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By Mostafa Sharifzadeh, Ebrahim Ghasemi, Kourosh Shahriar

"The Tabas Central Mine (TCM) is one of the underground coal mines located in the Tabas coal region, in the mid-eastern part of Iran. This mine is the first mechanized coal mine in Iran that uses the room and pillar method. Pillar design is one of the most important issues in underground coal mines, especially in room and pillar mining. In this paper, a new method for coal pillar design in the main panel of TCM is presented. This method is able to estimate the magnitude of the various loads (both development and abutment loads) that pillars might experience throughout the mining process. Also, the method reduces the pillar failure risk. Based on this method, proper pillar sizes in TCM are obtained (11.6 x 11.6 m (38.l x 38.1 ft)).INTRODUCTIONPillar design and stability are two of the most complicated and extensive mining problems related to rock mechanics and ground control subjects. Although these problems have been investigated for a long time, to date only a limited understanding of the subject has been gained. Prior to this, the dimensions of a pillar were largely determined by experience based on trial and error, intuition, or established rules of thumb; any research available tended to be isolated and sporadic. But nowadays, various pillar design formulas have been developed based upon laboratory testing, fullscale pillar testing, and back-analysis of failed and successful case histqries. In 1980, a number of ambitious field studies conducted by the U.S. Bureau of Mines developed the ""classic"" pillar design methodology. It consisted of three steps (Mark, 1999, 2006):1. Estimating the pillar load using tributary area theory2. Estimating the pillar strength using a pillar strength formula3. Calculating the pillar safety factorAlso, Bieniawski (1981) presented a step-by-step method to determine coal pillar dimensions in room and pillar mines. In this method, similar to the classic method, pillar load is estimated by using tributary area theory.Currently, in mqst of the room and pillar mines, remnant pillars in panels are recovered by retreat mining (pillar recovery). Hence, the above mentioned methods are not appropriate for pillar design, because in these methods pillar load is estimated by the tributary area theory, and the effects of abutment loads, which result from retreat mining and the creation of a mined out gob, are ignored. Abutment loads affect the pillars in the adjacent of pillar line and a load greater than what is estimated by tributary area theory is applied on the pillar. So, pillar design without considering the abutment loads leads to pillar failures during retreat mining. Pillar failures continue to be one of the greatest single hazards faced by underground coal miners. Pillar failures are responsible for unsatisfactory conditions, which include the following (Mark et al., 2003):"

Jan 1, 2010

By Guy Reed, Russell Frith

"Current coal pillar design is the epitome of suspension design. A defined weight of potentially unstable overburden material is estimated, and the dimensions of the pillars left behind are based on holding up that material to a prescribed or user-defined Factor of Safety. In principle, this is seemingly no different to early roadway roof support design. However, for the most part, roadway roof stabilisation has progressed to reinforcement, whereby the roof strata is assisted in supporting itself. This is now the mainstay of efficient and effective underground coal production. Suspension and reinforcement are fundamentally different in their roadway roof stabilisation approach and, importantly, lead to substantially different requirements in terms of roof support hardware characteristics and their application. In suspension design, the primary focus is the total load-bearing capacity of the installed support to ensure that it is securely anchored outside of the potentially unstable roof mass. In contrast, reinforcement recognises that roof de-stabilisation is a gradational process with an ever-increasing roof displacement magnitude leading to ever-reducing stability. In a reinforcing situation, key roof support characteristics relate such design issues as system stiffness, the location and pattern of support elements within the roadway, and mobilising a defined thickness of the immediate roof to create (or build) some form of stabilising strata beam. The objective is to ensure that horizontal stress acts across the roof of the roadway and is maintained at a level that prevents mass roof collapse. This paper presents a prototype coal pillar and overburden system representation where reinforcement, rather than suspension, of the overburden is the stabilising mechanism via the action of in situ horizontal stresses within the overburden, the suspension problem potentially being an exception rather than the rule, as is also the case in roadway roof stability. Established principles relating to roadway roof reinforcement can potentially be applied to coal pillar design under this representation. The merit of this assertion is evaluated according to documented failed pillar cases in a range of mining applications and industries found in a series of published databases. Based on the various findings, a series of coal pillar system design considerations and suggestions for bord and pillar type mine workings are provided. This potentially allows a more flexible and informed approach to coal pillar sizing within workable mining layouts, as compared to common industry practices of a single design Factor of Safety (FoS) under defined overburden dead-loading to the exclusion of other potentially relevant overburden stabilising influences."

