METC), the first multi-year extension of the METC since its inception in 2000. Canada’s Minister of Natural Resources, Amarjeet Sohi, added to that support when he spoke at the opening keynote session and announced the Canadian Minerals and Metals Plan (CMMP), a plan that aims to map out the future of the industry in Canada. Finally, the support for the mining industry was buttoned up with a visit to the conference by Canadian Prime Minister Justin Trudeau.More than 25,000 people from 135 countries attended the annual conference that features a robust trade floor, technical sessions and an investors’ exchange that aims to put mining companies in touch with potential investors. Mining companies and ambassadors from nations around the world are given the opportunity to present to small audiences throughout the conference and this year PDAC was able to sway the Prime Minister to speak on its behalf.Trudeau sat down with PDAC President Glenn Mullan on March 5 to talk about the METC extension and a host of other issues important to the Canadian and global mining industry, giving the home country a bit of a profile advantage when it came to making a pitch to investors.Trudeau entered the week of the conference in the midst of the most serious political scandal of his career and was defending himself against accusations of political interference with the top prosecutor in the land over a criminal case involving one of Canada’s largest companies, SNC-Lavalin. During the question-and-answer session at the Metro Toronto Convention Center, Trudeau seemed more than happy to keep to the discussion about mining. He spoke favorably about the industry during the half hour conversation and praised the industry for its work with Indigenous people as well as its efforts to advance technology and innovation. He made a case that Canada is a safe and reliable place for investment in the minerals sector.“We are at a time of change right now, of transformation with new technologies and global supply chains, and everyone is trying to adjust to the new realities that have accelerated so much these past years,” Trudeau said. “What we are trying to do as a country and what you have done as an industry is to try to look at where things are going – go to where the puck is going to be, not where it is. You, as an industry, know that investments in innovation, research, science — investment in technology and partnerships with Indigenous communities are all things that are going to give you opportunities to be competitive in the coming years.”"

Apr 1, 2019

By C. O. Brawner, J. Kalejta II

The classical approach to control rock fall and ravel in open pit mining has been to use catch benches. The width and volume of benches is most dependent on the bench height, size of loading equipment, blast damage to the face and mining regulations. This was compatible with open pit slopes of less than about 45°. As our understanding of rock mechanics and blasting control has improved over recent years, much steeper rock slopes can be developed at many open pit mines. However, narrower benches result with less rock fall capacity. The transportation industry has been very successful in using catch fences to protect highways throughout North America and Europe for years. The authors recommend that cable and ring net fences have a potential major application in open pit mining to allow steeper rock slopes with significant economic benefit. This paper outlines the application, design and operation of catch fences in surface mining for specific conditions. Typical case examples are presented.

Jan 1, 2002

By Moussa Wone

The Washington, DC Water and Sewer Authority (WASA) has implemented facility planning for the Anacostia River Projects portion of a program to bring its Combined Sewer System (CSO) into compliance with federal water quality regulations by 2025. The program includes approximately 19 kilometers (12 miles) of deep CSO storage/conveyance and flood relief soft ground tunnels, construction, vortex drop, overflow, maintenance and air release shafts, as well as near surface diversion structures and conveyances. The Project encompasses major technical and non-technical challenges including completion under a federal consent decree schedule, construction within the confines of heavily developed urban areas, difficult ground conditions, major infrastructure crossings, and close coordination with several major public agencies. This paper discusses the planning stage considerations related to the geotechnical investigation program, discusses obstructions that influenced alignment selection, and provides two examples of preliminary estimates of settlement induced ground movement due to the tunnel and shaft construction.

