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By Christopher Mark

The first International Conference on Ground Control in Mining opened with the topic of pillar design. Two classic papers were presented, one by Bieniwski and the other by Wilson. Unfortunately, the two methods were so radically different from each other that it was nearly impossible to reconcile them. Adding to the confusion were the many other pillar strength formulas (such as the Salamon-Munro, the Holland-Gaddy, and the Obert-Duvall, just to name a few) that were also available. Little wonder that discussions of pillar design in those days often ended with anguished cries of ?but which formula is the right one?? The past 25 years have seen substantial progress in the science of coal pillar design. Indeed, one testament to the improvement is the relative scarcity of papers on the topic at recent Conferences. Two factors have been largely responsible for the progress that has been made. The first has been the collection of large data bases of actual case histories of pillar performance in a variety of settings, from shallow room-and-pillar mines through deep cover longwalls. These have made possible the development of empirical design procedures that are closely linked to real world experience. The second important factor is the development of sophisticated computer models that can accurately simulate pillar behavior and roof/pillar/floor interactions. Together, these two lines of research have led to a new understanding of pillar mechanics that identifies three modes of pillar failure: ? Sudden, massive collapse, accompanied by airblast, for slender pillars (width/height<4) ? Squeezing, or slow, non-violent failure, for most room and pillar applications (4<w/h<10) ? Entry failure or bumps for deep cover and longwall applications (w/h>10) It is particularly satisfying that the insights gained from numerical models broadly support those obtained from the empirical studies. While far less controversial than in the past, pillar design problems continue to arise. One recent example is pillar design for highwall mining. NIOSH has just released a software package, called ARMPS-HWM, which employs a number of modern pillar design concepts. Since highwall mining web pillars are long and slender, the greatest danger is that of a sudden collapse. ARMPS-HWM suggests two possible prevention strategies, one which concentrates on the SF of the webs, and the other which creates a ?pressure arch? using properly sized barrier pillars. The paper will close with a discussion of some current needs in coal pillar design, including: ? Updating older empirical methods, such as ALPS, where changes in technology (new types of roof support, more demanding ventilation requirements, faster retreat rates) may have made some of the original case histories obsolete. ? Methods for determining site-specific coal strengths, focusing on bedding plane strength and other factors that may effect confinement, as input for both empirical and numerical design. ? Improved methods for evaluating coal pillar performance for environmental issues, such as surface subsidence and hydrologic impacts, which consider such factors as depth, w/h ratio, water immersion/drainage, and time dependent seam strength.

Jan 1, 2006

By Peter Fischer

Between 45,000 and 50,000 claims for subsidence are submitted each year to the German hard coal industry. In order to improve the service to claimants a quality management was established in 2005. This paper describes the process now used for handling these claims. A quality check has also been carried out by way of a customer survey, which was performed by an independent research agency. The results of the survey are presented in this paper. In Germany, research into mining subsidence mainly involves the prediction of ground movements caused by deep mining operations. Special areas of research are subsidence reducing aspects of the extraction panel planning, especially from the point of view of mining dynamics, as well as securing and restoration measures. This work seeks to prevent or minimize mining-induced damages close to the surface, for instance, buildings or infrastructure installations (such as pipelines), or underground mine openings (e.g. shafts). Roof collapses and surface fractures caused by shallow mine workings of an earlier era currently constitute a special area of investigation.

Jan 1, 2006

By Naj Aziz

The shear behaviour of reinforced rock joints is investigated for the bolt-grout-rock interaction and for failure mechanism. The effectiveness of the bolt application under lateral and axial loading conditions within surrounding materials is investigated in different medium strength. Double shearing testing of bolts were studied in concrete blocks of 20, 40, 50 and 100 MPa strengths, subjected to different pretension loads of 0, 5, 10, 20, 50 and 80 KN respectively. The experimental study was complemented with three-dimensional numerical analysis. Parameters examined include: shear resistance, shear displacement, induced strains and stresses during bolt bending process and its ultimate failure across the sheared joint planes. The conclusions drawn from the study were; the level of bolt resistance to shearing was influenced by the bolt profile configuration, the strength of the rock or medium influenced the level of load generated on the bolt, and the increase in bolt pretension has contributed to the increased shearing load of the bolted medium.