Jan 1, 2017

By J. Nielen van der Merwe

This investigation was done to develop a method to predict the lie of coal pillars. It has long since been known that coal pillars deteriorate over time, but there was no method to quantify the deterioration. It was found that the rate of pillar deterioration was essentially a function of two parameters, namely mining height and time. The higher the mining height, the more rapidly the pillars deteriorated. The rate of deterioration is not constant, but decreases exponentially with time. The pillar life should be viewed in conjunction with the safety factor. While the relationship between safety factor and pillar life is ambiguous, the trend is nonetheless for higher safety factor pillars to have longer lives. The safety factor can be used to quantify a failure probability. The pillar life prediction indicates when the pillars which are predicted to fail, can be expected to do so.

Jan 1, 1998

By David Hill

The Australian underground coal mining industry is increasingly operating in an environment that challenges traditional concepts of coal pillar design, against a background of heightened expectations and demands from other stakeholders with regard to the protection of both natural surface features and burgeoning civil infrastructure. The result is greater possibility of conflict between mine operators, developers and regulatory bodies, with potential for unnecessary sterilisation of Australia?s coal resources and/or escalating surface development / infrastructure protection costs. On the positive side some significant advances have occurred in the general level of understanding of pillar behaviour and stability, both in Australia and overseas. This paper examines some current issues in coal pillar design, focussing particularly on the application and limitations of analytical models of pillar loading. Established methodologies are reviewed and alternative approaches explored, including examples of key geometrical, geological and probabilistic concepts. Practical experiences from the Southern Coalfield of New South Wales (NSW) are examined for the purpose of highlighting critical variables. Finally, some suggestions are made with regard to the direction and opportunities for future research, with particular regard to coal pillar loading, in the interests of all stakeholders.

Jan 1, 2008

By Kazem Oraee

In underground coal mining, particularly room-and-pillar methods, the coal pillars play a significant role in roof stability. If the pillar dimensions are increased, the pillar bearing capacity also increases, but more coal remains in the pillar and therefore the recovery of mining operation decreases. Therefore, determining the optimum pillar dimension based on technical, economical and performance parameters is important. In this paper, the coal pillar is designed by using the concept of ground reaction curve (GRC). For this purpose, the GRC for coal pillars is drawn and then the elastic and plastic zone of coal pillar behavior is determined. Based on elastic and plastic zone, different equations are presented to draw a pillar reaction curve and the process of coal pillar design based on GRC is explained. As a case study, this new technique is applied to study the coal pillar state in Tabas coal mine of Iran. The results show that the presented new approach is successfully used in the design of the optimum coal pillar dimensions, and also determines the elastic and plastic behavior limit, which is important especially for the logical design of yield pillars.

Jan 1, 2009

By Morgan M. Sears, Mark Van Dyke, Gamal Rashed, John Rusnak, Khaled Mohamed

"In 2016, room-and-pillar mining provided nearly 40% of underground coal production in the United States. Over the past decade, rib falls have resulted in 12 fatalities, representing 28% of the ground-fall fatalities in U.S. underground coal mines. Nine of these 12 fatalities (75%) have occurred in room-and-pillar mines. The objective of this research is to study the geomechanics of bench room-and-pillar mining and the associated response of high pillar ribs at overburden depths greater than 1,000 ft. This paper provides a definition of the bench technique, the pillar response due to loading, observational data for a case history, a calibrated numerical model of the observed rib response, and application of this calibrated model to a second site. INTRODUCTION Bench mining is a an underground mining technique typically applied to room-and-pillar mines where full seam extraction on development presents an unacceptably high risk of injury from high pillar ribs or where the mining equipment is not designed to extract the full seam thickness. To mitigate the increased risk associated with high ribs and slender pillars, a more modest thickness is extracted from the top of the seam on development. This is followed by grading the floor and recovering the bottom of the seam with or without extraction of the pillars during retreat mining. A mine located in Eastern Kentucky extracts two seams at depths ranging from outcrop to 2,000 ft. In some areas of the mine, Seam A and Seam B are close enough together to be mined simultaneously. Seam A (top) is mined on development 7 to 9 ft. high for the entire length of the panel. On retreat, as each pillar is extracted, the continuous miner is ramped down into the floor (Seam B), two pairs of Mobile Roof Support (MRS) units are set, and the pillars are extracted at the full mining height of 14+ ft. During the pillar recovery process, the floor is extracted in each entry, from a ramp initiated outby the retreat line, sequentially just prior to extracting the lifts from the pillars (see Figure 1)."