Jan 1, 2008

By Wang Hongwei, Wu Yongping, Cao Peipei, Jiao Jianqiang

Fully mechanized top caving mining of steeply inclined extra-thick seams with variable angles has complex roof rock movement, failure, caving, and filling mechanisms. Moreover, the variable-angle coal seams make rock–equipment stability control challenging. We analyzed rock deformation and failure mechanisms, overburden bearing structures, and working characteristics of supports through physical simulations, field tests, and theoretical analysis of the no. 120210 working face of Zaoquan Coal Mine. Overburden rock movement has distinct regional characteristics, with a large caving height (to the main roof layer) in the upper area, and lower caving height (to the lower main roof) in the lower area. Support loading is regional and unbalanced along the inclined direction. The critical layer of overlying strata migrates, and bearing structures formed by breaking the critical layer exhibit cross-layer generalization along the inclination. The upper region has a cantilever beam structure in the basic roof rock layer; the lower region has an inclined masonry structure with multistage ladders in the breakage basic roof rock layer. Application of a false-inclined working face layout with the tailgate ahead of the headgate and an arc arrangement (radius 28.65 m, arc length 10–20 m) in variable angle areas, and regional control of support working resistance and top-coal caving amounts, control regional failure overburden. Safe and efficient mining was achieved, with the monthly production and recovery rates reaching 344,900 t and 85.86%, respectively. Our results expand the scope of fully mechanized top caving mining and have important theoretical and technological significance.

Nov 23, 2020

By Rameshwar Sah, Bharath Kumar Shanmugam, Govinda Raj Mandela, Marutiram Kaza, Harsha Vardhan, Harish Hanumanthappa

Iron ores obtained from different sources differ in their chemical and physical properties. These variations make the process of grinding a difficult task. The work carried out in this context focuses on three different samples of iron ore, viz., high silica high alumina, low silica high alumina, and low silica low alumina. The grinding process for all the three iron ores is carried out individually in Bond’s ball mill and the total retention time taken by each iron ore sample is calculated. The present investigation focuses on utilizing the calculated retention time of the iron ore as a standard grinding reference time to the laboratory ball mill for optimizing the grinding time of each ore. The desired P80 (150 μm) with an acceptable range of hematite liberation (> 75%) was obtained in the laboratory ball mill after reducing 6 min from the total retention time taken in the Bond ball mill.

By Rameshwar Sah, Bharath Kumar Shanmugam, Govinda Raj Mandela, Marutiram Kaza, Harsha Vardhan, Harish Hanumanthappa

Iron ores obtained from different sources differ in their chemical and physical properties. These variations make the process of grinding a difficult task. The work carried out in this context focuses on three different samples of iron ore, viz., high silica high alumina, low silica high alumina, and low silica low alumina. The grinding process for all the three iron ores is carried out individually in Bond’s ball mill and the total retention time taken by each iron ore sample is calculated. The present investigation focuses on utilizing the calculated retention time of the iron ore as a standard grinding reference time to the laboratory ball mill for optimizing the grinding time of each ore. The desired P80 (150 μm) with an acceptable range of hematite liberation (> 75%) was obtained in the laboratory ball mill after reducing 6 min from the total retention time taken in the Bond ball mill.

By J. Fritz, V. Gangrade, J. Briton, K. M. Ajayi, M. L. Harris, G. Cole, M. Young

Mine workers using diesel-powered equipment experience the highest occupational exposure to diesel particulate matter (DPM). This problem could be aggravated in underground stone mines due to their unique ventilation challenges with the large openings for airflow. Hence, adequate ventilation in these mines requires a combination of effective ventilation planning and delivering needed air quantities using auxiliary fans and stoppings. To meet this challenge, the National Institute for Occupational Safety and Health (NIOSH) developed the Air Quantity Estimator (AQE) software as a mine planning tool to help underground mine operators estimate the air requirements necessary to dilute DPM in the main air stream to statutory levels. The major parameters required for the calculations are the engine’s horsepower, DPM emission rate, the percentage operating time, catalytic converter efficiency, and filter efficiency. In efforts to provide major updates to this software, this study describes the recent development of a revised version of the Air Quantity Estimator (AQE 2.0). With the revised version, users have access to a comprehensive database of over 40,000 pieces of equipment, can define their specific target DPM level, and can create specific equipment for a customized database, in addition to having an improved easy-to-use interface. The software output provides an estimated total airflow necessary to dilute DPM based on the projected emissions, and the user can generate a related results report. The results also provide the mine personnel with a tool to identify vehicles that are high DPM contributors and could further be used to optimize the ventilation requirement by making changes to the percentage operating time of the engine. This software provides the mine with a user-friendly tool that could help reduce the DPM exposure of workers.

