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By D. R. Tweeton

A modified push-pull field test and a computer model of cation exchange were developed to aid in evaluating cation exchange parameters prior to in situ mining. Reliable determination of these parameters is essential when modeling restoration of groundwater quality. The field test involves a much larger volume and much less disturbance to the ore sample than is feasible with laboratory measurements. This test can be performed in two or three weeks. It is relatively inexpensive, requiring one injection- production well and two or more wells for collecting samples of leach solution. The use of the model in interpreting test results is illustrated with field data from an in situ uranium mine. Much of the research was performed by the University of Texas at Austin, and was partially funded by the Bureau of Mines.

Jan 1, 1986

By Norman R. Paterson

In November 1980 a combined airborne electro-magnetic (INPUT.) and magnetometer survey was conducted by Questor Surveys Limited in the State Line Area, Colorado-Wyoming. The survey was the result of discussions over a prolonged period between the authors and various investigators of the State kimberlite occurrences. As a result of these discussions and literature studies, it was decided that airborne geophysical methods would be potentially useful in the exploration for new kimberlite occurrences. The survey was designed by Paterson, Grant and Watson Limited and conducted by Questor Surveys Limited over an area in which more than 15 kimberlite bodies were known and on some of which ground geophysical surveys had been conducted. The survey was designed primarily to determine the airborne electromagnetic and magnetic responses of the known occurrences and to deter- mine whether these responses would be detectable under similar conditions in other parts of the State Line District and elsewhere.

Jan 1, 1984

By T. Weatherwax, A. Rai, J. Poor

"This paper provides an overview of the current use of auxiliary ventilation products and the challenges with limited air quantity in dead-end entry or working faces. The PVC’s low frictional factor, low physical constraint and minimum leakage properties were ideal to develop as ventilation duct in conjunction with the concept of ""Made in the US and Used in the US"". The PVC duct supports the operational and total cost of ownership with on-going success. This paper will discuss the continuous improvement made in ventilation ancillary products for optimum results. The paper will also cover mine site usage of second generation PVC vent duct underground and the results from the operational and technical side making a difference in health and safety and overall auxiliary ventilation. INTRODUCTION The Barrick Turquoise Ridge Inc. (TR) is located in northern central Nevada, and is situated within the Basin and Range province, near the northeast end of the Osgood Mountains (see Figure 1). The TRJV mine consists of typical Carlin type- gold mineralization characterized by low strength rock of altered limestone, siltstones, and mudstones. The weak nature of the ground facilitates the need for underhand cut and fills mining methods.Mining Method; Underhand cut and fill: The mine uses underhand cut and fill method which has 12’x12’ and or 14’x14’ top cuts with several different size undercuts. The ore body is accessed off of a secondary tertiary heading, utilizing a heading with a cross section of 14W x 14H or 15W x 15H configuration. In the wider and more massive zones, two headings in a production panel may be worked at any one time. Drift round lengths are determined by the ground conditions and drift dimension. An example of a typical topcut and associated undercut layout is shown in Figure 2."

Jan 1, 2016

By James H. Allen

The air lift method of pumping water is discussed. A review of several large diameter hole drilling projects that used reverse circulation air lift techniques is presented. Proposals are made for reverse circulation flow rates for slow rates of bit penetration (5 fph) as well as reverse circulation flow rates for faster rates of bit penetration (10 fph). The Ingersoll- Rand air lift equations are modified for rotary drilling operations. By establishing minimum reverse circulation flow rates and utilizing the modified air lift equations, the establishment of minimum circulation equipment sizes and a more definitive requirement for improved bit body design should result.

