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By Brendan Howard

Rio Tinto has a large globally distributed technical workforce and needs to ensure these employees have the requisite skills to not only manage technical risk and enable safe efficient production, but also ensure they are keeping pace with a fast-changing technological landscape. Traditional approaches to learning struggle for scale and an inability to respond to the extreme diversity of capability development needs. In response, Rio Tinto has successfully introduced innovative approaches to learning and employee engagement via leveraging the power of globally distributed networks for peer-to-peer knowledge transfer and providing mechanisms to recognise, reward and retain the individual technical contributors.

Feb 1, 2024

Little faith can be placed in a coal resource estimate without a clear understanding of the estimate's accuracy. Different types of coal resource estimates require different levels of accuracy. Prospecting surveys typically are done with widely spaced boreholes, while a much higher level of accuracy is required for mine design. Either way, a measure of the accuracy clearly indicates the level of confidence that can be placed in the results of the estimate. Geographic information systems (GIs) are becoming a commonly used tool for resource estimation because they not only provide a database management platform but also the graphical capabilities to visualize resource characteristics. interpolation methods used commonly in these resource studies do not typically provide a quantitative answer to the question: "How accurate is the estimate?" By comparing localized measurements at multiple locations to the interpolated thickness distribution used in a resource estimate, a quantitative analysis of accuracy can be obtained. The technique is demonstrated with a case study from Central Appalachia.

Jan 1, 2000

By Bruce Congleton

The Florida phosphate industry is a leader in environmental control, both in terms of dollars spent and significant achievements. For instance, since 1960 the phosphate industry has spent over $71 million for air pollution and control devices, including installation, research and development and maintenance. Water pollution control expenditures also total in the millions, with over $69 million spent in the same 10 year period. The industry also is a leader in water conservation measures, having spent nearly $ 18 million since 1966 for conservation devices. Since phosphate is mined by strip mining, land reclamation plays an important part in the environmental control picture. Here again, the phosphate industry has met the challenge with a voluntary program of reclamation which accounts for over 20,000 acres of land useable after mining has taken place. In terms of progress in environmental control, the industry has been able over the years to solve within the limits of technology the fluoride emission problems it once had, and is currently at work solving sulfur dioxide and particulate problems. In just the past year the industry also has been extremely successful in limiting phosphorus and nitrogen discharges into area streams. The industry continues to cooperate with state and local pollution control officials on matters of environmental control, and future plans include even closer cooperation and assistance, as well as increased expenditures.

Jan 1, 1972

By W. P. Diamond

The Bureau of Mines has been investigating several techniques, including the use of horizontal and vertical boreholes, to remove gas from coal in advance of mining. Horizontal boreholes drilled from underground workings as part of the mining cycle have been shown (Finfinger, 1980; Hagwood, 1983; Perry, 1978; Prosser, 1981; Thakur, 1980; VonSchonfeldt, 1982) to be very effective in providing short-term, immediate relief from high methane emissions. This technique has been widely accepted in the coal mining industry, but it does require close coordination to integrate the drilling and subsequent gas drainage and disposal into the projected mine development plan. Vertical boreholes can be placed several years in advance of mining to predrain gas from coalbeds over relatively large areas (Dunn, 1984; Elder, 1975; Lambert, 1980; Steidl, 1978; Stubbs, 1979). The vertical borehole technique has the additional advantage over horizontal boreholes of allowing work to be performed on the surface instead of in the more restrictive underground environment. However, except for the relatively large scale vertical borehole programs for both mine safety and commercial production in the Black Warrior Basin of Alabama (Dunn, 1984; Lambert, 1980; Stubbs, 1979), the technique has been underutilized. The primary reason for this seems to be a combination of the current economic climate in the coal industry, legal questions as to the ownership of coalbed gas, and potential roof damage from the stimulation treatments required to increase the characteristically low permeability of coalbeds to enhance gas production. The question of potential roof damage is the subject of this paper.