Feb 1, 2023

By T. Tamagawa

A gaseous chlorination process for hydrometallurgical treatment of a chalcopyrite concentrate was investigated. The overall process is visualized to consist of low temperature chlorination-selective oxidation, followed by aqueous chloride leaching and SX-EW for producing electrolytic copper elemental sulfur and ferric oxide. In this article, the chlorination phase of the processes is described. Initially, the chlorination behavior of chalcopyrite-concentrate micro-pellets was investigated using a small batch-type fluidized bed reactor. The optimum conditions thereby established was used in continuous chlorination tests. The chlorinated products thus prepared were used in the selective oxidation phase of the investigation.

Jan 1, 1999

By F. Burat

Large reserves of feldspar ore exist in the Aegean region of Turkey. The main colored impurities in these ores are iron- and titanium-bearing minerals such as anatase, rutile, sphene and ilmenite. In this study, a potassium feldspar ore containing mainly quartz and coloring impurities was subjected to beneficiation tests involving magnetic separation and flotation, which were applied either separately or in combination. Bench-scale flotation experiments using cationic collectors G-TAP and Flotigam V-4343 and using HF and H2SO4 as modifiers were employed to separate feldspar from quartz and to remove part of the titanium impurities. The best results were achieved with a combination of high-intensity wet magnetic separation and flotation. A feldspar concentrate containing 16.28% Al2O3, 10.75% K2O, 2.84% Na2O, 69.97% SiO2 and 0.16% Fe2O3 was produced. A quartz concentrate containing 2.30% Al2O3, 0.48% K2O, 0.42% Na2O, 0.07% Fe2O3 and 96.20% SiO2 was also obtained

Jan 1, 2007

By Richard F. Flanagan, Robert H. Marshall

The Republic of Singapore’s Public Utilities Board is implementing the Deep Tunnel Sewerage System Project. The project’s deep tunnel component, 48 km of deep, large diameter sewer tunnels has been successfully completed (the works are in the defects liability period). Six International Design/Build tunnel contracts utilized eight Earth Pressure Balance TBMs ranging up to 7.23 m in diameter to deal with varied ground types ranging from deep soft clays to fresh granite. Numerous access/workshafts were constructed and using various support systems. This paper provides an assessment/overview of the tunnel contracts, tunnel excavation methods and equipment, and the shaft systems. Suggested enhancements to similar future projects are provided.

Jan 1, 2007

By M. Bunch

"THE SUPER CYCLE IS GONE The utopia of the rising sales volume, for mining companies from 2002-2011, was entirely due to rising production volume and prices. The Australian mining sector experienced an 18 percent annual growth rate in revenues, and 11 percent growth in prices. (1) However, EBIT remained flat during the same time period. In addition, Australian mines saw a 7 percent annual decline in both labor and capital productivity. (2) Mines in the U.S. and Canada produced similar results, whereas the world-wide mining industry has seen a productivity drop of 40% since 2001. (3) The decade “Bull Run” of rising prices was trashed by companies that chased low-quality assets while increasing debt on their balance sheet. It seemed everyone believed the “super cycle” would last forever, while completely ignoring the history of cycle downturns. Worldwide mining operations are as much as 28 percent less productive today than a decade ago, according to new McKinsey research. The results from McKinsey’s new MineLens Productivity Index (MPI), which adjusts for declining ore grades and mine cost inflation, show that the pronounced decline in productivity is evident across different commodities and is seen in most mining players and geographies. (4) McKinsey sees three important areas of focus to address the root causes of productivity decline. 1) Embed effective management operating systems at mines 2) Prioritized operational excellence and capabilities development 3) Focus on innovation Reality has now settled back in and companies are struggling to make ends meet. The basic management staple of controlling costs and improving the production/productivity that was lost in the excitement is now back in play. Traditional cost-cutting approaches, such as across-the-board spending cuts, layoffs, and hiring freezes are only short-term initiatives and will not permanently improve a company’s cost structure or improve long- term competitiveness. This can only be accomplished by engaging front-line employees and empowering them to make necessary improvements in their daily work. It is time for leaders to lead and develop cultures of continuous improvement within their organizations in order to sustain their mining project to the end of mine life. Successful operating managers require two different skill sets of Leadership and Management; knowing how to lead people in their organization and how to manage the work they do."