Jan 1, 1976

By M. E. Rossi

This paper discusses the use of Conditional Simulation (CS) models to provide mill feed grade profiles for different time periods. The conventional approach of classifying block estimates as ore or waste generally does not adequately represent dilution, lost ore and the anticipated grade control data, including variability of mill feed from the pit and possible stockpiles. The detailed simulation of grade control practices can be done, but at the Pre- or Feasibility stage of the project may be impractical, since drawing dig limits on multiple benches is tedious and time consuming. Using the Feasibility Grade Control (FGC) method as developed by the Centre for Computational Geostatistics (CCG, University of Alberta-Edmonton), the CS models can be processed quickly to establish dilution and lost ore, and predict daily or short-term feed to the mill. The simulated nodes can be aggregated into selective mining units with adequate representation of likely geometries to be recovered from the pit, to mimic anticipated selectivity. An example from a large copper deposit is shown. The study provides an estimated stream of tonnages and grades fed to the plant by mining periods of interest and based on a specific mine design and schedule. The resulting cash flows support the economic and financial analyses of the Feasibility Study; also leads to improving mine schedules; and aids in developing blending schemes if necessary. INTRODUCTION The conventional approach of separating mineralized material into ore or waste categories does not always include a realistic amount of dilution and ore loss. Also, often it does not provide a good estimate of the grade that will be fed to the mill. If the grade control estimates are unbiased, they will over the long run represent the long-term average of grades fed to the mill; but the anticipated variability of mill feed from the pit and stockpile sources may be misrepresented. Some references on traditional grade control implementations can be found in Chunnett (1982); Davis et al. (1989); Srivastava et al. (1992); and Nowak (1992). Alternative methods based on economic variables improved significantly on the purely grade-based control methods, see Douglas et al. (1994). Further developments involved the use of geostatistical conditional simulations (CS) and profit models, which in several cases have been successfully implemented (Aguilar and Rossi, 1996; Rossi, 1997; Deutsch et al., 2000; Norrena and Deutsch, 2002; Neufeld, 2005; Jewbali and Dimitrakopoulos, 2009). But they can be impractical, mostly due to the lack of understanding of the methodology involved; even if semi-automatic dig limit drawing is implemented, there is always a need for is tedious and time consuming checking and corrections, even if using a single profit model derived from the simulated grades.

Jan 1, 2019

By P. T. Bissert, L. Yan, M. D. Klein

"Federal regulations require that refuge alternatives (RAs) are located within 305-m (1000-ft) of the working face and spaced at one-hour travel distances in the outby area in underground coal mines in the event that miners cannot escape during a disaster. The Mine Safety and Health Administration mandates that RAs provide safe shelter and livable conditions for a minimum of 96 hours while maintaining the apparent temperature (AT) below 35°C (95°F). The National Institute for Occupational Safety and Health used a validated thermal simulation model to examine the mechanisms of heat loss from the RA to the ambient mine and the effect of mine strata composition on the final internal dry bulb temperature (DBT) for mobile tent-type RAs. The results of these studies show that most of the heat loss from the RA to the ambient mine is due to radiation (51%) and conduction (31%). Three mine width/height configurations and three mine strata compositions were examined. The final DBT inside the RA after 96 hours varied less than 1°C (1.8°F) for the three mine width/height configurations and less than 2°C (3.6°F) for the three mine strata compositions. INTRODUCTION Following a mine disaster, workers will try to escape the mine. If their escape is futile, they can take shelter in a refuge alternative (RA). In 2008, the Mine Safety and Health Administration (MSHA) mandated RAs in mines to ensure that a safe and livable shelter is provided for a minimum of 96 hours, and that the apparent temperature (AT) does not exceed 35°C (95°F) inside the RA [1]. An ongoing concern with RAs is the potential to exceed this limit. The temperature rise inside an RA is due to the metabolic heat released by the occupants as well as heat released by the carbon dioxide scrubbing system. The National Institute for Occupational Safety and Health (NIOSH) tested a 10-person tent-type training unit RA in its Safety Research Coal Mine (SRCM) to investigate heat buildup in RAs. The 10-person capacity for the tested RA is based on 1.4 m2 (15 ft2) of floor space per miner. NIOSH-developed simulated miners, which are heat input devices that generate both sensible and latent heat, were used to represent the metabolic heat generation of an average miner (117 W) for testing in the SRCM. It was found that the number of occupants in an RA may need to be reduced based on the ambient mine temperature, which varies from mine to mine [2]. To further research temperature rise inside an RA, ThermoAnalytics, Inc. (TAI) was contracted by NIOSH to perform thermal simulations of the tested 10-person mobile tent-type RA. TAI developed a thermal model of the SRCM using RadTherm software, which incorporates a human thermal model (HTM) to represent the equivalent metabolic heat loss of a miner within the RA’s enclosed environment. The thermal model was previously validated by comparing simulation results with test results [3]. During a mine disaster in which miners would have to take shelter in an RA, mine ventilation may not be available. As such, mine ventilation was off for both the testing in the SRCM as well as in the simulations. This paper discusses the heat loss mechanisms and the effects of mine strata composition and mine width and height associated with a ten-person tent-type RA."