Jan 1, 1985

By Martha McJunkin, Lawrence Pietrzak

This paper describes and demonstrates the application of systems analysis and mathematical modeling techniques in the planning of actual tunnel projects and research and development to improve tunneling techniques. A recently completed tunnel project located in Utah is used as an example. Although cost estimating computer programs are used in tunnel project planning, the introduction of performance modeling, simulating the time to excavate, has added advantages that are explored here. The performance/cost tunneling model (TM) described herein mathematically simulates on a high-speed digital computer the important activities of a number of tunneling techniques accounting for activity interactions, variable external environments, mechanical failure, and other uncertainties. A cost accounting segment is included to facilitate cost-effectiveness comparisons. It is shown that, when combined with informed judgment and appreciation of limitations, the TM can be a useful tool that may help improve tunneling operations and cost estimation, for example, by achieving more balanced system designs or bounding the performance/cost implications of geologic and other uncertainties. Ultimately, this might lead to more competitive bids and greater profits. The need for systems analysis and modeling in tunneling research and development (R&D) is well recognized and documented.(1-5) In R&D one must seek broadly useful solutions to the basic problems of face fragmentation, materials handling, ground support, and environmental control. These solutions must take account of the interdependence of these elements and, for a variety of ground conditions, the limitations or constraints that any innovation in one element may impose on total system performance and cost. In this regard the structure and logic of the TM has been kept as simple and modular as possible so

Jan 1, 1974

By Alastair R. Biggart

ABOUT BENTONITE TUNNELLING Much has been written and many learned papers given on this subject whose generic term is Slurry Tunnelling. This paper is about the particular form of slurry tunnelling known as the Bentonite Tunnelling System. This method. of tunnelling was invented by J.V. Bartlett of consulting engineers, Mott Hay and Anderson in 1964. The general principles are incorporated in British Patent No. 1083322. It was not until the early 1970's that serious experimental work was started to prove the technical feasibility of the process. In the U.K. in 1971 Edmund Nuttall Limited started on an experimental length of 3.8m diameter tunnel at New Cross in London. In Germany at about the same time Wayss and Freytag were starting on a 3.7m diameter collector sewer tunnel in Hamburg. In Japan early slurry tunnelling work was carried out in the 1960's. In the early 1970's a large number of slurry tunnels of various diameters were carried out in that country. This paper is being presented at a time when this system of tunnelling has become an accepted method throughout the developed world. As a result of the work carried out so far there is now a large amount of data existing regarding the effects on the ground in the immediate area of the tunnel, settlement at the surface and the ability of the system to cope with ground varying from clays to coarse gravels and containing large erratics such as granite boulders. The decade of the 1970's has therefore seen a very rapid pace

Jan 1, 1979

By D. PATIL, B. K. Parekh

Water is the mainstay for the beneficiation of fine-size coal and minerals, but it is also the least desirable constituent of the final product. The basic concept of the novel process described in this paper is based on the differential surface heat absorption capacity of the individual particles. When a differentially heated solid mixture is placed on a moving belt that has been coated with low-temperature melting resin, the hotter component of the mixture will stick to the belt while the relatively cooler component will stay free on the belt and fall off at the end of the belt run. Experiments were conducted with pyrite, coal and quartz particles of 6 × 18 mesh size. The goal of the test program was to find the optimum conditions at which there exists a required temperature difference between minerals and coal particles by controlling the operating and system variables. Preliminary test results show that there is a potential for separating mineral matter from coal using the thermo-adhesive separation technique.

By T. E. Wilson

An exploration bore core sample of coal ought to be reduced from its original cylindrical form to a particle size distribution and particle composition that reflects, insofar as possible, a process stream of? raw? coal it represents. Often, coal cores are reduced with a laboratory crushing machine, the product of which may not match the raw coal size distribution or size fraction composition. This study employs drop-shatter impact breakage followed by dry batch tumbling in a steel cylinder rotated about its transverse axis in order to characterize the core material in terms of first-order and zeroth-order breakage rate constants. These are indices of the propensity of the coal to degrade during excavation and handling. Initial drop-shatter and dry tumbling tests were done with synthetic cores, to reduce material variables and . conserve difficult-to-obtain coal cores.? Cores of three different coal beds --Illinois No.6, Upper Freeport, and Pocahontas No. 5 -were subjected to drop-shatter and dry batch tumbling tests to determine breakage response. Comparison of coal preparation plant feed with a crushed bore core and a bore core prepared by drop-shatter and tumbling (all from the same Illinois No.6 coal mining property) indicated that the size distribution and size fraction composition of the drop-shattered/tumbled core more closely resembled the plant feed than the crushed core.