Jan 1, 2017

By John A. Rusnak

"This paper discusses the variation of coal strength based on the megascopic coal lithotypes for Central Appalachian high-volatile A coal beds. The composition of coal beds is complex and variable, depending on the depositional environment associated with original plant material, inflow of clastic material, and water level fluctuations in the original swamp/mire environment. Thus, different types of coal and sediment are formed within each coal bed. These differences in coal composition were first classified by Marie Stopes, a paleobotanist, in 1919. The classic coal megascopic lithotypes are vitrain, clarain, and durain, which correspond to bright, bright banded, and dull coal, respectively. Stopes also identified that the lithotype fusain, which is mineral charcoal, has no inherent strength and can act as a plane of discontinuity. In this study, two other coal-bed lithologies are also considered—bone and carbonaceous shale. This makes for a comprehensive suite of coal-bed stratigraphic components apart from rock partings. A total of 1,000 uniaxial compressive strength (UCS) and 440 indirect tensile strength (ITS) tests were conducted on cores from southern West Virginia that were specifically logged and described using the megascopic coal lithotype nomenclature. Statistical analysis is presented showing the results for each lithotype group with mechanical properties correlated to the lithotype. Previous studies have analyzed the mechanical breakage properties associated with coal lithotypes, which correlate well with these results. However, coal rank does appear to be a contributing factor, and this study is confined to only high-volatile A bituminous rank. Application of these results would be well suited to a rock mass classification system to address coal pillar rib stability. This would allow for rib support design and implementation to consider relative coal strength by visual observation of the seam stratigraphy through ongoing observations within a mine. Changes in seam composition can be readily identified, allowing the adjustment in rib support design. Another application would be for the determination of numerical modeling inputs based on detailed seam stratigraphy. However, these results, even with the standard strength reduction criteria, may not be applicable to currently accepted empirical coal pillar design procedures."

Jan 1, 2017

By Kristineq Pankow

The August 2007 Crandall Canyon mine disaster raised national awareness of mining-induced seismicity (MIS) in Utah as well as general interest in how seismic monitoring might improve mine safety in the region. Unlike the situation in most other mining areas in the U.S., local seismographs in Utah?s Wasatch Plateau (WP) and Book Cliffs (BC) coal fields are an integral part of a modern real-time earthquake information system developed by the University of Utah Seismograph Stations (UUSS) as part of an Advanced National Seismic System. The UUSS earthquake catalog contains a continuous record of MIS at all active mine sites in the WP-BC region since 1978 (more than 18,000 seismic events = M 4.2). We describe characteristics of MIS and current seismic monitoring capabilities in the WP-BC region. We then demonstrate, using MIS from an example Utah coal mine, the ability to refine event locations with estimated absolute errors of ~200 m or less using a combination of (1) a double-difference relocation methodology and (2) ground truth information provided by mine operators. This approach enables sufficient spatial resolution to correlate MIS with mining activities, providing a useful tool to help improve mine safety.

Jan 1, 2008

By Amirhossein Molavi Tabrizi

In this paper we introduce a realistic model for mine openings that explicitly considers the effects of local irregular topography. Also, we consider the effect of entry orientation and rock anisotropy on the induced stress fields around mine openings under the given in-situ stress field. A triangular mesh formulation is derived for representing complicated irregular surface topography and underground openings. Each element contains three internal collocation nodes. Parts of the surface which are far from the mine openings are discretized by infinite elements. The rectangular infinite elements with three internal nodes are introduced specifically for this problem so they are compatible with the triangular elements. With the corresponding boundary element method (BEM) formulation, we then investigate the combined effect of the topography and entry orientation on the stress fields induced by openings in anisotropic rocks under in-situ stresses. A single rectangular opening in the anisotropic ground with topography and in-situ stresses is simulated using data from the Carroll Hollow mine in Ohio. The results of these simulations show that topography, rock anisotropy, orientation of the regional stress field and mine opening geometry all have appreciable effects on the stress fields around underground openings, yet these factors can all be accounted for in an efficient code with no need to discretize the model domain. Future applications using this new BEM formulation will provide useful guidance on selecting the optimal opening orientation in the mine in order to minimize undesirable stress concentrations around underground mine workings.