Jan 1, 2007

By Andre Cezar Zingano

"The objective of this paper is to estimate the coal seam strength and the pillar safety factor for low coal seams using back analysis and rock mass characterization. The coal seam strength is very important to estimate both pillar capacity and mine section design. There are two approaches to estimating coal seam strength: (i) by geomechanics characterization of the boreholes cores; and (ii) by back analysis from pillars successes and failures, or some in-situ tests. For low coal seams (1.2 m, or 47 in.), the confinement of the center of the pillar is very important to defining global pillar strength because the low seam height increases the confinement of the pillar core, even in small pillars. We used in this case study one underground coal mine in the Parana State where the coal seam thickness is 0.8m the pillar height is 1.3m, the entry width is 5m and seam depth is 130m. A panel test was prepared to study the pillar behavior for use of the retreat mining method. The designed pillar size was 6x5m and 1.3m high with a predicted safety factor of 1.0 based on the Hoek and Brown failure criterion is 5.3 MPa. Once no pillar failure was observed, the pillar safety factor was assumed at 1.0 and the coal seam strength was backcalculated. The back analysis estimated the coal seam strength to be 6.2MPa. The confinement of the pillar center directly affects the coal pillar strength, and also the coal seam strength estimated by back calculation.IntroductionThe coal seam strength is very important to estimating pillar strength and mine section design. There are two approaches to estimating coal seam strength: (i) by geomechanics characterization of the coal seam using borehole cores; and (ii) by back analysis from pillar successes and failures, or some in-situ tests like panel test or ultimate pillar capacity (Salamon and Munro, 1967; Maleki, 1981; Peng and Dutta, 1992). For the first approach, lab tests (mainly triaxial tests) and borehole geomechanics descriptions (quality and quantity of the discontinuities) determine the coal seam strength by the Hoek and Brown failure criterion (Hoek and Brown, 1997). For the second approach, a panel test to study the pillar behavior can be built to define coal seam strength by back calculation. The safety factor for the pillars in the test is 1.0, based on the estimated coal strength from the geomechanics characterization. In this case, the probability of failure is 50%. If some pillar failure occurred, and the real pillar size was measured, the back analysis could be applied to define pillar strength and the coal seam strength."

Jan 1, 2015

By D. W. H. Su

This paper presents the results of ill situ horizontal stress measurements using a Minifrac system in several northern Appalachian coal mines. The effect of stress magnitude and orientation on longwall gate entry stability was analyzed using a series of three-dimensional finite element analyses. The best headgate stability is achieved if the maximum horizontal stress is aligned with the direction of longwall retreat or if the panel is oriented such that the maximum stress relaxes over the headgate due to the presence of the newly formed gob. The degree of horizontal stress damage to longwall gate entries depends largely on the stress magnitude and roof geology. Accurate assessments of support or design techniques which may mitigate longwall headgate or tailgate instability in areas of thinly laminated roof and high horizontal stresses must account for the in situ horizontal stress state and site specific roof geology. The ability to measure stresses and map geology is thus essential to prevent ground control failures at the longwall headgate.

Jan 1, 1995

Effective strata control, utilising fully encapsulated roof bolts, is dependent on the installed quality of the reinforcement elements. One mechanism by which fully encapsulated roof bolts may become less than fully effective is by gloving (glove fingering) and un-mixing of the resin. Following some small roof failures containing gloved bolts, investigations have been undertaken in some New Zealand coal mines to determine the extent of, and mechanisms involved in, the gloving of fully encapsulated roof bolts for a range of roof types and installation methods. Gloving, in this context, refers to the resin cartridge partially or completely enveloping a length of the bolt, typically with unmixed resin filler and catalyst/hardener remaining within the cartridge. Results have shown that gloving and un-mixing is a systematic and widespread phenomena, occurring across a range of resin and/or bolt manufacturers, and across a variety of roof types. Gloving was found in bolts installed using: hand held pneumatic and continuous miner mounted hydraulic methods, under run of mine (ROM) conditions by mine workers, and under controlled "best practice" conditions. The roofs bolts investigated are all 1800mm (6ft) long, and have shown that, on average, 485mm (-19") of the bolt length is gloved and/or unmixed. This equates to a 27 percent reduction in effective bolt length. The effected length of bolt is sufficient to impact on the load transfer/reinforcement capabilities of the bolt system, and hence impacts on the design assumptions and subsequent stability assessments. Furthermore, there is a direct relationship between the mechanism for the gloving of bolts and an increased occurrence of resin loss and reduction in encapsulations length in soft (less than 10 MPa) and/or highly fractured rock. Investigations have concentrated on developing an understanding of the mechanisms involved. This has been undertaken using both field installations and recovered bolts, as well as test bench trials. The mechanisms involved have been confirmed as being: the development of a pressure front as the bolt encounters the resin and is spun up the hole, which, in turn, leads to over-pressurisation and radial expansion of the resin cartridge, resulting in an increase in diameter of the plastic resin cartridge, which allows the bolt to be spun up into the cartridge without making sufficient contact to shred the cartridge or the hardener tube, resulting in an unmixed portion of resin.