Jan 1, 2016

By Kazumasa Taguchi

At the Kakogawa works of Kobe Steel. Ltd., the agglomeration facilities are composed of a pelletizing plant and sintering plant. This aim is to utilize raw materials efficiently and stabilize the raw material resources. Therefore at Kakogawa works, the blast furnaces (BF) have been operated with high pellet ratio and various developments for pellet properties have been achieved to improve the blast furnace performance. These developments include dolomite-fluxed pellets, new-porous pellets and crushed pellets. As a results of these improvements, pellets have achieved almost the same performance as sinter at high temperature regarding properties such as the softening, melting and reduction behaviour. However, some problems on shape have remained to be solved. Spherical pellets flow easily into the center of the furnace and form mixed layers of pellets and cokes. Therefore, in BF operations with these pellets it becomes more difficult to keep proper and stable gas distribution.

Jan 1, 1983

By Ali Jaberi Zamharir, Abolfazl Shoghian‐Alanaghi, Hossein Aghajani, Arvin Taghizadeh Tabrizi

In this study, the leaching rate of molybdenite concentrate was evaluated in sulfuric medium, and the influence of the diverse oxidants including hydrogen peroxide, manganese oxide, copper sulfate on the leaching rate was studied. Also, the effect of the addition of the ethylene glycol to the hydrogen peroxide was studied and results showed that with the addition of ethylene glycol, the leaching rate is increased 55% from 41% up to 80.3%. The optimum condition is achieved as 0.7 M of H2SO4, 4.4 M of H2O2, and 3.5 M of EG at 30 °C within 4 h of leaching time and 500 rpm. Also, inserting the oxygen with the pressure of 6 bar to the leaching autoclave, the leaching rate is increased more up to 86.4%. Finally, the leaching process was studied kinetically and the determined mode of controlling factor was specified based on the activation energy which equals 46.252 kJ/mole indicating the chemical reaction mode.

Jun 5, 2022

By James E. Lawver

During the past century, the Florida Phosphate Industry has established an enviable record of innovative technology in nearly all aspects of mining and beneficiation. A notable exception is the lack of technology to improve the present practice of storing waste clay in earthen dams. The rule which has been adopted by the Department of Natural Resources states, "Since storage of clay wastes for long periods of time interferes with expeditious reclamation and since above grade storage of clays takes otherwise useful land out of production and raises potential health and safety problems, below grade storage and rapid reclamation techniques are encouraged." The two waste products from the beneficiation plant are clay slimes (-0.1 mm in size) and sand tailings. The sand tailings do not present a problem since the tailings rapidly dewater to a dry weight of about 100 pounds/ft3 and make good land fill. By contrast, disposal of waste clay slimes is a formidable task. The basic problem is simply that the waste clay not only dewaters very slowly, but also that the ultimate solids content is very low and in most cases the volume of the clay greatly exceeds the available volume of below ground storage of the mined land.

Jan 1, 1984

By Rusdian F. Kayadoe, Michael B. Hutahaean, Sandi A. Firmanulhaq

Deep Mill Level Zone (DMLZ) mine is located in Papua, Indonesia operated by PT Freeport Indonesia (PTFI) with approximately 1,500m below surface. The ore body extend 1230m width from northwest to southeast by 300–400m length east-west. The mine currently produces at full production of 80,000 tons per day until 2041. Part of the extension of current active production block and mitigation sits 225 m above the production block 1 (PB1) and 2 (PB2A and PB2B) which located in 2590L, named production block#4 (PB4W and PB4E). As the mining continues at PB1N, PB2A, and PB2B, the cave growth vertically and laterally to south perimeter of the footprint affecting the integrity of PB4W/E footprint. Currently, PB1N and PB2N are in active production whilst PB4E development continues from South against PB1N cave, as can be seen in Figure 1. A slight overlapping between PB1E and PB4E intentionally to promote cave connections between the two caves. Despite low stress model in the PB4E near existing caves, the PB4E cave propagation expected by the large strain and will be propagating in tension failure to the PB1E cave. Hence, designing the drill drives edge and first drawbell location as close as possible to the PB1E cave is necessary to guarantee cave connection. Since PB4 footprint development commenced in December 2021, there have been a substantial cave propagation observed from existing downhole monitoring. As the PB4 footprint designed perpendicular to existing DMLZ PB1 cave, adjustment of the development edge design is necessary to reflect the progression the loosening zone propagation to the South. Final life of mine design for extraction, undercut and ventilation level were decided in October 2023 considering latest update cave (fractured/ yielded) boundary. Numerical model of potential rock mass damage also aids the decision to locate the drift edge design. Predicting the cave progression impact is critical to both production at the existing active blocks and development of the new area. The use of cave shape data from year 2021–2023 gives an insight of the cave shape estimation at the end of 2024 when the undercut drift will be developed. This paper presents actual cave growth of active production blocks and its relative vertical progression impact as the result of drawing in order to plan for acceptable rate and provide mitigation once the minimum acceptable rock mass condition and minimum pillar threshold achieved.