Jan 1, 2016

The trend for using larger equipment in open pit mining to achieve cost effectiveness raises the question about the optimum economic point of scale in the current world of globalization. The present paper treats this question through the prism of a new methodology of assessing the impact of the size of production equipment on the economic outcomes of coal mining ventures. The methodology incorporates a production scheduling optimization model that implements both principles of mine planning, coal quality optimization and waste deferment. The implementation of the waste deferment principle dealing with the spatial and time aspects of the mine sequence arrangement allows the adequate modeling of the optimality of production equipment scale through the use of mine investment parameters, such as, purchase and ownership costs and discounted cash flows analysis. A case study is provided to illustrate the applicability of the new methodology.

Jan 1, 2004

By H. J. Sutherland

This paper reviews the results of the subsidence research prop ram at Sandia National Laboratories. The manuscript highlights the following: the application of empirical methods (profile functions) to the subsidence above longwall panels in the U.S.; the use of the "rubble model" to describe the behavior of broken strata as it distends when it falls to the Mine floor (or top of the rubble pile) and then is subsequently compacted as it is loaded by overlying elements of strata; and, the application of physical modeling techniques (centrifuge simulations) and numerical techniques to study the failure mechanisms in highly structured stratigraphy. The capabilities of the latter two are illustrated ')y comparing their predictions to the results of a field case that has complicated stratigraphy.

Jan 1, 1982

By Kwangmin Kim, Junnhyeok Park, Taehee Lee, Minkyu Kim

Mine tailings storage facilities (TSFs) can be a significant source of fine, respirable dust. This dust poses concerns, especially for nearby communities, because of its detrimental impact on respiratory health. To address these concerns, this study examined the effectiveness of commercially available polymers, known for their biocompatible and environmentally friendly features, to prevent dust generation from upstream-type TSFs in active mining operations. It focused on two areas in TSFs: the tailings beach and slope/dike surfaces. Two types of polymers—polyethylene glycol and poloxamer—were selected, and their effectiveness was evaluated in a series of phased laboratory and field tests. The lab tests investigated the moisture-retention capacity of the tailings after treatment with the polymer solutions as well as the ability of these solutions to reduce dust emissions. Polymers were applied to a tailings bed surface in the lab and dust was generated from this surface using a wind tunnel. PM10 and PM2.5 concentrations were measured using laser-diffraction dust sensors, and the polymers were found to have reduced dust emissions up to 95%. Small-scale wind-blowing tests were conducted in the field (specifically, in a controlled environment at a TSF) to evaluate polymer effectiveness on the tailings beach and slope/dike areas. The tests revealed that the AP could efficiently suppress approximately 80% of PM10 and PM2.5 dust emissions at both types of areas. Finally, 1000 gallons of AP solution were discharged at the top of tailings beach and slope/dike areas, respectively, and found to be effective. The results of these tests showed the high potential of the biocompatible polymers to be a feasible solution for reducing the respirable dust emissions from upstream TSFs in arid and semi-arid regions.