Jan 1, 1998

By Mustafa Kumral, Yuksel Asli Sari

Economic evaluations of underground mining operations are made based on the estimated or simulated grades of the block model as the actual values are not known. Depending on how the planning decisions are made, the risk of the operation can be managed and decreased. This research introduces a mixed-integer linear programming (MILP) model for stope sequencing optimization that considers the uncertainty associated with net present value (NPV) using chance-constrained programming (CCP). The introduced method permits achieving a balance between maximizing NPV and reducing the associated operational risk through transforming the problem into a multiobjective problem, where the objectives are maximizing the NPV and minimizing the risk. This risk is expressed in terms of the standard deviation of project outcomes, taking into account multiple possible scenarios. In a case study, the efficiency of the method was demonstrated as a decision-making tool capable of translating a specified risk or reliability level into a stope sequencing plan.

Jan 1, 2024

By Nick Karlin

Dragados USA is constructing the LA Effluent Outfall Tunnel, a 7-mile, 18 ft internal diameter effluent discharge tunnel, utilizing a 21.6 ft (6.585 m) Herrenknecht Mixshield TBM. This paper highlights the means and methods used for TBM launch from a 55 ft diameter shaft excavated in wet with diaphragm wall support of excavation. This included SEM excavation of jet grout blocks for starter and tail tunnels, temporary concrete structures and steel installations, TBM sealing system, umbilical management for TBM hydraulic, electric and bentonite circuits as well as complex segment delivery logistics. The many launching challenges were overcome thanks to the innovative approaches from the project team.

Jun 13, 2023

By Jeffrey L. Zelms

There is no known, practical substitute for lead in the automobiles, communications systems, medical equipment and computers that Americans use every day. However, there are many who say lead should be stopped at its source -- banned. As America's largest lead producer, The Doe Run Company has ralized that it must do more than mine and reclaim lead efficiently and safely. It must also earn the public's consent to operate if it is to continue to be a viable business. LEAD - THE BRILLIANT PERFORMER: REFURBISHING AN IMAGE It's been an embarrassingly long time since I was a college student. However, I remember there was no course at the University of Missouri's School of Mines and Metallurgy that had anything to do with the public relations aspects of mining or, put another way, the politicization of mining. It's been an embarrassingly long time since I was a college student. However, I remember there was no course at the University of Missouri's School of Mines and Metallurgy that had anything to do with the public relations aspects of mining or, put another way, the politicization of mining. I haven’t perused the course catalog for Penn State’s College of Earth and Minerals Sciences. But I strongly suspect I wouldn’t find such a course there today, either. A statement by the chairman of one of the country’s largest chemical companies leads to the point I want to make. He described his business this way. He said, “We’re a public affairs company that just happens to produce and market chemicals.” Like chemicals, minerals and mining are politicized today. To the extent that we don’t understand that reality, we don’t understand that reality – and act on it – we’re less likely to survive in this business. Some of you may well be saying to yourselves, “This guy Zelms is an alarmist.” That’s fair enough. Because it is absolutely true that there’s n o known, practical substitute for lead today. And it’s also absolutely true that, knowingly or not, Americans use lead everyday. It’s in our automobile batteries. It’s an integral part of communications systems. High tech (and low tech) medical equipment contains lead. And lead is an essential component of computer and TV screens. But even with all these uses, lead has a negative image today. An image so negative that its very existence is threatened. If you doubt that, consider these two statements made in 1989. Statement one. “It is probably reasonable to argue that exposure is the single most important and critical environmental health problem in the U.S., and possibly also the world…” Statement number two. “Many of the uses of lead should be terminated. We need to go back to the ultimate source: that is, taking lead out of the ground and putting it into the product stream and we need to turn it off at the ultimate source. Not the approximate lead in gasoline, or lead in air, or lead in food. Go right back to the source and start cranking it down." (End quote.) Those are what I call strong statements. And they weren’t made by some celebrity spokesperson for the environment like Meryl Streep. Both these statements were made by Dr. Ellen Silbergeld, whose long list of professional and academic credentials includes: o Adjunct professor and research scientist at the University of Maryland Medical School and Johns Hopkins: o Chief toxic scientist and director of the Toxic Chemicals Program of the Environmental Defense fund; o and President of the Society for Occupational and Environmental Health. If Dr. Silbergeld were the only person making these kinds of statements, it would be one thing. But she’s not a voice in the wilderness, by any means. Also for those of you who say, well since there’s no known substitute for lead, how on earth could it be banned. I refer you to a number of bills before Congress that would permit the EPA to ban any product if it is determined that its

Jan 1, 1992

By John R. Wright

This paper reviews the increased use of mechanization in order to develop lateral headings efficiently and economically. Particular emphasis is placed on the role of the Electric-Hydraulic Drill Jumbo in achieving this goal. Also, the use of modified mining equipment to suit various operating conditions is discussed.

