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By V. L. Franzen, Z. J. Hladysz, C. A. Kliche

The Wharf Resources mine, located in the Bald Mountain Mining District approximately 6.4 km (4miles) west of Lead, South Dakota, has operated a surface gold and silver mine and heap leaching processing facility since 1983. Wharf Resources intends to mine and process gold and silver ore from the Wharf Expansion area which is located on the eastern flank of the currently permitted Foley Ridge Mine. The Trojan Pit for the Wharf Expansion area was initially designed with an overall highwall slope angle of 45o. During mine permit presubmission meetings with personnel from the SD Department of Environment and Natural Resources (SD DENR), the question arose as to whether a detailed slope stability analysis of the proposed Trojan Pit highwalls was completed to justify the 45o slope. Wharf’s response was that the highwall design was based, in part, upon studies completed in1987 on the Annie Creek and Foley Ridge Mines; and, in part, upon subsequent slope stability analyses conducted by Wharf mine personnel through 1996. It was suggested by the SD DENR that the stability study be updated to reflect structural geological conditions in the Wharf Expansion area.

Jan 1, 2000

By Gregory T. Ziegler

A complex soil profile and high water table, together with a below-grade active subway tunnel, an above-ground elevated railway line, and the heavily travelled Northern Boulevard all passing above the tunnel alignment, combined to make mining of New York?s Northern Boulevard Crossing what is widely considered to be the most challenging portion of the multi-billion-dollar East Side Access project. The Northern Boulevard Crossing is a vital link in this project which, when completed, will connect the Long Island Railroad to Grand Central Terminal in Manhattan. How the sequential excavation method (SEM) tunneling was successfully accomplished, despite the obstacles, was a textbook exercise in practical innovation coupled with close cooperation between the owner, the construction manager, Hatch Mott MacDonald, the designer, Parsons Brinckerhoff, the contractor, Schiavone-Kiewit, and spe-cialty geotechnical contractor, Moretrench.

Sep 1, 2013

By Christopher J. Bise

INTRODUCTION Perhaps no other area reflects the art as well as the science of mining-engineering design quite as obviously as strata control. This is due to the fact that the design of mining structures is difficult because rock rarely behaves as a homogeneous medium. Further, the original state of stress and the mechanical proper- ties of the in situ rock are somewhat difficult to deter- mine. However, those aspects that are hard to treat mathematically can and have been successfully approached by model studies and in situ measurements. This chapter will review the fundamentals of strata- control design and will provide examples of applications to typical problems. STRESSES AROUND MINE OPENINGS A close examination of Fig. 1 reveals that, prior to mining, stresses exerted in the overburden can be in both the horizontal and vertical directions. In the example problems of Chapter 1, it was shown that the maximum compressive stress (uv) at any depth (D) below the surface can be approximated as follows: [ ] Further, the lateral stress (oh) is related to the maxi- mum compressive stress by utilizing Poisson's ratio (µ): [ ] As soon as a heading is driven, such as the one in the coal seam shown in Fig. 2, the stresses shift to the sides, or abutments, of the opening. Clearly, these compressive stresses around the opening exceed the pre-mining conditions. The problem of designing an underground opening, therefore, is to determine the maximum stresses and to note if they exceed the ultimate strength of the rock. Table 1 lists several rocks with their corresponding strengths. Figs. 3 to 5 depict the boundary stress concentrations around circular, ovaloidal, and rectangular openings. M is the ratio of the horizontal stress to the vertical stress, or as defined above, p/(l-p). This text will concentrate on the state of stress represented by M = 0.33, which corresponds to the condition of no lateral deformation in a rock having a Poisson's ratio of 0.25. For an ovaloid with an opening width-to-height ratio of 2.0 (Fig. 4), the boundary stress concentrations are at their maximum values at the comers of the opening, with values in excess of 3.0. If the depth of overburden is 500 ft, then the maximum boundary tangential stress ([ ] ) of the ovaloid is: [ ]