Jan 1, 2014

By Matthew J. DeMarco

Research personnel at the U.S. Bureau of Mines have conducted longwall gate stability studies at four western U.S. mines attempting to employ yield pillars for improved ground conditions. Located in the Book Cliffs and Wasatch Plateau coalfields of north-central Utah, these operations are generally characterized by multiple-seam mining, cover depths averaging 450 - 600 m (1,500 - 2,000 fl), occasionally extending beyond 760 m (2,500 ft), abrupt cover depth variation due to the overlying canyon/mesa topography, and massive, rigid sandstone roof units. Such conditions encourage severe gate and panel coal bumping, as well as various types of roof instabilities and occasional floor-heave problems. To alleviate these adverse conditions, several mines have employed yield pillars to-reduce hazard-inducing excessive gateroad stress concentrations. This paper describes the evolution of gateroad designs at four of these operations, the specific mining conditions involved, and the general stability performance attained by using yielding gate systems. Mine experiences are "compared" in terms of basic setting conditions, and the general concepts of yielding system applicability and success potential are summarized.

Jan 1, 1993

By J. R. Koehler

The failure of yield pillar-based gate mad designs to provide adequate ground control performance is primarily related to the use of "critically" sized chain pillars. A "critical" pillar is one that falls into a range of pillar sizes that are too large to either yield nonviolently or yield before the roof and floor sustain permanent damage, but are too small to support full longwall abutment loads. To directly compare the in-mine performance of critical and yielding pillar designs, the U.S. Bureau of Mines recently completed a field study in a tapering gate road at the Sunnyside No. 1 Mine, Sunnyside, UT. Extreme pillar stresses and associated coal bumps characterize the response to first panel mining of a 16.8-m-wide critical design. Significantly lower pillar stresses, early yielding of the pillar and adjacent panel rib, and an absence of coal bumps suggest that a narrower 12.2-m-wide design more closely approaches proper yield pillar dimensions. Probehole drilling of several 10.6-m-wide pillars revealed low stress levels and substantial pillar and panel rib yielding prior to abutment onset. suggesting a properly functioning yield pillar design.

Jan 1, 1995

By Stephen P. Signer

To improve the understanding of the support interaction mechanics between grouted bolts and coal mine roofs and to help lay the foundations for improved design and evaluation techniques, the 0.8. Bureau of Mines has conducted laboratory, field, and analytical studies of the load transfer mechanics of grouted roof bolts. Mechanisms by which load is transferred from a bolt through the grout to the rock mass are analyzed. Strain gauges were installed on over 70 bolts and tested to observe the rate of load transfer when a force was applied at the bolt head. Laboratory and field tests were conducted to determine bolt-grout- rock interaction behavior in both the elastic and postyield phases. Long-term laboratory tests were run to determine the time-dependent properties of both polyester resin- and-gypsum-grouted bolts. Numerical studies using finite- element techniques were compared to the experimental results. Elastic tests showed that 90 pct of the applied load was transferred within 24 in of bolt length. Long-term tests indicated that creep is more significant in gypsum-grouted bolts than in resin- grouted bolts. Plastic studies showed that yielding of steel will translate down the length of the bolt from 6 to 20 in.

Jan 1, 1988

By Khamis Y. Haramy

This paper summarizes ground control studies of longwall panel entry systems in two Western U.S. coal mines. Presented are comparisons of in situ pressure change measurements and assessments of chain pillar and entry behavior under a wide range of cover. Results indicate that no one entry system design is universally applicable, and that site-specific factors need to be considered for panel entry design. Relationships between overburden depth, face advance, and magnitude and location of the forward abutment are discussed for western operations. In addition, analysis indicates that use of yield pillars may reduce or eliminate some stress-related problems that plague longwall panel entry design.