Jan 1, 1981

By T. P. Weldum, W. Conger

"These studies address the relationship between mill media sizing and its grinding efficiency. Starting with the results from a review of the literature, the issues of initial media sizing for a new ball milling circuit, and then optimal media sizing for an existing milling operation, were studied. The Functional Performance parameters “Mill Grinding Efficiency” and cumulative “Mill Grinding Rates” from both plant and test-scale equipment were used, and provide valuable new insight into this topic. A plant media sizing diagnostic tool is presented, as are newly developed testing equipment and evaluation methods, and recent case studies. REVIEW OF MEDIA SIZING LITERATURE For a plant metallurgist to answer the question “How can I maximize plant profit by manipulating this grinding circuit variable?” she must know what effect the variable has on grinding circuit efficiency. Despite the significant cost of grinding media and its potential effect on production capacity, the ‘best’ media sizing remains ill-defined for any given ball mill circuit in the industry today. The underlying reasons for this will be discussed. But the importance of this issue drove Metcom and its industrial partners to take on the challenge of how to engineer the ball charge for an existing grinding circuit. In the absence of any proven method, the first step was a review of the literature. Sponsored by Cleveland-Cliffs, Inc., a broad review of the literature was undertaken, producing “The Effect of Media Sizing on Ball Milling Efficiency” (McIvor, 1997). Among hundreds of publications that were reviewed that discuss the topics of media sizing or wear, forty-five were studied in detail. These were grouped into: plant experiences; laboratory and pilot plant investigations; media wear studies; population balance modeling studies; and general papers on ball milling which included the topic of media sizing. The reader is encouraged to refer to that review. The findings remain unchanged, although some relevant papers have been written since (e.g. Staples et al, 1997; Banasi et al, 1999; Orford et al, 2006; LaMarsh, 2015). The main findings of the review were as follows."

