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By Gabriel S. Esterhuizen

The design of support for underground excavations is a complex process in which the interaction between supports and the rock mass must be evaluated. The strength reduction method (SRM) is useful because it provides a stability factor of the supported excavation that can easily be compared between support alternatives. The method is based on numerical model analysis where the stability factor is determined by reducing the rock mass strength until collapse is indicated in the model. This paper presents the results of validation studies that were conducted using the FLAC3D stress analysis software to compare SRMcalculated stability factors to the empirically based Coal Mine Roof Rating (CMRR) and the Analysis of Roof Bolt Systems (ARBS). The objective was to determine whether the SRM, with its basis in mechanics, would predict similar outcomes as the fundamentally different ARBS and CMRR methods with their basis in empirical observations. A total of 450 different scenarios were evaluated in which the geology, horizontal stress, depth of cover, entry width, support spacing, and support length were varied. The results showed that the SRM-calculated stability factors were able to satisfactorily capture both the ?weak bed? and ?strong bed? adjustments in the CMRR. The SRM results were found to be well correlated to the ARBS stability factors for the 450 cases considered. Further analysis showed that the SRM accurately captures the effect of bolt length, depth of cover, and entry width on the overall stability of an entry.

Jan 1, 2013

By Nengxiong Xu

The WTZ coal mine is located adjacent to an auxiliary dam in P. R. China. The mining-induced ground movements are calculated using a 3-D numerical procedure based on the finite difference method (FDM) to judge whether the extraction of the coal seam will have a negative impact on the dam. First, the values of the rock mass mechanical parameters in the numerical model are estimated using the available literature that relates intact rock and discontinuity properties to rock mass parameters. Then, based on available surface subsidence monitoring data for an area in WTZ mine, the main mechanical parameters of coal and rock masses are calibrated by a back analysis procedure that combines an experimental design technique with numerical simulations. Then the reliability of these rock mass parameters is verified. Finally, according to the planned mining sequence, predictions of mining induced surface subsidence are computed in steps, and the boundary of the ground movement area of each step is determined. The nearest distance from the boundary of the surface movement area to the edge of the dam foundation was found to be about 1347 m. The maximum surface subsidence within the mining area turned out to be 2.7 m, and the maximum settlement point was found to be close to west-south corner of A2 mined area. These findings led to the conclusion that the coal seam mining would not cause dam damage.

Jan 1, 2013

By C. Srinivasan

Microseismic emissions are generated by deformation and cracking of rock around an opening inside a mine. The rock tends to achieve equilibrium in a new geometry under changing stress conditions was found to provide useful clues to the impending roof falls and ground instability. The typical characteristics of these microseismic event patterns is shown to be of diagnostic value in sensing in advance rook fall that invariably follow such events. In most of the longwall faces, the main problem faced was due to strata behavior in the presence of massive sandstone bed, which is generally difficult to cave. Microseismic monitoring system was used to monitor strata behavior during longwall mining operation at Rajendra underground coal mine of South Eastern Coal Fields limited (SECL). More than 44,000 microseismic events with local magnitude between -3.4 and 0.5 were recorded during the monitoring period from September, 2001 to March 2003. Analysis of these events was correlated with respect to roof falls. The time series of range of source parameters such as Radiated energy, seismic moment, Energy Index, Seismic Schmidt number, time of occurrence and location of fractures before and during roof fall exhibit qualitatively distinct patterns about six hours before roof falls. &ong the several seismic parameters investigated the microseismic event rate as precursor was found to be most significant indicator of an impending roof fall. The results are discussed as case study in this paper.