Feb 1, 2025

By L. Barnewold, A. Merchiers, M. Pütz, P. Jeschke, M. Dammers

The mining industry faces many difficult challenges, for example, lower ore grades, smaller and deeper deposits, and longer transportation distances. In the past, there have been remarkable innovations in both equipment and the types of mining methods for which it is used, which have resulted in economies of scale. This has led to an increased use of bulk mining methods, like sublevel and block caving, which has increased productivity and reduced costs. Haulage alone plays a major role. Current haulage techniques are a significant cost driver, which account for between 15 and 30% of the overall capital investment (capex) in a mine and are an increasingly part of the operating costs (opex). The paper introduces a simulation tool of main haulage system in underground mining. Therefore, performances and the costs of the three most common underground main haulage systems, rail, truck, and conveyor, are calculated using a developed modeling tool. The tool was applied and validated in a case study carried out with the LKAB Kiruna Mine in northern Sweden.

By John B. Goddard

In-situ leaching of uranium by aqueous ammonium carbonate containing oxygen or hydrogen peroxide as oxidant results in the partial dissolution of sulfides. While some of the sulfide sulfur is oxidized to sulfate, a considerable portion is oxidized only to thiosulfate and polythionates. Polythionates poison the anion exchange resin used to extract uranium. At the Palangana operation in southeast Texas, the trithionate ion (S3062-) was found by infrared spectrometry to be the major resin poison. Treatment of ion exchange feed solutions with hydrogen peroxide only resulted in partial conversion of reduced sulfur species to sulfate, and trithionate conversion was particularly slow. Poisoning of the resin also occurred from the ammonium chloride eluant, which built up trithionate because of recycling. This was essentially eliminated by chlorinating the eluant prior to yellow cake precipitation.

Jan 1, 1984

By James E. Jones

The coal mining industry is being called upon to vastly increase production in the coming years. Many mining operations will have to prepare an environmental impact report of some kind and all will have to comply with various types of environ- mental regulations. Therefore there is a great need within the industry for access to environmental data, information, and literature. This paper discusses the informational resources available, the current lack of access to these resources, and the Environmental Data, Information and Literature (EDIL) Bank of the Kentucky Institute for Mining and Minerals Research. The bank's major emphasis concerns the environmental, social and economic aspects of producing clean solid, liquid, and gaseous fuels from coal. The data bank promotes information interchange between other related governmental and private projects and the energy development community.

Jan 1, 1976

By Dean Brox

Tunnel boring machines (TBMs) have been used for the construction of various tunnels for mining projects for the purpose of access, conveyance of ore and waste, drainage, exploration, water supply and water diversion. Several mining projects have seen the successful and economic beneficial use of TBMs, and there is an increasing awareness of the benefits of TBMs for mining projects. Key technical considerations for the use of TBMs for the construction of tunnels for mining projects include geological issues (rock type, rock alteration, rock strength, rock abrasivity, durability, ground water in flows), depth of cover and the potential for overstressing/rockbursts, site access and terrain, portal locations, TBM constraints, minimum tunnel size, tunnel support requirements, contractor and labor experience, and project schedule demands. TBMs offer key project schedule benefits with high rates of progress, which is a unique economic advantage recognized for mining projects where timing is of the essence in order to advance mining development and achieve early startup for operations. A thorough evaluation of the anticipated ground conditions should be performed as part of the decision to adopt a TBM for a mining project. Minimum specifications for TBMs are necessary in order to prevent the incorrect type of TBM from being used. Appropriate geotechnical investigations are necessary in order to provide key information on the anticipated subsurface conditions for careful planning and design of the proposed tunnel alignment. The overall site and geological conditions associated with some projects may suggest that it is not appropriate to use TBMs for some mining projects due to a perceived higher risk. Key words: TBM, Tunnel boring machines, Tunneling in mining