By Kwangmin Kim, Junnhyeok Park, Taehee Lee, Minkyu Kim

Mine tailings storage facilities (TSFs) can be a significant source of fine, respirable dust. This dust poses concerns, especially for nearby communities, because of its detrimental impact on respiratory health. To address these concerns, this study examined the effectiveness of commercially available polymers, known for their biocompatible and environmentally friendly features, to prevent dust generation from upstream-type TSFs in active mining operations. It focused on two areas in TSFs: the tailings beach and slope/dike surfaces. Two types of polymers—polyethylene glycol and poloxamer—were selected, and their effectiveness was evaluated in a series of phased laboratory and field tests. The lab tests investigated the moisture-retention capacity of the tailings after treatment with the polymer solutions as well as the ability of these solutions to reduce dust emissions. Polymers were applied to a tailings bed surface in the lab and dust was generated from this surface using a wind tunnel. PM10 and PM2.5 concentrations were measured using laser-diffraction dust sensors, and the polymers were found to have reduced dust emissions up to 95%. Small-scale wind-blowing tests were conducted in the field (specifically, in a controlled environment at a TSF) to evaluate polymer effectiveness on the tailings beach and slope/dike areas. The tests revealed that the AP could efficiently suppress approximately 80% of PM10 and PM2.5 dust emissions at both types of areas. Finally, 1000 gallons of AP solution were discharged at the top of tailings beach and slope/dike areas, respectively, and found to be effective. The results of these tests showed the high potential of the biocompatible polymers to be a feasible solution for reducing the respirable dust emissions from upstream TSFs in arid and semi-arid regions.

By Scott G. Britton

Microcomputeranalysis has long been a technique for engineering professionals to improve the theoretical and practical design of continuous mining systems. Such work has been typically composed of modeling observed events and then introducing a variety of known elements with predicted results to compare against the results of the model. Programs written in BASIC, Cobol, Fortran or other language dominated such efforts. These programs have taken years to develop and prove out. This article explores a new management tool used daily at Tanoma Mining Co. (TMC) to track and improve continuous mining systems through the use of microcomputers and Lotus l-2-3 software. Data provided by section foreman, shift foreman, and maintenance personnel are analyzed against predetermined goals. In this way, new production targets are developed, weaknesses in the current mining systems are identified, and the results of changes are measured. The current results of this system on the productive output of TMC systems is on the order of 10% improvement. Thin seam coal mining is an industry within the broader industry of coal mining. Thin seam mining faces the same cost pressures and engineering problems as its higher-seam competitors without the advantages of moving volume per foot of extracted material to stay at an economic parity with others requires additional creativity within the management teams to extract higher productivity gains from the existing workforce and mining systems. TMC operates a deep mine in Indiana bounty, PA, about one hour northeast of Pittsburgh.

Jan 1, 1991

By Behrouz Tehrani

The size, complex issues, and requirements to construct large number of tunnels, for a single project, expeditiously, and without exceeding the overall project budget, a program Construction Management (CM) team is highly recommended to be selected early during design process to provide guidance/direction relative to contract packaging and scheduling. This paper is not focused on the project itself, however, the emphasis is on experiences gained from the project. Wishing that some of the strategies described in this paper will be of value to owners of underground project.

Jan 1, 2008

By Diler Katircioglu-Bayel, Oner Yusuf Toraman, Safak Gokhan Ozkan

One of the most energy-intensive processes for producing submicron range calcite is stirred media mill. In the present work, numerous operating parameters such as solid mass fraction, grinding media size, media filling ratio, and grinding time have been investigated using a vertical type stirred media mill. The results are evaluated on the basis of mean particle size, specific surface area, and specific energy consumption. After conducting this study, optimum experimental conditions found to be as 70% media filling ratio, 25% solid mass fraction, 1 mm grinding media size, and 120 min grinding time. Besides, energy savings up to 22% were achieved with the choice of proper media size.