Jan 1, 2005

By Kevin W. Harris

Multiple-seam coal mining is a major issue in underground coal mining that adds additional complexity to the practice of ground control. As reserve exploitation is driven by economics, it is now difficult to mine coal without the existence of previous workings above and/or below the active seam; this is particularly true in the Appalachian coalfields. The frequency in which problematic multiple-seam interactions are now encountered has resulted in significant research regarding the underlying mechanisms of the problems and methods of mitigation. In the last few decades, a great deal has been learned about these interactions and the ability to minimize problems associated with these hazards has greatly advanced, resulting in better economics and improved safety. Minimizing the adverse effects of stress interactions often requires a thorough understanding of site-specific geotechnical parameters and previous mining geometry. This is especially evident in bump-prone ground, where pillar behavior is highly dependent on local conditions. This paper presents a case study in a deep cover, Central Appalachian coal mine where three bump events occurred. Initially, empirical design software was used in an effort to analyze the situation and prevent further instability. The empirical study proved ineffective. A detailed investigation of the bump events using the boundary element software LaModel 3.0 was then performed. This study resulted in a site-specific calibration standard that will be applied in numerical pillar design for the remaining reserve.

Jan 1, 2014

By Hanjie Chen

A mine panel collapse may occur when pillar sizes are too small or the surrounding rock strata (roof or floor) yields. After a small pillar fails, its loading is rapidly transferred to adjacent pillars that in turn fail. If the surrounding rock strata yield, the loading on pillars will redistribute. which may result in some pillars under high stress. This paper analyzes the causes of two cases of mine panels failures in two room and pillar mines. One case of massive pillar failure occurred in a phosphate mine and the other, mine panels failure, is in a coal mine. In the phosphate mine, both the roof and floor strata were a thick competent shale stratum. The finite element analysis shows that the major reason for the massive pillar failure is that the pillar sizes were too small in a panel. In addition, the high cliff topography has some influence on the failure. In the coal mine, the failed area was about 1,000 ft long by 760 ft wide (covering more than 3 panels) involving 390 pillars. The harrier pillars between the panels were punched on retreat into small chain pillars and the extraction ratio in this failed area was more than 80%. The roof remained intact, and pillars were crushed and punched into the floor. Based on the stress analysis, it is found that multiple panel collapse occurred because the barrier pillars were punched into small pillars and the loading on panel edges increased due to floor failure.

Jan 1, 1999

Virtually all mineable Appalachian coal seams exist in a multi-seam environment. This makes it inevitable that most seams will eventually experience interaction induced ground control and mining problems. Indeed, it has been estimated that every working face will experience interaction effects from previous or current workings at least once during its lifetime (1), and that these problems are considerably exaggerated when seams are in close proximity -- a distance of less than 110 feet. The continued increase in multi-seam problems has resulted in considerable research activities over many years (2,3,4,1). Theoretical analysis, numerical and physical model studies, statistical and empirical analysis of numerous interaction related field data have been applied to multi-seam mining situations and have identified many useful trends and design criteria (4,5,6,7). To fully utilize research results and transfer multi-seam mining technology to field engineers, a design model -- USEAM was constructed (8). This model, designed for close seam under-mining situations, was computerized to facilitate utilization. In the current research, a new computer program "MSEAM" was developed to produce a model for both under- and overmining close seam situations. It is hoped that both of these software packages will aid field engineers in using important interactive design criteria to gain a better understanding of interaction mechanisms. Through advance planning with these programs, detrimental interaction may be avoided and minimized, and occasionally a design can be selected which will allow interaction effects to be utilized to the benefit of mining operations.

Jan 1, 1987

By D. Reddish

The combination of free standing steel supports, such as arches, and rock bolts (mixed support) has Frequently been in used in UK coal mine roadways when it is considered that the strata and/or environmental conditions would not be suitable for rock bolts solely. However, how such mixed support systems operate is not fully understood. Due to the differences in the support method provided by rock bolts and free standing steel, the total support generated is not simply a case of adding the contribution to the support of the roadway given by the two systems. This paper describes a numerical investigation into mixed support systems when used in coal mine roadways. A series of 2D and 3D geomechanical models are described and the method of modelling the rock bolts and steel supports in coal mine tunnels is discussed. The numerical models described include rock boltd only roadways, steel supported roadways and mixed supported roadways in a variety of geological and in-situ stress conditions. Conclusions are formed that allow an insight into mechanisms of strata reinforcement provided by the support systems modelled. Further to this, a review of the numerical modelling of pre-tensioned rock bolted systems is described identifying the contribution to support efficiency given by the adoption of tensioning in full column resin anchors. The results obtained highlight that the effectiveness of the pre-tensioned load is dependant on the rock mass quality and in- situ stress level at the site where it is to be used.