Feb 1, 2014

By Dean Brox

Tunnel boring machines (TBMs) have been used for the construction of various tunnels for mining projects for the purpose of access, conveyance of ore and waste, drainage, exploration, water supply and water diversion. Several mining projects have seen the successful and economic beneficial use of TBMs, and there is an increasing awareness of the benefits of TBMs for mining projects. Key technical considerations for the use of TBMs for the construction of tunnels for mining projects include geological issues (rock type, rock alteration, rock strength, rock abrasivity, durability, ground water inflows), depth of cover and the potential for overstressing/rockbursts, site access and terrain, portal locations, TBM constraints, minimum tunnel size, tunnel support requirements, contractor and labor experience, and project schedule demands. TBMs offer key project schedule benefits with high rates of progress, which is a unique economic advantage recognized for mining projects where timing is of the essence in order to advance mining development and achieve early startup for operations. A thorough evaluation of the anticipated ground conditions should be performed as part of the decision to adopt a TBM for a mining project. Minimum specifications for TBMs are necessary in order to prevent the incorrect type of TBM from being used. Appropriate geotechnical investigations are necessary in order to provide key information on the anticipated subsurface conditions for careful planning and design of the proposed tunnel alignment. The overall site and geological conditions associated with some projects may suggest that it is not appropriate to use TBMs for some mining projects due to a perceived higher risk.

Jan 1, 2013

By T. Shumka, M. J. Druckenmiller

"INTRODUCTION As we push further into the 21st century and closer to a more efficient mine, safety and operational enhancements are the two major keys towards attaining success. The Crusher Vision Automation System (CVAS) is a technological advance that will allow an operator to achieve higher safety and higher operational goals in the same piece of equipment. The CVAS is a patent pending system and method for measuring and maintaining the closed side setting (CSS) on gyratory crushers. In the same equipment and technology package, the CVAS will also allow safer placement of main shaft pieces for maintenance and replacement. This technology yields multiple uses and allows a site to significantly enhance safety and operational efficiencies. This measurement technique is used to provide more accurate data and faster data collection times than current techniques used today. It will give crusher operators accurate and reliable measurement for the CSS in a live, operating environment. Measurement data can be collected in five minutes allowing for fast adjustment of the mantle position and subsequent enhancement and streamlining of a crusher and downstream flowsheet. The advantage of this system is that it is permanently mounted at the crusher location, where the operator can turn the system on and off as many times as they like throughout the day with a goal of maintaining a constant CSS gap based on production and maintenance criteria to help streamline operations and enhance safety efficiencies.Regarding its other main functional area, mainshaft maintenance, it allows this work to be performed remotely while keeping personnel safer and out of harm’s way. SAFETY ENHANCEMENT The safety factor enhancement with this system is extreme. It does not require the use of overhead cranes, cleaning out the crusher, lowering people into the crusher or having the operator lower paint cans or lead balls into the crusher pocket while the crusher is in operation for measuring the setting. In order to perform the CSS measurements, the operator only needs to operate the laser through manipulation of a joystick while watching the video feed. Danger of a person falling into the crusher while trying to take measures is eliminated, as are the effects of handling lead balls and tracer dyes."