Jan 1, 2003

By Sean Harvey

One of the manifestations of the dynamically induced failures in deep coal mines is the violent ejection of coal from the ribs. A possible protection against such failures is the use of a specifically designed dynamic support system with reinforcement units having the sufficient capacity to absorb the kinetic energy of the dynamic failure and a skin support that can adequately contain the disintegrated coal. With this method of mitigation in mind, a recently introduced yielding rock bolt, trade name Roofex, has been identified (Harvey and Ozbay, 2009) as a possible energy absorbing component of a dynamic support system. According to the manufacturer?s specification, the Roofex bolts can yield 300 mm (or more) displacement while holding 80 kN pull load. In order to assess the performance of this support unit in coal ribs, a series of in situ pull tests performed in two coal mines in Colorado. The results show that, under conventional pull test loading conditions, Roofex yielding bolts perform very close to their claimed specifications, thus showing a potential for their use as the main energy absorbing component of a dynamic support system. Further studies are required to confirm the in situ performance of these bolts under dynamic loading conditions and also to develop a containment component for a dynamic support system for the mitigation of dynamic coal rib failures.

Jan 1, 2009

By N. P. Kripakov

The U.S. Bureau of Mines (USBM) is conducting research to develop a practical computer-based tool that will allow coal mine planners to anticipate rock mass behavior surrounding mine entries prior to actual mining. More specifically, this tool estimates to what degree and extent the immediate roof and floor strata and the coal pillar ribs surrounding an opening will weaken or fail for a given set of mining parameters. The technical approach couples together two numerical techniques: the boundary-element method and the finite-element method to allow for an approximate three-dimensional simulation of actual mining situations. Outputs from plan-view, linear-elastic, boundary-element models executed at different mining stages are used as input to a detailed, section-view, finite-element model to estimate the degree and extent of failure expected to occur around the periphery of an entry system. Using a pseudo-elastic approach. elastic rock mass properties are continually updated as different zones are predicted to fail. The procedure is relatively easy to use and is being set up to work interactively with the user who will not be expected to be a computer expert. Inputs include easily understood parameters obtainable from the field and rock mechanics laboratories. Examples of computer-generated output from generic sample models representing typical mining situations are presented and results discussed.

Jan 1, 1994

By Sandin E. Phillipson

The Mine Safety and Health Administration?s Roof Control Division responded to a massive ground failure at an underground marble mine in northern Georgia. The ground failure occurred in a benched area that had been abandoned in the early 1990s. It involved the failure of an estimated 19 pillars, in conjunction with a massive roof fall of an undetermined extent that was at least 60 ft high. Pillars in the benched area had been mined nominally 40 x 40 feet to a height of 50 feet ft, with 40-ft mining widths, although it seems likely from measurements and accounts from mining personnel that pillars were even smaller than intended. Average overburden depth was 500 ft, and the rock mass was characterized by three sets of intersecting geological discontinuities that not only defined very blocky conditions that were conducive to pillar spalling and volume loss, but they were also adversely oriented in such a way as to cut diagonally through pillars at a high angle. The recently released S-Pillar software from NIOSH was used to determine pillar safety factors in the failure area and indicated that pillars were undersized for the conditions. S-Pillar was used to assess pillar stability in active areas to evaluate the likelihood of experiencing similar collapses in the future. S-Pillar correctly identified the pillars in the bench area as having been at risk for instability, in light of their ultimate failure. A two-dimensional finite element model was used to evaluate the possible stages of failure and to assess the likelihood of continued failure in the benched area that might affect more distal mine openings. Although stone mines are generally characterized as having more forgiving conditions than those found in softer sedimentary rocks, the failure shares some characteristics with domino-style massive pillar collapses experienced in coal and trona mines. First, the minimum dimension of the benched area approached 350 ft; second, the pillars defined by benching had small width-to-height ratios (0.8), and; third, the pillar failure area was slightly greater than 4 acres. The massive pillar collapse and associated roof fall illustrate the importance of incorporating pillars that have been properly sized for depth and for the final bench height. Furthermore, the designed dimensions must be adhered to during the actual mining process. Finally, the importance of understanding the geological conditions and their effect on the rock mass is critical.