Jan 1, 1989

By Andre Zingano

The objective of this paper is to compare the behaviors of different types of roof bolts: (1) One-Step Bolt (OSB), (2) Fully grouted Bolt (RB), (3) Combination Bolt (CB), and (4) Torque tension Bolt (TB). Two dimensional numerical models were built for both bolted and unbolted roofs. The geological sequence and rock properties used in the numerical models represent the typical roof condition for Pittsburgh coal seam. Using the unbolted roof as a base case, a comparison is conducted by monitoring the roof vertical displacement at the center of the entry and at the bolt positions, the axial force in the roof bolts, and stress distribution in the bolted area. The grout/rock interface is assumed to be perfect. The estimated roof displacements showed that the differences among the four types of roof bolts are small. The major differences are in the shear stress at the grout/rock contact and in the shear stress along the immediate roof bedding interface as well as in the bolt axial stress. There is less axial stress for the OSB compared to RB and CB as the diameter of the OSB is much bigger and the contact area between grout and rock is twice as large as for RB and CB. The higher strength of the OSB contributes to keep the bedding planes in the roof closed.

Jan 1, 2007

By Lorraine Kent

Comparison of in-situ stress overcore measurement results with those determined from laboratory evaluation of Acoustic Emission (AE) testing on oriented sub-core samples has been carried out for a variety of mining environments. These include UK and German Coal mines at moderate depth, shallow-level South African Coal mines and deep-level South African gold mines. Results show that the `Kaiser Effect' or 'Stress Memory-Damage is readily determinable throughout the brittle deformation process, although particular care is required in interpretation of results during the 'bedding-in' phase of testing and the region associated with unstable crack growth prior to failure. The results suggest that AE provides a useful complimentary method for comparison with existing methods of stress determination. The success of the method can, however, be dependent on both rock type and the likely magnitude of in-situ stress in comparison to the strength of the rock. Keywords: in-situ stress, acoustic emission, Kaiser Effect

Jan 1, 2002

By Jessica M. Wempen, William G. Pariseau, Michael K. McCarter

"Quantitative analysis of mine-wide subsidence at the kilometer scale and details of stress distribution about an advancing longwall face are estimated using an adaptation of the finite element method. The method is well suited to the tasks at hand. For greater realism, variability of strata properties is taken into account as are the effects of joints and cleats on elastic moduli and strengths. Evolution of pillar stress and entry closure remote from the face is readily quantified in a series of analyses that simulate face advance. Computed results compare favorably with the evolution of closure measurements about an instrumented pillar in a two-entry headgate. The appropriateness of the finite element method is confirmed. This method is based on first principles that avoid empirical schemes of uncertain applicability and numerical models “calibrated” by fitting computer output to mine measurements.INTRODUCTIONMine-induced seismicity is intimately related to strata mechanics associated with longwall coal mining and room and pillar mining, as well. Strata deformed beyond an elastic limit often tend to fail rapidly by brittle fracture and, thus, to emit acoustic signals in the form of elastic waves. Understanding the induced seismicity in coal mining offers the potential for early warning of hazardous conditions. Many years of experience with seismic phenomena associated with hardrock mining suggest considerable complexity should be expected. However, recent coal mine studies (Pariseau, 2014; Pariseau, 2015; Pariseau and McCarter, 2015; Pariseau and McCarter, 2016) have shown high correlations of seismicity with element failures in finite element simulations. The main lesson learned from these studies is one elaborated by Iannacchione et al (2005); deviation from normal activity is an early warning of ground control difficulty. For example, an abrupt increase in seismic event rate, or equivalently, an increase in element failure in finite element simulation of panel advance, is a cautionary indication for ground control. Present and past study results demonstrate the effectiveness of finite element simulations for mine design and early detection of potential ground control issues."

Jan 1, 2018

By Vincent A. Scovazzo

Many accepted and useful methods have been developed and used for pillar design. Each method has its own particular strengths and weaknesses. Three methods addressed in this paper are; empirical, analytical, and numerical. Each of these methods have their place in pillar design. Analytical methods result in close approximation of the ideal pillar (most economical, stable, or yielding) and are suitable for use in final mine design and in analyzing existing problems. BOYD uses the analytical method to develop site specific mine pillars design equations. An analytical method, one of many developed by BOYD, is presented here and is based on the procedure used by Wilson (1) and others in development of their empirical equations.