Jan 1, 1986

By C. J. Veal, C. I. House, S. R. Bellamy

INTRODUCTION Coal gold agglomeration (CGA) is a new concept in gold processing. It involves the recovery of oleophilic (oil-loving) gold grains by causing them to adhere selectively to the surfaces of coal oil agglomerates. Under optimum conditions very high recoveries of gold. can be achieved. The agglomerates are recycled to build up gold loading to typically 1000 - 5000 g/tonne. Bullion can be produced by burning the loaded agglomerates with subsequent recovery of gold from the highly loaded ash either by dissolution/electrowinning or smelting. A wide-ranging programme of laboratory testwork has been performed to investigate the response of different ore types to the process. This has shown CGA to be most applicable to ores in which the gold is liberated or easily liberatable, relatively coarse (ca 500 µm) and fine (<5 µm) gold grains being recoverable with equal ease. The best opportunities for CGA seem to be: • placers containing fine gold not recoverable by gravity concentration • low grade gravity concentrates to avoid multiple magnetic/gravity separation stages and amalgamation • free milling ores where the gold can be liberated at a reasonable ore particle size eg >d80 50 µm • tailings past or present from gravity concentration plants. CGA testwork ranging in scale from laboratory to pilot plant on tailings produced by gravity concentration in the 19th century Australian gold rush has already been reported (Bonney, C F, 1988; House, C I, Townsend, I C and Veal, C J, 1988). An economic appraisal for a Canadian free milling gold ore has also been published (Buckley, S A, House, C I and Townsend, I G, 1989). This paper describes results of a detailed laboratory programme to assess CGA as a means of recovering gold from a beach sand deposit in New Zealand. The area from which the samples were taken consists of quarternary interglacial marine, lagoonal, fluvial and eolian deposits. The heavy minerals present are predominantly ilmenite and garnet and small concentrations of gold. In certain locations the sands and gravels are consolidated by a limonitic cement. In the 19th Century some parts of the deposit were mined and the ore processed using stamp milling and gravity concentration. Gold recoveries were low, probably below 50%, due primarily to the fine size of the gold grains, the flaky nature of the gold and also imperfect liberation by the stamp mills. Our laboratory testwork was divided into three parts: i) Preliminary studies on an initial sample to assess the feasibility of treating the ore by CGA ii) Extended studies on further samples from various locations in the deposit to confirm predictions from (i) iii) Conventional gold recovery techniques. EXPERIMENTAL PROCEDURES All CGA tests were performed by agitating a slurry of ore in water in a 0.6 dm3 pyrex beaker fitted with four vertical baffles. When required, potassium amyl xanthate collector was added and the slurry conditioned for 5 min. Coal (ex BP Coal Australia&apos;s Tahmoor Colliery) previously ground to a d80 50 µm was added followed by a commercial grade of gas oil (density 840 kg/m3). The agglomeration time was 30 min. The agglomerates were separated from the tailings by screening, both were then dried and analysed for gold by fire assay. This test procedure provides a reasonably accurate estimate of gold recoveries that might be expected from our 1 tph pilot plant. Ore samples were ground either dry in an agate ring disc mill or wet in a steel batch tumbling

Jan 1, 1989

By Lloyd M. English

During the past 30 years, the research arena has changed significantly in all fields, mining included. The relative representation of the topics of research, how the research is performed and who has performed the research have all changed. Although there are a lot of subjective ideas and anecdotal "analyses" concerning these changes, there has been no actual study of these trends to verify the facts. This study was divided into six five-¬year periods for the purposes of comparison. Some of the trends analyzed are co-authorship, research areas, research sponsors and cooperative efforts. In today&apos;s research arena, 30 years is a long time. Technology has advanced more rapidly than in any time previously and that pace continues to increase. There are more researchers, more tools for research and an increasing number of companies, agencies and institutions engaged in research. The pace of change and its impact is often discussed and debated at professional meetings and in institutions that engage in research. These conversations will often influence the research decisions of the participants in directions to take or subjects to pursue.

Jan 1, 1995

By Tae-kyeong Yeu, Jong-Choi, Cheon-Hong Min, Hyung-woo Kim, Jae- Won Oh, Sup Hong, Minuk Lee, Sung-Soon Kim, Chang-Ho Lee, Ki-Young Seong

"Collecting mineral resources from the seabed using a seafloor crawling robot is the firststep in the mining operation. The second-step is lifting the collected ore up to the water surface. For lifting through a riser pipe, prevention of pipe clogging (flow assurance) and economic and eco-friendly up-transferring is of the utmost concern.During collection of mineral ores, the production rate can be highly variable because of the variability in the distribution of the mineral deposit, variations in seafloor topography, fluctuations robot speed, and variations in performance of the mining robot, etc. Direct transfer of the collected ore to the riser pipe might cause unpredictable and serious problems such as over-loading of the lift pump, reduction in the life of the equipment, pipe clogging, severe increase of down-time, critical damage of equipment, further propagation of damages, and total failure after all.As a counter measure to these potential problems, a buffer station has been adopted, which is capable of storing the collected ore for a certain time and simultaneously regulating the transfer of the ore into the riser pipe. A pilot buffer has been developed by KRISO/KIOST (see Fig. 1)."