Jan 1, 2004

By Shugang Li

The layout and efficiency of the degasification system is heavily dependent on the distribution of and the methane migrating mechanism in the mining induced fractures in the overburden strata In this paper, physical modeling and numerical simulation are employed to study the mining-induced fracture zones and the stress distribution in these zones. The physical models show that both the fracture and compaction zones form a parabolic shape in the over- burden strata along the panel transverse direction. When this is generalized to the panel longitudinal direction, the shape of the mining induced fracture zone over the longwall gob can be represented by a 3-D elliptic paraboloid function. Through the observation of bed separation, fracture density and distribution pattern in the physical models, it is believed that the development of the parabolic fracture zone can be divided into three distinguishable phases. The expansion characteristics and sizes of the fracture zones can be estimated. The numerical stimulation studies can be used to estimate the extent of the stress release zones. The stress release zones can be also divided into a high compressive stress - fracture closure zone, stress relieved - fracture expansion zone, and intact zone. The methane desorption model is then used to analyze the methane migrating pattern in the fracture zone. The developed model has been verified by the results of a longwall gob degasification tests at a coal mine in Yangquan, China with a fair agreement. Such studies show that the model can provide a reasonable accurate tool for designing the gob-well degasification system for longwall mining operations.

Jan 1, 2005

By Ernest A. Curth

An estimated 49 billion tons or 29 percent, of the coal reserve base to a depth of 1,000 feet in the eastern United States fall in the 28- to 42-inch range. Often left out as a consequence of selective mining, it is a paramarginal source that will become increasingly important. At present, all active thin seam longwalls are located in the Eastern Coal Province, and a number of operations have been suspended due to the erosion of the market for metallurgical coal. Extensive premining studies, appropriate mine planning, reliable equipment that is designed with ergonomics in mind, adequate roof support, intensive training, and strong face discipline are the ingredients that provided a measure of consistency in production for the last 10 to 16 years, particularly in the Pennsylvania bituminous coalfield where single drum shearers dominate. Plows, which were found to be very productive in suitable strata in Europe, are used in the Pocahontas field. Low seam four- and six-legged shields have been introduced recently. The future holds automation at progressive levels. The first step is batch control with the benefits of quickly applied roof support and reduction of workmen exposure to environmental hazards.

Jan 1, 1981

By Charles D. Albright

FMC built its first angle bolter in 1969. This was a single mast unit which could drill holes for conventional bolts or angle holes for installing roof trusses. From this drill we learned very quickie that the mast design was an important factor to the success or failure of any angle bolter. The first mast installed on this machine (EXHIBIT 1) was fixed in length with endless chain and hydraulic motor feed. It took less than a shift underground to determine that the fixed length was not going to work. The undulating top created conditions where the mast was too long to be positioned at a 450 angle. Several mast designs were tried and discarded before we felt we had the answer to our problems. (EXHIBIT 2} We developed a mast that would extend or retract without moving the position of the drill unit. This allowed the operator to "wedge" the mast between the floor and roof before starting his drill feed. This arrangement worked exceptionally well, but unfortunately the demand, as perceived by our Sales Department, for angle bolters did not materialize. This unit became an "orphan" and was used by many coal mines until it died a natural death. FMC did not decide to re-enter this market again until 1979. At this time many coal producers were contacted to determine what features should he incorporated into a dual mast angle bolter. From this information we were able to arrive at three main areas of concern that we should consider when designing a new machine. 1. Eliminate overturning moment on drill unit. 2. Provide some sort of steel support near roof line to aid in starting a 15° hole. 3. Dual mast units need a method of raising center of mast rotation to facilitate various mining heights and still maintain a 45° angle and proper distance from rib. I would now like to discuss each of these individually. EXHIBIT 3 indicates the overturning moment resulting from the feed cylinder thrust and the reaction of the drill hit against the roof. To eliminate this moment a mast was designed using two feed cylinders mounted in the plane of the drill center line, thus removing all overturning moments on the drill unit carriage. This mast has been used extensively in vertical drilling with no downtime attributed to wear on mast guides and drill unit supports. The cylinders are designed to provide uniform thrust and feed speed throughout the total stroke. For manufacturing and economic reasons, the final mast design on the first drill was not used for this new drill. A drill steel support mounted on the mast, and positioned by a hydraulic cylinder provides the needed guidance near the roof for starting a hole at a 45° angle. (EXHIBIT 4) This support does not surround the drill steel but simple cradles the drill steel for "collaring" the hole. Once the hole is started, the support can he lowered. The support plate is hinged to allow the drill mast to pass. The advantage of having vertical motion of the center of rotation on a dual mast drill is shown in EXHIBIT 5. Following the criteria recommended by Birmingham Bolt Company, the truss bolts should he at a 45° angle and one fifth of the width of the entry from the rib. Therefore, in an entry 20 ft. wide, the hole should be drilled 4 ft. from the rib and at the 45° angle previously mentioned. With the limitations inherent to dual boom drills, that is, the masts cannot pass each other nor can one mast pass the center line of the machine even if the other is positioned out of the way, it is impossible to accommodate much variation in seam height and maintain the recommended criteria. As shown in EXHIBIT 5, a center of rotation 17 inches above the floor will start a hole 4 ft. and 45°angle at a height of 67 inches. Any height above 67 inches