Jan 1, 2018

By Robert J. Henning

The term olivine was first used in 1790 by J. Werner, and the corresponding mineral was so named because of its olive-green color (Hunter, 1941). Olivine is the principal component of the rock known as dunite. While by classic definition dunite is composed of 90% or more olivine, commercial use of these terms has resulted in more specific definitions. Commercially, the term olivine is used to designate a material that consists of 85% or more forsterite and contains 45 to 50% MgO, 39 to 42% SiO2, 5 to 8% Fe2O3, and has an ignition loss (LOI) of 1 to 2%. The term dunite designates a rock that contains 36 to 45% MgO, 36 to 39% SiO2, and has an ignition loss of as much as 10% (Teague, 1983). GEOLOGY Olivine is found in basic igneous and basic metamorphic rocks whose age varies from pre-Ordovician to Tertiary. Economic deposits are of magmatic origin and are restricted to the dunite variety of the peridotite group of ultrabasic igneous rocks. Olivine also occurs in basic igneous rocks such as gabbro, basalt, and diabase and more rarely as an accessory mineral in granite and metamorphosed crystalline limestones. Mineralogy The term olivine refers to a group of orthosilicate minerals in isomorphous series with magnesium-rich forsterite (Mg2Si04) as one end member and iron-rich fayalite (Fe,SiO,) as the other. In most olivines the ratio of magnesium to iron varies from 16: 1 to 2: 1. Commercial olivine deposits contain a mixture of forsterite and fayalite with the fayalite content restricted to less than 15% (Reed, 1959; Teague, 1983). Accessory constituents may include primary minerals such as ilmenite, magnetite, diopside, chromite, and garnet and secondary minerals such as chlorite, serpentine, talc, and vermiculite as alteration products. Chemical and Physical Properties The chemical composition of olivine can be expressed as either (Mg, Fe), SiO, or 2(Mg, Fe)O.SiO,. Table 1 presents chemical analyses for some commercial olivines. The physical properties of olivine are shown in Table 2. Distribution of Major Deposits Commercial olivine and dunite deposits are found in Norway, Japan, Spain, India, Italy, the United States, Sweden, Austria, Pakistan, and Mexico. Noncommercial deposits have been reported in New Zealand, Zimbabwe, South Africa, New Caledonia, Greece, Brazil, and Canada (Teague, 1983). The present markets for olivine are characterized by low unit value, high volume, and high sensitivity to freight costs, so few deposits are commercially viable. Literature from the USSR indicates that considerable research on olivine refractories is being done. (Afansa'ev, 1988), lending credibility to the conjecture that commercial deposits are being mined there. In eastern Canada synthetic olivine is being produced by calcining chrysotile asbestos mine tailings. In the United States numerous lenses of olivine extend in a belt from northeast Georgia northeastward across western North Carolina. Total reserves in North Carolina and Georgia are estimated at between 125 and 200 Mt. The largest US deposit is Twin Sisters Mountain, located in Whatcom and Skagit Counties in the state of Washington. This deposit, which has an outcrop area of 93 km2 and a relief of about 1 525 m. is estimated to contain 1 800 Mt of fresh, unaltered olivine (Teague, 1983). In addition, the US Bureau of Mines reports reserves of 50 Mt on Cypress Island in the state of Washington, and the literature reports eight complexes in southeastern Alaska, some containing cores of olivine as large as 1.6 km in diameter (Taylor, Jr., 1967). The world's largest deposit of olivine occurs in the Aaheim area of Norway, where reserves are estimated at a 2 000 Mt. Several other Norwegian deposits contain as much as 5 Mt each. In Japan the production of ultrabasic rocks is currently about 6 Mtpy, but the bulk of this output is serpentinite. Olivineldunite accounts for only 17% of this production. The major olivine deposit in Japan is located at Horoman Hill on the northern island of Hokkaido. Reserves at this deposit are estimated at 100 Mt (Anon., 1990). Spain is one of the largest producers of dunite. Reserves in the La Coruna District in northwestern Spain are estimated at 100 Mt. India, also a major dunite producer, has a large deposit at Salem in Tamil Nadu. In Italy olivine/dunite is mined from a deposit near Turin. In Sweden the largest deposit is at Arutats and is reported to be comparable in size to the Twin Sisters deposit in the United States. At present the only production in Sweden is from a deposit 30 km south of the town of Gallivare. Reserves at this deposit are reported to be between 1 and 2 Mt. Other significant deposits are: 1) in Austria at St. Stefan near Leoben, 2) in the Swat District of the North West Frontier Province in Pakistan, and 3) in Mexico at Cuidad Victoria in Tamaulipas (Anon., 1990).

Jan 1, 1994

By J. R. R. Bowling, A. McFadden, M. Francoeur

The abstract discusses the increasing use of extensive duct-fan systems in underground hard-rock mine development. It highlights the challenges of designing these systems, particularly the risk of partial vacuum and the need for careful booster fan positioning. The paper explores factors influencing the design of these systems, including component limitations, operational wear margins, and power constraints. It also defines the concept of partial vacuum and its impact on ventilation ducts. The authors propose an algorithmic approach for specifying the location and blade pitch of in-line booster fans to prevent system failure.

Mar 17, 2022

By Richard Seal

Nabarlek is situated in the Arnhem Land Aboriginal Reserve about 270 km due east of Darwin in the Northern Territory of Australia. During the dry season (May to November) Nabarlek is accessible from Darwin over the Arnhem Highway-- a distance of 330 km. Throughout the wet season (December to April), except for a few days, access is provided by aircraft from Darwin to the Nabarlek airstrip. Because of the limited access during the wet season, reagents and supplies have to be stock- piled for six months on the site to maintain operations. With the mine and plant being remotely located on private Arnhem land with very limited access outside the site fence, operating personnel are flown to Darwin every six days for their days off.

Jan 1, 1980

By J. Launay

In order to control and dispatch the sewage water coming from 3 tunnels toward 2 downstream sewage tunnels, a large cavern has been excavated in a suburb of PARIS. Located at a depth of 47,00 m, it has been excavated using the NATM procedure through swelling clay, weathered sandstone, and marl and chalk. It is 16,50 m high, 12,40 m wide and 60, 00 m long, with an elliptical cross-section and its two ends are egg-shapped. The final lining of the cavern is composed of 30 to 40 cm of shotcrete, steel ribs and passive anchor bars. The excavation stages and related movements were surveyed by extensometers, pressure cells and convergence devices. The design, method of construction of the cavern and the results of the measurements made are commented.