Sep 1, 2014

By Sukru Sumer

East Pit Lake is an artificially created lake that resulted from the remediation and reclamation of surface coal mining operations at TransAlta Utilities&apos; Whitewood Mine in the Wabamun area west of Edmonton, Alberta. The original excavation resulted from the creation of a mine end cut at the northern extent of the mining operation. The area of the surficial drainage basin that feeds East Pit Lake was relatively small. Therefore, most of the inflow and outflow from the lake would result from regional ground water flow. There was a concern about the lake&apos;s ability to provide a suitable habitat for a sportfish population. To determine the final recovered water level and rates of recovery, a two-dimensional ground water flow model was used. Data supplied by nested piezometers in and around the mine were used to calibrate the computer simulation and assess predicted recovery.

Jan 1, 1995

By Charles A. Weinstein

INTRODUCTION As a set of management practices, "Knowledge Management" (KM) has disappointed many of its early advocates. The core notion behind KM can be summed up in the oft- quoted adage, "If we only knew what we know." KM describes a set of tools, practices, and approaches for using data, information, and expertise-knowledge-resident in an organization to improve the performance of that organization. The idea was incubated, hatched, and grew among some the largest and most successful companies in the world. Some of these companies created "Chief Knowledge Officers." Many more collectively invested billions in a huge range of KM efforts, all designed to use their organizations&apos; information and expertise to innovate, improve margins, sell, or accomplish any of a myriad of sound business goals. Some KM efforts were successful, and many were not.* Today, it is indisputably the case that KM as a named set of practices has fallen out of favor. Why, then, should KM be discussed at a conference on "Things that Actually Work" for plant operators? Because, in many instances, KM has actually worked. The practices that represent KM done right offer significant opportunities for plant operators to achieve real gains, especially in times of resource constraints and in the face of ever-increasing technical and commercial goals. The KM fad is all but over. The KM benefits continue to accrue to those who have applied the lessons learned from that fad, and implemented sound * Fair disclosure: I am not unbiased with respect to the potential impact of KM. Teltech has been a pioneer and leader in KM, both as a practitioner and as a leading consultant to other organizations.

Jan 1, 2004

By V. McLemore

New Mexico ranks 2nd in uranium reserves in the U. S., which amounts to 15 million tons ore at 0.277% U3O8 (84 million lbs U3O8) at $30/lb (EIA, 2006). The most important deposit in the state is sandstone within the Morrison Formation (Jurassic) in the Grants district. More than 340 million pounds of U3O8 have been produced from these deposits from 1948-2002, accounting for 97% of the total production in New Mexico and more than 30% of the total production in the United States. Sandstone uranium deposits are defined as epigenetic concentrations of uranium in fluvial, lacustrine, and deltaic sandstones. Three types of sandstone uranium deposits are recognized: tabular (primary, trend, blanket, black-band), roll-front (redistributed, post-fault, secondary), and fault-related (redistributed, stack, post-fault). Several companies are planning to mine these deposits by in-situ leaching.