Jan 1, 2012

By J. R. Koehler

Although two-entry yield pillar-based gate roads supported by wooden cribs have been commonly used throughout longwalling in the Wasatch PlateadRoan Cliffs coalfield of central Utah, a three-entry yield-abutment gate road configuration was recently trialed in the Hiawatha Seam at the Genwal Resources (GRI) Crandall Canyon No. 1 Mine, near Huntington, UT. Pillar, entry, and cable bolt performance were monitored through second panel mining using a fairly extensive array of geomechanical instruments installed over a span of four crosscuts. Ground pressure and entry closure measurements confirmed that the 9.1-m-wide (30-ft) yield pillar was partially shielded from first panel longwall loads by the 36.6-m-wide (120-ft) abutment pillar, and consequently, experienced only minor yielding until the approach of the second panel face. Complete yielding of the 9. I-m-wide (30-ft) pillar occurred when the second panel was approximately 6.1 m (20 ft) inby the instrumentation site. Average cable bolt loads and differential roof sag remained low through second panel mining and tailgate entry ground conditions were excellent; however, very high ground pressures in the abutment and yield pillars, and second panel rib strongly suggest a high potential for coal bumps utilizing this gate road configuration at mining cover depths in excess of 396 to 457 m (1300 to 1500 ft). This conclusion is supported by the suspected occurrence of small coal bumps along the abutment pillar ribs, observed indirectly as fresh debris in the middle entry just behind the second face. This paper presents a case history developed from the geotechnical measurements and on-site observations of this unique application of a yield-abutment gate road configuration and cable support system in the Hiawatha Seam.

Jan 1, 1996

By Kelvin K. Wu

A coal waste disposal dam failed on Buffalo Creek near Saunders, West Virginia, on February 26, 1972. This accident resulted in the loss of 125 lives, left over 4000 people homeless, and resulted in millions of dollars in damage to several downstream communities. As a result of this tragic event, major changes occurred in the mine waste disposal practices used by the U.S. coal industry. This paper summarizes changes in U.S. coal-waste disposal practices in the nearly 35 years since the Buffalo Creek dam failure and identifies safety issues that need to be addressed for continued improvement. While many organizations and individuals have played roles in the improvements that have occurred, this paper focuses on the role played by MSHA and its predecessor agencies.

Jan 1, 2006

By Shosei Serata

The Stress Control Method improves productivity and safety in underground coal mining. The method stabilizes the roofs and floors of mine openings in both shallow and deep coal beds, regardless of whether or not there are ground stability problems. This paper describes the means by which a tapered pillar experiment is used to collect in situ data, which is then used as input for a computer model. The resulting computer model is then used to optimize Stress Control design for the mine under study. The behavior of any underground coal mine is not elastic, as is generally conceived in the conventional view of rock mechanics, but rather is highly time-dependent and site-specific. Unfortunately, conventional rock mechanics methods based on the elastic principle are not able to capture the highly non-elastic nature of ground behavior which actually occurs. To capture actual behavior, a new method of study is required. In this regard, geomechanical study of an underground coal mine may be compared to studying the behavior of a living fish. Its true behavior zannot be understood by examining it "dead in the laboratory. It Is the "live" nature of the coal mine that is required for design optimization of the Stress Control Method in the given mine. The Stress Control Method is based on a time-dependent theory of the global behavior of the mine ground, which generally contradicts the conventional elastic theory of ground behavior. Therefore, site-specific adaptation of the Stress Control Method required a comprehensive understanding of the global behavior of the mine as a function of time and site-specific ground conditions.