By W. G. Pariseau

Conventional barrier pillars in underground coal mines are intended to protect mains and sub-main entries for relatively long periods of time. Inter-panel barrier pillars that may be used in especially deep coal mines, say, below 800 m (2,400 ft), are intended to protect longwall panel faces and adjacent panel entries for the life of nearby panels. Barrier pillar failures have serious consequences, especially when failure is sudden and catastrophic. Design of barrier pillars is thus of considerable importance to safety and efficiency of operations. Locally, failure occurs at the limit to elasticity when stress tends to exceed strength. Strength of rock is stress dependent, so an analysis of stress is central to rational design of barrier pillars. There are several approaches to stress analysis for coal mine pillar design that range from the simplified but popular tributary area method including variations that use empirical definitions of the tributary area (volume) to more sophisticated numerical methods such as the boundary element method and the finite element method. Despite ease of use, empirical methods are limited and always suspect when applied to conditions beyond their scope of definition, while boundary element methods do not generally include pillars in the solution domain. The finite element method is not so restricted and thus is a natural choice for conventional and inter-panel barrier pillar safety analyses. Caving of roof strata certainly affects the distribution of stress about longwall faces and nearby barrier pillars. Conventional wisdom that considers roof strata to respond as cantilever beams indicates the longer the span the greater are loads on longwall faces and face supports. Failure of roof beams, caving, shortens spans and relieves face and support loads. The same view is applicable to barrier pillars in that long roof spans outside of barrier pillars leads to higher pillar loads than short spans. Hence, caving should be beneficial to barrier pillar safety. However, the benefit may be small depending on the extent of caving and only in the form of a slight reduction in overburden weight transmitted to the barrier pillar, especially in case of inter-panel barrier pillars. FINITE ELEMENT MODEL Finite element models for stress analysis in rock mechanics are formulated in consideration of physical laws, kinematics, and material laws. These models meet the essential requirements for equilibrium of stress, satisfy strain displacements relations, and in a general sense, relate stress to strain through material laws, often referred to as constitutive relations. The last may be complex and replete with nonlinearities. A de facto engineering material law is the elastic model in the form of Hooke?s law for linear, homogeneous materials that may be anisotropic. A limit to elasticity is imposed by strength in the form of a failure criterion or yield function that accommodates triaxial stress states. Examples used in rock mechanics are the well-known Mohr-Coulomb (MC)criterion, the popular Hoek-Brown (HB) criterion, and the Drucker-Prager (DP) criterion. The first is linear in stress, while the second is nonlinear. Both do not include any effect of the intermediate principal stress. The last is also linear in stress but includes the intermediate principal stress. All show an increase in the major principal stress at failure with confining pressure. In the UT2/3 finite element programs, the failure criterion Y is a nonlinear, anisotropic form and is also the plastic potential [1]: [YJI=+ 11NYJI=+- (1) ] where N is an exponent, usually 2, and J2 and I1 are nonlinear anisotropic forms of the second invariant of deviatoric stress and the first invariant of principal stress. The form (1) reduces to DP when N=1and isotropy prevails. When Y = 1, the limit to elasticity is reached and plastic deformation is possible. The material constants that enter (1) are all computed from unconfined compressive, tensile, and, in case of anisotropy, shear strengths. These latter strengths may be estimated from conventional laboratory test data. Of course, joints in field-scale rock masses induce different values. How different is often a matter of conjecture. For comparative studies, laboratory rock properties seem adequate. Inelastic, that is, plastic behavior occurs with strain beyond the elastic limit. Strain hardening, ideal plasticity, and strain softening are possibilities. Ideally brittle behavior with complete loss of strength is an extreme form of strain softening [2]. Caving may also be considered as strain softening with a less drastic reduction of material properties. As intact roof strata fail, fall, and form a rubble pile below, a new material is formed with greatly reduced elastic moduli and strengths, say, 1/100th of the original intact moduli and strengths. From another viewpoint, caving is simply a natural cut and fill process. Input for stress analysis by the finite element method includes: 1. Preexcavation stress state 2. Geology (stratigraphic column) 3. Structure (major faults, joint sets) 4. Elastic moduli 5. Strengths, and specific gravities of each rock type 6. Excavation sequence Output from an analysis includes distributions of: 1. Stress 2. Strain 3. Displacement 4. Local factor of safety (element fs) The last is defined as the ratio of strength to stress and in view of the failure criterion (1), is the ratio [fsJstrengthJstress=] where the numerator is the maximum possible value and the denominator is the actual value of the square root of the second invariant of deviatoric stress. This invariant is a measure of shear stress intensity but also reduces to uniaxial tensile and compressive strengths as the case may be. An fs greater than 1 indicates an elastic state of element stress; a value of 1 indicates the limit to

Jan 1, 2009