Jan 1, 1989

By D. B. Gentzler, J. L. Kohler

A method of monitoring production information (raw tonnage and machine state) from each working section has been developed. The method is based on the sensing of electrical parameters in each section load center, and the reporting of this information through the existing mine-wide monitoring system. A decision-theoretic type of pattern classification technique has been used to define the machine states. The basis of the method is presented in this paper, along with a proposed hardware and software implementation scheme. Information issues central to the development and use of the proposed production monitoring system are also discussed.

Jan 1, 1990

By Grant R. Brown

The objective of this paper is to describe a study sponsored by the U.S. Department of Energy during which a model was developed to optimize haulback mining procedures in single and multiple seam contour mines, The study objective was to achieve financial- based productivity increases approaching twenty percent. This paper reviews the results of the first year's Phase I activities, which include four main tasks: formulate a methodology that can be used to select equipment and mining procedures that result in optimal performance in a particular haulback mining situation; conduct field studies of representative single and multiple seam mines to obtain quantitative background information for development of the formulated methodology: develop the methodology into a useful design tool for mine operators; and prepare plans for field tests to evaluate the effectiveness of the developed tool.

Jan 1, 1981

By Wilbur I. Duvall

INTRODUCTION This chapter outlines some general principles and procedures that a rock mechanics engineer can use to arrive at a logical design for the size, shape, and spacings of underground openings in various types of com¬petent rock formations. Rock formations can be clas¬sified into six major categories which are useful for design purposes, provided the necessary input data are available regarding the geology of the site, the physical properties of the rock, the in-situ stress field in the rock, and the general geometry of the underground openings. The US Bureau of Mines (USBM) developed a rock classification system based upon these concepts and found it to be useful for design purposes (Obert, et al., 1960; Obert and Duvall, 1967). This classification sys¬tem is given in Table 1; however, an extra column has been added to the original classification to indicate the appropriate design techniques for each rock class. In this classification system, two main classes of rock are considered: competent rock and incompetent rock. Competent Rock Competent rock is any rock which, because of its mechanical and geological characteristics, is capable of sustaining underground openings without the aid of any structural support except that provided by unmined rock in the form of pillars and side walls, etc. Roof bolts and small random props which support only local loose rock are not considered structural supports. Competent rock is further subdivided into three ad¬ditional categories-massive, laminated, and jointed¬ which are defined as follows: Massive Rock: Massive rock is a rock formation where the spacing between mechanical defects such as joints, partings, or faults is equal to or greater than the critical dimensions of openings, or where the strength of the bond across these mechanical defects is com¬parable to the rock strength. Laminated Rock: Laminated rock is a rock forma¬tion divided by approximately parallel planes of weak¬ness into lamina whose thicknesses are small compared to critical dimensions of openings and where the bond between the lamina is weak compared to the rock strength. Elastic Rock-This is rock whose physical proper¬ties will permit the use of elastic theory to predict strains and displacements from applied stresses. Inelastic Rock-This is rock whose physical proper¬ties are such that strains and displacements are a strong function of time as well as applied stress. Incompetent Rock Incompetent rock is any rock which, because of its mechanical and geologic characteristics, is not capable of sustaining underground openings without the aid of additional structural support in the form of linings, steel sets, or systems of props. This classification system for rock depends not only on the mechanical and geologic characteristics of the rock but on the size of openings and their depth be¬low the surface. For example, many competent rocks at shallow depths for small stress fields could become inelastic rock at greater depths and larger stress fields, or competent massive rock for small openings could be¬come laminated or jointed rock for larger openings. Thus, to classify rock for design purposes requires a knowledge of the geologic properties of the rock mass, the physical properties of the rock, the general size of the openings to be mined, and the average range of the in-situ stress field to be encountered. To design underground openings and structures in rock, it is necessary to use criteria of failure for rock under various stress conditions, and to use safety factors to allow for differences between laboratory and in-situ strength properties of rock and to account for errors in¬troduced by the various assumptions made in the design process. Criteria of failure based on maximum stresses have been found to give reliable results in practice. Thus, it is assumed that rock will fail in tension when the tensile stress exceeds the tensile strength of the rock as determined by a standard modulus of rupture test on samples of rock core. If the tensile stresses in rock are small, then it is assumed that the rock will fail at a value of compressive stress equal to the compressive strength of the rock as determined by standard uniaxial compres¬sive strength tests on samples of rock core. These fail¬ure criteria, when used with appropriate safety factors, can be expressed as:

Jan 1, 1982