Jan 1, 1986

By Anton Sroka, Antoni Tajdus, Axel Preusse, Krzysztof Tajdus

"In Europe, the magnitude and range of mining deformation predicted on the surface have been, in most cases, determined using methods based on Gauss' influence function (e.g., Knothe's theory, Ruhrkohle method, Stochastic method). The increase in the application of numerical methods (finite element method FEM, finite difference method FDM, etc.) provides an opportunity to offer a different approach in describing mining deformations. However, this phenomenon is very complex, and due to numerical limitations, a two dimensional analysis was made (in plane strain) in most cases. Such 2D models could not accurately describe the mining geometry and geological conditions. The authors of this paper carried out the calculations in 3D models which describe a mining situation and the character of the strata in one Upper Silesian Polish mine. Furthermore, the authors include some tips for three-dimensional modeling.INTRODUCTIONThrough the years, many numerical models have been used to describe a phenomenon of underground mining exploitation influence on the ground surface. However, such rock masses are highly disturbed (cracks, fractures, changes in water conditions, etc.), and it is very difficult to suitably describe, in a mathematical manner, such materials. Therefore, many of the numerical models created have been corrected in various degrees.At first, models widely used to describe the behavior of strata in the region of exploitation appeared as elastic models, where scientests assumed that a whole strata behaved in a linearly elastic manner, according to Hook's law. Those models have been modifed to received suitable VALUES (of settlement and range of subsidence troughs. Scientests created this amongst others: elastic models with contact between the rocks layers (Shippam, 1975; Salamon, Chugh and Yang, 1993), elastic models with no tension (Chrzanowska-Szostak, 1988), and elastic models with a contact on the subsidence limit plane (Tajdus K., Tajdus A., 2005). However, in most cases, those models did not bring the expected results and the differences between shapes of measured and the calculated subsidence trough were substantial."

Jan 1, 2010

By L. J. Terrill

Lateral displacement in the immediate roof beam at the Waste Isolation Pilot Plant (WIPP) is a significant factor in assessment of excavation performance for the design of ground control systems. Information on roof beam lateral displacement, expansion, fracture formation, as well as excavation convergence, is gathered using a variety of manually and remotely read instruments. Visual observations are also used when possible. This paper describes the methods used to measure lateral displacement, or offset, at the WIPP. Offset magnitudes are determined by the degree of occlusion in drillholes that intersect the offset plane. The Borehole Lateral Displacement Sensor (BLDS) was developed for installation at WIPP to monitor offset at a high degree of accuracy at a short reading frequency. Offset measurements have historically been obtained by visual estimation of borehole occlusion. Use of the BLDS will enable relationships between time dependent roof beam lateral displacement and expansion to be established in much shorter periods than is possible using visual observations. The instrument will also allow remote monitoring of roof beam displacement in areas where visual estimations are not possible. Continued monitoring of roof beam displacement, convergence, and expansion, is integral to timely and pertinent assessments of WIPP excavation performance.

Jan 1, 1996

By Alexander Garcia

Roof and rib falls are the basic ground control hazards associated with underground roadways during development, stand up and, if applicable, retreat. Falls of ground can happen following the deterioration of supports or rock conditions over time, and particularly as a consequence of continuing rock deformation and/ or failure to install adequate support. Once developed, the risk of a failure is increased due to the effects of time as well as to front abutment stresses through retreat mining. The measurement of strata displacement using monitoring equipment is a form of ground control risk assessment. These monitoring systems are active, or ?live?, in a sense that risk is assessed real-time. However, there are circumstances in which falls of ground can occur without the prior recording of excessive movement. In addition, monitoring equipment is typically placed at set intervals, and strata conditions could vary between these points. Consequently, a visual assessment of other factors contributing to the risk of a fall should be made in order to complete a ground control risk assessment. Such surveys are usually one-off, thus capturing roadway conditions at one particular point in time. Ongoing deterioration is not documented through such one-time surveys, and there is a requirement for real-time or live assessment where a system is in place so that observation data can be updated on an ongoing basis, and a useful summary of prevailing roadway states produced on demand. To address the shortfalls of one-time assessments, a ?live? computerbased quantitative ground control risk assessment process has been developed. It combines visual observations processed in a quantitative manner with existing monitoring data into an interpretable output which indicates zones of roadway where there is an increased risk of a fall of ground from the roof or sides, so that remedial action can be carried out to mitigate that risk. Through improved procedures, it is now possible to generate a ground control risk assessment for each roadway, and one which can be updated frequently. This paper aims to outline and describe the assessment process.