Jan 1, 2007

By John C. Gould

GENERAL DESCRIPTION The Climax mine is located 161 km (100 miles) southwest of Denver on Fremont Pass astride the Con¬tinental Divide. Climax employs 2800 people to pro¬duce 42 670 t/d (47,000 stpd) of molybdenum ore. The Storke level, the main underground level, produces 19 970 t/d (22,000 stpd); the 600 level, the lowest ac¬tive underground area, produces 7260 t/d (8000 stpd); and the open pit presently produces 15 430 t/d (17,000 stpd), Fig. 1. A panel caving method is possible because of the favorable geology and geometry of the Climax ore body. Geology The Climax deposit is composed of three separate ore bodies formed in a massive Tertiary stockwork which penetrates Precambrian granites and schists. The ore bodies are elliptical in plan with overall dimensions of 914 x 1219 m (3000 x 4000 ft). In section the ore bodies are arcuate with an overall height of 457 m (1500 ft), although the depth is not firmly ascertained. Ore grade decreases rapidly into a highly siliceous cen¬tral core and more gradually toward the outer bounda¬ries of the deposit. The mineralization is relatively continuous in the ore zone and contains few dilution-causing waste inclusions. Molybdenite is contained in pre-ore fractures which were largely recemented during the three mineralization pulses. Postore fractures, with a spacing of a few inches to several meters (feet), render the deposit amenable to caving when it is undercut. The peripheral rock caves similarly to the ore, but the central core is competent and is difficult to cave. Caving Feasibility Successful caving action requires an undercut area of approximately 122 by 122 m (400 by 400 ft). When the undercut area exceeds this minimum distance, the arching effect is lost, and the ore column collapses. Ore extensions from the main cave area less than 122 m (400 ft) wide usually cannot be caved. Waste or low¬grade areas within the deposit can be left if they are large enough to carry weight around openings passing through them. Experience indicates that these areas should be over 30 m (100 ft) in length and width. Smaller unprofitable units of waste, such as postore dikes, are mined to avoid weight problems and result in ore dilution. Successful caving and ore recovery are dependent upon timely ore removal from the undercut zone because columns of immobile ore inhibit caving and concentrate weight onto the underlying workings. Climax experience indicates that a finger (drawpoint) spacing* averaging 10.4 m (34 ft) yields an excellent caving action and a 92.5% ore recovery at the estimated grade. An additional 15% of the ore is recovered-at a diluted grade (Fig. 2). Mine Layout The slusher drift is the primary production facility (Fig. 3). The ore is undercut and caved into the fingers,

Jan 1, 1982

By M. S. Klima, P. T. Luckie

Proper analysis of washabiity data can lead to the development of a maximum yield coal preparation plant flow sheet. Simulations, as simple as spreadsheet mass and water balancing, are important in examining yield maximization and middlings liberation. Key to such attribute tracking flow sheet simulations is the distribution model, expressing the probability of a species reporting to the product stream. There are many such models in the literature. This paper examines a functional form that can represent or fit most of the proposed distribution functions.

Feb 24, 1997

By Anthony B. Szwilski, Dalip Sarin, Richard D. Begley

This paper will present the results of an analysis of several abandoned coal mine projects and includes field data for over a dozen different reclamation projects recently completed in the state of West Virginia. The analysis was performed with the objective of summarizing and or classification of the environmental consequences with reference to the characteristics of the mining facilities (surface, underground, etc.). The analysis also addressed the itemized cost of remediation with respect to procedures, environmental concerns and time. The results of the analysis are that each abandoned coal mine site in West Virginia have/had many unique features and in most cases include a combination of environmental concerns that complicate comparisons. The study also revealed that the abandoned mine land program for mines abandoned prior to 1977, that is being financed by a tax on the production of coal, has produced many benefits for the state of West Virginia. This grant program administered by the Office of Surface Mining, has resulted in a high quality methodology of remediation that has been successful for many years in greatly minimizing and/or eliminating environmental concerns from abandoned coal mines.

Feb 24, 1997

By J. E. Friant

The Mini-DiscTM cutter drill bit is a radical design departure from the traditional tri-cone rockdrill bit. Miniature disc type cutting tools as small as 3.25 inches (82.5 mm) diameter are fitted to a bit body to cut individual concentric kerfs. The action is the same as that commonly used on large tunnel boring machines but miniaturized. The high performance rate and efficiency of a disc cutter are the result of producing a large proportion rock chips rather than sand or powder. The Mini-DiscTM drill bit, referred to as the “Disc Bit” has other unique features as well. It can be re-greased between runs. It can be rebuilt in the field in about 15 minutes, cutters can be replaced and the Disc-Bit appears to require less down hole hydraulic power than conventional bits. Thoroughly tested in the laboratory, the bit has recently been undergoing field trials in well drilling, blast hole drilling and shaft drilling. As any engineer knows, the laboratory can not shake out all the problems but it eliminates the more glaring weaknesses. Performance results have been exhilarating, and a few mechanical problems were discovered and largely overcome. This paper is a progress report.