Jan 1, 1982

By Adrian L. Moodie

Austar Coal Mine (formerly Southlands and Ellalong Collieries) has had a long association with difficult strata control conditions associated with mining depth and a highly jointed/cleated coal seam. The conditions include poor longwall face conditions, cyclic loading, heavy tailgate (TG) roadway conditions, and difficulties in maintaining stable roadways on development at 5.2 m (17 ft), as well as the geotechnical challenges of an 8.5-m (27.9 ft) -wide roadway required for installation faces. The introduction of Longwall Top Coal Caving (LTCC) to this environment has aided in the management of some of these issues, but LTCC has also given rise to other geotechnical considerations. Additional geotechnical issues associated with LTCC not only require management during operations, but also require consideration when evaluating new mining areas at Austar Coal Mine or potential LTCC extractable resources throughout Australia and the world. In September 2006, LTCC commenced at Austar Coal Mine in longwall panel A1. Since this point the LTCC face has been increased from 147 to 216 m (482 to 709 ft)and finally to 227 m (745 ft) in width, and it has also been rehanded and modified in the three fully extracted panels to date. The application of LTCC in panels A1, A2, A3, and now A4 has been very successful, both from a coal resource recovery point of view and in the management of the principal hazards of spontaneous combustion and strata control. This paper focuses on the geotechnical aspects of the application of LTCC at Austar Coal Mine and also reviews some advances in general strata control management at the mine.