Jan 1, 2012

By Shuangsuo Yang

Based on field observations and physical modeling of simulated materials, the dynamic equilibrium principle on the whole interaction process between the surrounding rocks and support of large deformation roadways in coal mines has been developed. It explains the methods of forming the bolted strata and its changing load capacity with deformation. It also points out the factors and conditions for forming the bolted strata as follows: (1) many entries in coal mines are subject to large deformation. During their service life, it goes through the following process, elastic > plastic > fiacture > broken > loosening, etc. During this dynamic process, the mechanisms of supporting structure are changing and therefore the interaction between support and rocks experiences a process of dynamic equilibrium. Furthermore, the required supporting force for stabilizing the surrounding rocks shows overall decreasing trend; (2) the bolted strata is a special supporting structure consisting of bolt, rock skin protection devices and rock strata within the bolted horizon. As deformation increases, the supporting structure of the broken strata within the bolted horizon experiences a process of periodic change, from equilibrium > not equilibrium > equilibrium. Corresponding to this change, the supporting capacity of the bolted strata also fluctuates and gradually decreases; (3) under the bolted strata, the stability of a large deformation roadway is dynamic and step-wise; and (4) the formation of bolted strata, especially bolted broken strata depends on the existence of compressive force. Supporting the bolted strata is not constrained by the quality of the surrounding rocks. It has broad range of application.

Jan 1, 2005

By Kevin Beauchamp

In many cases traditional support designs cover the many variations in ground conditions and bolt performance by a conservative factor of safety. The result is that most bolts are ineffectual most of the time and yet the response to occasional roof collapses is an even more conservative design. The probabilistic analysis presented in this paper takes several important parameters of a support design into account such as span, bolt strength, bolt length, water pressure, seismic accelerations, joint orientation, bed thickness and joint strength and allows the effect of variations in these parameters to be evaluated simultaneously. The analysis demonstrates the application of the probabilistic approach to both blocky, wedge-dominated conditions and bedded deposits dominated by laminations. All mine excavations have a designed stand-up time. By taking into account of the possible variations in the design parameters explicitly, it is possible to produce a support system designed to ensure stability over a given period of time. Rather than use a factor of safety criterion, the approach uses a percentage reliability or probability of failure. By understanding the probability of failure of the support system, it is possible to improve the performance of ground support without any increase in cost or conversely to decrease the cost while maintaining the performance of ground support. This approach reduces reliance on empirical experience and leads to a better understanding of the key factors that influence stability and can provide a much more accurate and optimized assessment of support design and performance. The result is a more cost-effective support system and we hope that a broader application of this approach to ground support in underground mines will lead to a greater acceptance in the industry of probabilistic analyses and of terms such as Probability of Failure and Reliability of Support.

Jan 1, 2003

By David I. Hoyer

It is shown that by monitoring longwall leg pressures in real time, warning can be given for significant weighting events and the formation of roof instabilities, such as roof cavities, several hours in advance. Longwall Visual Analysis (LVA) is a software package that continuously monitors shield pressures and shearer position in longwall mines. LVA has been running on 19 Australian longwalls for up to four years, and as a result a very substantial database of shield pressure trends in a wide range of longwall situations has been collected. This database has been analyzed to develop indicators that will give operators and geotechnical engineers advance warnings of developing conditions such as weighting events and difficult roof conditions. LVA displays live charts of data, such as shield leg pressures, loading rates, and yield frequencies. Data analysis techniques were applied to historical data records from multiple longwall sites in order to develop a ?Cavity Risk Index? (CRI). The CRI indicates the risk of roof cavities developing, and it is based on pressure trends that indicate significant yielding and loading rates spanning a region of relatively low support. Case studies from different longwalls are given, showing how the CRI can give real-time advance warning of the formation of roof cavities with their anticipated location on the face. The limited number of case studies done so far indicate that the predictions have a high degree of reliability, but more work is required to quantify this.

Jan 1, 2011

By T. J. McMahon

This Bureau of Mines study describes the development of a large-scale, three-dimensional, finite-element model of a deep-vein Coeur d?Alene District mine. The three-dimensional model was prepared from combined digitized mine maps and generated levels that may also be analyzed as independent two-dimensional models. A comparison of the stress changes and displacements was made following a simulated vein excavation in both the three-dimensional and two-dimensional models. A one-cut excavation was simulated with the two-dimensional model and a multiple-cut excavation was simulated with the three-dimensional model. The compared results from the two analyses are discussed in terms of the inherent differences between the models.

Jan 1, 1989

By M. Zaki Rashad

In this paper, if three slant distances are measured from three given points of known coordinates to an unknown point, the position of this point (X, Y, and Z coordinates) can be determined. A computer program was designed for observing the movement of a point in the roof in Abu-Tartour mine (western desert, Egypt) to measure the convergence. This method, for general using, is very fast and can be applied without any restrictions.

Jan 1, 1990