Jan 1, 1999

By Tad S. Golosinski, R. Larry Grayson

Online education is not new. During the last decade, it has reached the stage where many universities offer a variety of courses, degrees and programs without any associated residency requirements. The most successful of the online universities, University of Phoenix, offers hundreds of accredited programs for close to 100,000 students throughout the world (www.phoenix.edu). Online education is considered to be a valid equivalent to traditional, classroom-based education. It is best suited to the needs of mature students with full-time jobs and a desire to deepen their knowledge. While most of the e-business has experienced severe setbacks during the last two years, e-education shows no signs of slowing down. On the contrary, the number of students and institutions offering online education keeps growing. The value of e-education associated expenditures was expected to reach $300 billion in 2001 (Sanoff,2001), making it a serious and mature industry.

Jan 1, 2002

By D. Royston

SAG mill liner development draws primarily on practical experience from SAG milling operations supported by computer-based modeling of charge motion in SAG mills and on established good design practice. Liner design needs to respond to the process aspects of mill liner action that are critical to good SAG mill performance, i.e., the impact of shell liners on the grinding action and of grates and pulp lifters on pulp discharge. In recent years, the trend in large SAG mills has been to use wide-spaced shell lifters with large lifter face angles, primarily to reduce packing and ball/liner damage, and to use larger, hence fewer, mill liner parts to reduce downtime at liner change-outs.

Jan 1, 2007

The Carlin Trend is North America&apos;s premier gold producing district. It is located in northeastern Nevada&apos;s Elko and Eureka Counties along a northwest trending belt about 65 km (40 miles) long and 8 km (5 miles) wide (Thorstad, 1989; Jones, 1989). This trend is the worldwide reference site for epithermal, sedimentary rock-hosted microscopic gold deposits. At least 19 deposits have been discovered to date, varying in size from 933 kg to 1.08 kt (30,000 to 35 million contained oz) of gold (Fig. 1). Newmont Gold Co. and its parent, Newmont Mining Corp., jointly constitute the largest mineral right holders in the district. They own or control more than 1000 km&apos;- (386 sq miles) in and around the Carlin Trend and own all or part of 16 out of the 19 mines and prospects identified to date. Since the initiation of Newmont&apos;s exploration activities in the Carlin Trend in 1961, 2.24 kt (72 million oz) of cumulative gold resources have been identified. Cumulative production from all mines since the start-up of Newmont&apos;s Carlin mine in 1965 to the end of 1989 was about 202 t (6.5 million oz) (Jones, 1989). The incentive of sustained high gold prices and innovation in processing technology resulted in a significant acceleration of gold output over the last few years. Newmont Gold alone produced more than 43.5 t (1.4 million oz) in 1989. That is equal to 22% of the cumulative 1965 to 1988 output, and an almost 200% increase over its 1986 output.

Jan 1, 1991

By D. R. Wilburn

This summary of international mineral exploration activities for 2008 draws upon available information from industry sources, published literature and U.S. Geological Survey (USGS) specialists. The summary provides data on exploration budgets by region and mineral commodity, identifies significant mineral discoveries and areas of mineral exploration, discusses government programs affecting the mineral exploration industry, and presents analyses of exploration activities by the mineral industry based upon these data. Two types of information are reported and analyzed in this annual review of international exploration for 2008: 1) budgetary statistics expressed in U.S. nominal dollars provided by Metals Economics Group (MEG) of Halifax, Nova Scotia (Metals Economics Group, 2008a, b), and 2) information on regional and site-specific exploration activities that took place in 2008 and compiled by the USGS. The MEG information summarizes planned company budgets for worldwide exploration activities in 2008, primarily for precious metals (gold, platinum-group metals and silver) and base metals (copper, lead, nickel and zinc). MEG includes information on additional mineral commodities only where it is available. Information on uranium exploration was included in the MEG overview for the first time in 2007, although this information was not included in the USGS analysis. The MEG survey methodology was changed in 1999 to include companies with exploration budgets between $100,000 and $2.9 million, as well as those companies included in prior studies whose anticipated budgets were above $2.9 million. MEG estimates that its post-1999 surveys cover at least 90 percent of world nonferrous nonfuel mineral exploration budgets. The 2008 survey is reported by MEG to cover an estimated 95 percent. Companies that chose not to participate in the MEG study, private companies that do not publish data, and government-funded exploration activities make up the majority of the remaining 5 percent. MEG included 91 more companies in its 2008 survey than it did in 2007 USGS compilations of site data described here primarily include nonfuel minerals, with an emphasis on base metals, diamond and precious metals. Analyses are based on information provided by USGS mineral commodity and country specialists and by other USGS scientists, as well as industry contacts and trade journals.