Jan 1, 2011

By Madan M. Singh

Mining under bodies of water such as oceans, lakes, rivers, streams, ponds, and other impoundments, is not a new technique. However, in the United States it has been fairly restricted to date. In order to recover the maximum amount of the nation's reserves, in the future, it is important that further mining under such bodies of water be planned. However, it is imperative that this is not done at the expense of danger to the nation's miners or appreciable property damage. If all the bodies of water are considered large, and it is assumed that these constitute a hazard when mining in their vicinity irrespective of their size and geometry, a significant percentage of the coal reserves are likely to be sterilized. How- ever, by adopting special mining plans and procedures, it may be possible to release reserves for exploitation that would otherwise be unmineable since the surface of bodies of water below which they lie are relatively small in size. In 1977, the Bureau of Mines issued Information Circular (IC) 8741, entitled "Results of Research to Develop Guidelines for Mining Near Surface and Underground Bodies of Water". This document was based on the work done by Skelly and Loy (under Contract No. H0252083) and K. Wardell and Partners (under Contract No. H0252021). How ever, these guidelines have limited application, because these did not (1) define the bodies of water of concern, and (2) take into account the nature of the strata being encountered. These guidelines assumed that all bodies of water which would be undermined were large. For the purposes of this discussion, water bodies may be divided into three categories, depending upon their potential to cause damage to the underlying mining activity: ? catastrophic ? major ? limited Bodies of water which pose the threat of catastrophic destruction in the mine, should there be an inrush, include oceans, large lakes, big inland reservoirs, and rivers that could flood the mine complete- ly in a short period. Those with major potential for damage would include lakes and streams which might present a danger to both life and property if not considered in the mining plans. Finite bodies of water which have a volume considerably smaller than the mine volume offer a limited potential for damage in the case of an inrush. These include flowing streams which have a relatively small rate of replenishment and which can be dealt with by pumping or isolation in the event of a breakthrough into the mine. Such bodies of water may be inconvenient and cause a temporary disruption of production, and could even cause some damage to equipment, but only in rare instances would personal injuries occur. The scope of this paper is limited to the exploitation of stratified mineral deposits with overlying -face bodies of water. Vein and dessiminate ore deposits are not discussed, nor are breakthroughs into adjacent mines in the same horizon. Overlying, water-logged strata also pose a serious threat to mining, but are not treated in this discussion. Pending further investigation these strata may be considered as bodies of water with catastrophic potential for damage, with the base of the strata being considered the bottom of the water body. When the body of water is large, so that it may cause catastrophic damage to the mine in the event of an inrush, the guidelines suggested in IC 8741 are applicable. In order to develop criteria and procedures for mining under smaller bodies of water, however, it is necessary that the nature of the strata disturbance due to underground mining be examined.

Jan 1, 1981

By Dennis R. Dolinar

A room and pillar coal operation in central Pennsylvania was experiencing roof cutters and long running roof falls caused by high horizontal stresses. The roof conditions created hazards for the miners, and caused several production panels to he abandoned prematurely. The mine requested assistance from the National Institute for Occupational Safety and Health (NIOSH) in applying the "advance and relieve" mining to reduce the affects of the horizontal stress during panel development. The "advance and relieve" plan that was developed called for removing a pillar on one side of the panel as it was being advanced, thus creating a cave. The caving then relieved a portion of the horizontal stress across the panel. Because the horizontal stress direction is key to the success of this method, stress mapping as well as mining experience was used to establish the direction of the horizontal stress. Subsequent field measurements provided an estimate of the stress magnitude. Three panels were mined using this technique, and good roof conditions were achieved in all these panels. Instrumentation was used to monitor the stress changes in the roof created by the cave. Stress relief of over 1.000 psi was measured 120 ft from the cave and to depths of 20 ft into the roof. The lateral extent of the stress relief zone across the panels appears to be about 400 to 500 ft. This case history has provided much insight into the practical application of the "advance and relieve" method discussed in this paper.

Jan 1, 2000

By Michael Gauna

In 2010, the number of fatal rib falls in U.S. underground coal mines exceeded fatal roof falls for the first time ever. While recent trends have seen roof fall fatalities reduced by about 62% since the 1990s (from an average of 9.6 per year in the 1990s to 3.6 per year during the last five years), the incidence of rib fall fatalities has remained approximately constant (about 1.5 per year). In addition, injury incidents associated with pillar rib failure have been steady at approximately 100 per year. The persistence of rib fall injuries, underlined by the recent increase in rib fall fatalities, has led to this investigation of the coal rib failure parameters and methods available to mitigate rib failure in U.S. underground coal mines A detailed study of the 21 fatal rib fall incidents that have occurred since 1995 (excluding coal burst incidents) indicates that the two most important risk factors are the mining height and the depth of cover. The depth of cover was 700 ft (213 m) or greater in 81% of the fatalities, and the mining height was at or exceeded 7 ft (2 m) in every instance but one. Other risk factors included multiple seam interactions, rock partings in the seam, and retreat mining. The accident history reveals that joints or slickenside features within the rib increase the hazard. Approximately threequarters of the rib fatality victims were roof bolting machine operators and continuous mining machine operators. This paper includes a brief overview of techniques for rib control; including bolts, standing support, bent steel straps, and rib strapping. The available mining equipment features for installing rib support and protecting operators from rib falls are also discussed. A proactive approach to rib control using available technologies will lower the risk to miners and is an endeavor that must be pursued to reduce rib fall accidents.