Jan 1, 2015

By Bill Tucker, Mike Black

"PROJECT OVERVIEW Crossrail, Europe’s largest construction project, will increase London’s transportation capacity by 10% when it opens in 2018. The Crossrail scheme is a combination of surface and underground railway that stretches 118km east-west through central London from Reading, Berkshire and Heathrow airport in the west to Shenfield, Essex and Abbey Wood in the London Boroughs of Greenwich and Bexley in the east. Crossrail will serve 40 stations, ten of which are new, and bring 1.5 million people within 45 minutes commuting distance of London’s key central business districts. 21km of the Crossrail route comprises twin-tunnels beneath the heart of central London. It is the central section of the route, and the challenges that had to be overcome to construct its tunnels under the historic capital that forms the subject of this paper. The route of the Crossrail tunnels can be seen in Figure 1. These tunnels weave their way through the city’s underground landscape, linking eight new underground stations which connect to the existing London Underground network, providing interchanges with nine existing lines as well as the National Rail and Docklands Light Railway networks.Crossrail began construction of enabling works in May 2009 and launched the first of eight tunnel boring machines (TBMs) in May 2012. 42km of major tunneling work was completed in May 2015, and included 11km of sprayed concrete lined tunnels at the five mined stations (Bond Street, Tottenham Court Road, Farringdon, Liverpool Street and Whitechapel) in addition to the bored tunnel sections. The remaining three sub-surface stations at Paddington, Canary Wharf and Woolwich were constructed as large open boxes prior to the TBMs passing through. Crossrail, Ltd. is a special purpose company formed by the project’s joint sponsors, Transport for London and the Department for Transport, to manage design, construction and commissioning of the project. In 2009, Crossrail engaged Bechtel Ltd. as its delivery partner and a joint venture, Transcend (comprised of CH2M, AECOM and the Nichols Group), as its programme partner. The project is being managed by an integrated programme management team which is staffed by Crossrail and its partners. The railway, when opened, will be operated by Rail for London. With tunneling completed in accordance with the project’s master control schedule, the new railway is scheduled to commence dynamic testing in late 2017, with a phased opening of the tunneled sections and stations through Central London in 2018."

Jan 1, 2016

By Martin B. Zimmerman

It is becoming evident that traditional methods of econometric analysis are inadequate in estimating-the long-run supply of minerals. Econometrics is limited to extracting estimates from observations of the theory predicts that the least cost deposits will be exploited first.1 The estimation of parameters from past data then must lead to biased projections of the future. Mining conditions in the future will be worse than in the past and it is the impact of the future conditions on cost that we need to know. In this paper we present a methodology for dealing with this problem. We estimate a "cumulative cost" function that yields the long-run marginal cost of mining as a function of cumulative output produced over time.2 This is relatively easy to do for coal mining in the United States where exploration for new deposits is not a major factor in supply. The first step of the procedure relates cost to the rate of output and to the geological conditions of the mine. The second step combines geological information on remaining deposits with the cost function to yield the cumulative cost function. A central theme of both these steps is the interaction of economics with geology. The best deposits are selected first and in each step of the estimation allowance must be made for this fact. The problem of depletion is part of the general problem of structural change. The change through depletion in the nature of the exploitable mineral stock is only one factor that calls for an analysis sensitive to the changing circumstances of the industry. The factors impinging most heavily on the coal industry today are the strict environmental regulations legislated

Jan 1, 1977

By J. R. Mackie

Reserve Mining Company, the first large-scale taconite pellet producer in the United States, mines it's crude ore at the Peter Mitchell Mire located on the eastern end of the Mesabi Iron Range near Babbitt, MN. The ore is processed at Reserve's beneficiation plant on the north shore of lake Superior at Silver Bay, M. The mine and plant are linked by a 47 mile, double track, railroad which is owned and operated by Reserve. (see Fig 1). At rated capacity, the mine can produce 33 million It/yr of crude ore, 15 million It/yr of waste rock and 1.0 - 1.4 million yd3/yr of glacial till stripping. Haulage of all mined material is accomplished using trucks. Ore is transported by tractor-trailer side dump units which have capacitys ranging from 83 to 110 long tons. Waste rock and glacial till is transported in end dump units of 50 to 120 LT capacity. Loading is accomplished by 11/13 yd3 power shovels and 7/10 yd3 front-end loaders.

Jan 1, 1985

By B. Ladanyi

An adequate knowledge of the overall behavior of a rock mass at a given site is fundamental to the satisfactory design of a rock slope. The be- havior is controlled by a variety of factors, in- cluding rock type, geological structure, stress and ground water conditions. There are essentially three lines of approach that may be used to obtain information on the in-situ rock mass behavior for the purpose of the design of a rock slope: (1) Direct measurements of rock mass properties by means ol laboratory and field tests. (2) Evaluation of rock mass properties from a study of slope failure case histories and sta- tistical information on stable and unstable natural rock slopes. (3) Evaluation of in-situ behavior of rock mass by using a physical or mathematical model technique.

Jan 1, 1980