Jan 1, 1995

By Jessica M. Wempen, Michael K. McCarter

"Differential Interferometric Synthetic Aperture Radar (DlnSAR), a satellite-based remote sensing technique, has potential application for measuring mine subsidence on a regional scale with high spatial and temporal resolutions. However, the characteristics of Synthetic Aperture Radar (SAR) data and the effectiveness of DlnSAR for subsidence monitoring depend on the radar band (wavelength). This study evaluates the effectiveness of DinSAR for monitoring subsidence due to longwall mining in central Utah using L-band (24 cm wavelength) SAR data from the Advanced Land Observing Satellite (ALOS) and X-band (3 cm wavelength) SAR data from the TerraSAR-X mission.In the Wasatch Plateau region of central Utah, which is characterized by steep terrain and variable ground cover conditions, areas affected by longwall mine subsidence are identifiable using both L-band and X-band DlnSAR. Generally, using L-band data, subsidence magnitudes are measurable. Compared to X-band, L-band data are less affected by signal saturation due to large deformation gradients and by temporal decorrelation due to changes in the surface conditions over time. The L-band data tend to be stable over relatively long periods (months). Short wavelength X-band data are strongly affected by signal saturation and temporal decorrelation, but regions of subsidence are typically identifiable over short periods (days). Additionally, though subsidence magnitudes are difficult to precisely measure in the central Utah region using X-band data, they can often be reasonably estimated.INTRODUCTIONDifferential Interferometric Synthetic Aperture Radar (DlnSAR) is a satellite-based remote technique that can be used to measure surface displacement over large regions with high spatial resolution. Under good conditions, displacements can be measured with centimeter to subcentimeter accuracy (Buckley, 2000; Massonnet and Feig!, 1998). DlnSAR also has high temporal resolution, and imaging periods typically range from 10 to 50 days (Rosenqvist, Shimada, and Watanabe, 2004; Roth, 2004). In the last two decades, the application of DlnSAR for mine subsidence monitoring has been demonstrated in coal basins in Europe, Australia, China, and the United States (Camec and Delacourt, 2000; Ge, Chang, and Rizos, 2007; Ge et al., 2008; Ismaya and Donovan, 2012; Ng et al., 2010; Perski, 2000; Perski and Jura, 2003; Popiolek and Krawczyk, 2006; Wegmuller et al., 2005; Wright and Stow, 1999; Zhao et al., 2014; Xinglin et al., 2014). Overall, these studies have demonstrated good data resolution, strong relationships between mine development and subsidence, and reasonable agreement between displacements measured by DinSAR and displacements measured by conventional surveys."

Jan 1, 2016

By Klaus Opolony

The world's most popular method of longwall mining requires multiple entry systems for the panels. In contrast to this mine layout the roadways in German coal mining are used for advanced mining from the rock mechanic point of view or are even re-used by a second panel. This procedure of roadway use is presented within this paper using a 3D visualisation software tool. In the previous conferences in Morgantown several papas had addressed the basics of rock mechanic background, planning tools and variants. This paper gives a practical case study for reuse of a roadway in a German coal mine. The heading and the use of various alternatives are compared under the aspect of efficiency and costs. Within the comparison the specific requirements and benchmarks of German coal mines are taken into consideration. The costs for a multiple entry system and first of all the development rates that can be achieved with common road heading systems are compared with international layout alternatives. A prospect includes a discussion of pro and con for various development methods. Devices are given due to this prospect if and how multiple entry systems are applicable to German coal mines. The paper gives an initial point for international comparison and is a base for further discussion.

Jan 1, 2003

By Aarao de Andrade Lima

Mechanical properties typical of coal are used in the comparisons of pillar strengths based on finite elements and the empirical equations of Holland-Gaddy, Salamon-Munro, Obert¬Duvall, and Bieniawski-PSU. A correlation among the strength parameters which are employed in the empirical equations, in Mohr-Coulomb and Hoek-Brown failure criteria is established. Emphasis is given to the important distinction between the mechanical properties of small rock specimens and those related to the rock mass. An elastoplastic version of Hoek-Brown criteria has been developed and implemented in a finite elements code. The strengths calculated using the empirical equations showed a good agreement when the ratio width by height of the pillars varied from I to 8, except for Holland-Gaddy equation which exhibited lower values. Under the hypothesis of associative perfect elastoplasticity used, pillar strength calculated using Mohr¬Coulomb yield criterion became excessively high for all the models having a pillar width by height ratio above 2. The finite elements solution based on Hoek-Brown criterion predicted strengths around fifty percent larger than Bieniawski-PSU equation when the pillars width by height ration varied from 3 to 8, showing good agreement below that range. It has been concluded that, under the hypothesis of percfect plasticity, stress analysis techniques may overestimate the strength of rock structures subjected to high confining stresses.

Jan 1, 1997