Jan 1, 2009

By J. N. Eskilsson, W. P. Chen, J. L. Kaplin, V. S. Romero

The Massachusetts Water Resources Authority is currently improving its primary water supply system for the Boston Metropolitan area. The improvements planned by the Authority, which provides water for 46 communities and over 2.5 million people in eastern Massachusetts, include the MetroWest Water Supply Tunnel (MWWST) to provide redundancy in the transmission system, a large capacity water treatment plant and extensive covered storage facilities. The 28.3 km (17.6 miles) long, mostly 4.3 m (14 ft.) I.D. MetroWest Water Supply Tunnel will allow repair of the aging Hultman Aqueduct, which for 56 years has served as the transmission main from the water supply reservoirs to Boston. On completion of the tunnel, the old pipeline aqueduct will be repaired and brought back into service as a parallel, redundant transmission main. This paper describes design considerations and the design process for pressure tunnels in general and the MWWST in particular. It provides an overview of how the design of pressure tunnel and shaft components progresses.

Jan 1, 1997

By Timothy P. Smirnoff, Tracy K. Lundin

INTRODUCTION The City of Phoenix, Arizona is located in the Phoenix Basin watershed which is prone to flash flooding several times each year. The runoff from these storms moves from the mountains in the north to the Salt River in the south. An extension of Interstate Highway 10 (1-10) will pass through the city east to west to form an Inner Loop through the downtown business district. PROJECT DESCRIPTION The I-10 Inner Loop extension will be a depressed roadway which would intercept the surface drainage of the Phoenix Basin and separate the watershed into two regions. To prevent flooding of the depressed roadway, runoff storm water collected from the northern half of the drainage area will be conveyed beneath the roadway to its natural outlet at the Salt River. A conveyance system composed of pressure tunnels beneath the city, shown in Figure 1, was proposed to achieve this goal . Table A presents the prominent features of each of the tunnels. This paper will describe geologic and engineering parameters specific to Phoenix which were used in the design of a series of tunnels to convey storm water from the I-10 Inner Loop to the Salt River. The design of tunnel initial and final support is described along with support and construction methods used by the Contractor.

Jan 1, 1985

By F. Touboul, M. Thiercelin, K. BenNaceur

Introduction The need to develop accurate predictive hydraulic fracturing simulators arises from the consideration of vertical containment for the fracture. Fracture height growth from a pay zone into adjacent layers has been shown (see Cleary [I]) to depend on three sets of parameters for the different strata: - elastic properties, - closure stress variations, and, -fracturing fluid leak off, and poro-elastic stresses. Qualitative analysis of the effects of these parameters has been reported in the literature. The first effects were described by Van Eekelen, using simple elasticity considerations [2]. The effect of stress variations was described numerically by Simonson and a1. [3] and experimentally by Thiercelin [4]. Effects of back stresses induced by fluid invasion on fracture propagation were considered by Cleary [5]. In order to couple these effects, a numerical code al- lowing the simulation of three dimensional growth of a hydraulically induced fracture has been developed with the ability of representing the effects of heterogeneities on fracture lateral and vertical extension. The model is based on a new variational formulation of the boundary integral representation of three-dimensional elasticity. The fluid flow and elasticity equations are solved using a moving mesh representation which offers enough flexibility to enable the simulation of any closure stress distribution. Simpler models representing fracture height growth (P3DH models) have been developed [6] [7] that approximate the fracture by a series of one dimensional segments, and the limitation of such approaches is examined in this paper. 1 Description of the model 1.1 Fracture Geometry Hydraulic fracturing simulations involve the coupling of solutions to elastic deformations, fluid flow in the fracture, and fluid leak off into the formation. Since the use of direct solution techniques (i,e,,3D finite elements) is prohibitive, the method used in this study is baaed on a boundary integral representation of the 3D elasticity equations. 1.2 3D Models The classical representation of the problem of a fracture in an infinite medium by boundary integrals is [8]: [ ] where u is the unknown displacement field, r n is the traction operator, I? is the fracture surface, and K is the Kelvin tensor of fundamental solutions to the elasticity operator. Using the notation: [ ] for the displacement discontinuity (or fracture width), one can attempt to solve the boundary integral relation using surface integrals (91 or the displacement discontinuity technique, first introduced by Crouch [lo], and extended to three-dimensional problems [Ill. However, numerical problems arise since the Kelvin tensor has a singularity in

Jan 1, 1986