Jan 1, 2011

By David Bigby

A remote reading dual height telltale system has been developed to provide mine management with early warning of impending roof failure. This system is a logical development from the visual dual height and triple height telltales which are increasingly being used worldwide for routine monitoring of mine roof. The paper describes the principles and history of telltales from their origins in France, their refinement and routine use in the UK and their subsequent spread around the world. They are now being used in various forms in USA, Canada, Germany, Spitzbergen (Norway), Poland, Ukraine, Russia, Australia, South Africa, Mexico, India, Egypt and China. The remote reading telltale system has coal mine intrinsic safety approval in Europe and the United States (MSHA) and the first commercial system was installed in a German colliery at the beginning of the year. Up to 100 dual height telltales can be connected, in a simple "daisy chain" configuration, to each of 4 underground interrogation units. These are connected through a twisted pair link to a surface computer which displays the readings, updates the database, generates warnings and provides the user interface. The paper describes the features and principles of operation of the system which differs considerably from conventional mine-wide monitoring systems. A European Community funded research programme is currently underway with the aim of developing improved alarm generating algorithms including evaluation of interfacing a neural network to the system. The paper concludes by exploring other potential applications of the system for ground control monitoring currently in development, including extensometry, stope closure monitoring and support load measurement.

Jan 1, 2001

By Christopher Mark

The past decade has provided a wealth of practical experience with longwall pillar design. Design formulas developed specifically for longwalls have proven their value in numerous applications. Analytic methods, including numerical models, have a1 so made important contributions. These advances have been based on basic research into abutment loads, coal pillar mechanics, and the interaction between pillar performance and entry stability. The goal of this paper is to review the state of the art in longwall pillar design from the standpoint of the practitioner. Actual case histories are presented to illustrate the current capabilities and limitations of pillar design methods. The paper also discusses the advances that can be expected in the future.

Jan 1, 1990

By E. Bauer

During 1987 and 1988, the Eighty Four Complex Mine of BethEnergy Mines, Inc. used the open entry longwall recovery method to recover one partial and three complete longwall faces. Various cement- concrete supports were utilized to support the open recovery entry until the approaching longwall face cut into this entry. This recovery method and the supports used were studied by the mine personnel and the Bureau of Mines. This paper discusses the findings, results and conclusions of that study.

Jan 1, 1988

By M. Ashraf Mahtab

A feature of interest in stability of excavations in domal salt is the phenomenon of gas outbursts which has occurred in five of the six mines in Louisiana salt domes. Gas outbursts are sudden erruptions of salt and gas from the face or roof of a mine opening. They are associated with anomalous zones in salt, depth of mining, and the method of excavation. Potential risks from gas outbursts include an unplanned connection to a reservoir of water or hydrocarbons and, possibly, a loss of the mine. It is proposed that a gas outburst is initiated by disking in biaxial compression and propagates by spalling of the cavity walls and further disking. The outburst is terminated by a combination of dilatancy hardening, increase in stress along the cavity axis, and enlargement of the cavity to the boundaries of the pressure pocket. Identification of burst- prone areas will require research into in situ measurement of material characteristics and further under- standing of the mechanism of gas outbursts. Shock blasting in advance of mining appears to be a promising technique for controlling gas outbursts.

Jan 1, 1981

By Thomas Barczak

Pumpable roof supports provide an alternative longwall tailgate roof support and have grown in usage during the past few years. Heintzmann Corporation has been installing pumpable roof supports at the RAG Resources Emerald Mine in western PA since 1998, where they have provided effective roof control in their longwall tailgates. Despite the success of these supports in this application, questions remain regarding critical design issues for optimizing the use of this support technology. The support loading profile is characterized by a high initial stiffness with peak loading occurring at less than one inch of convergence, followed by significant load shedding with a post failure capacity comparable to that of wood cribbing. Therefore, the key to optimizing the support utilization is to provide sufficient load density to prevent convergence from occurring beyond the peak loading capacity. This requires an understanding of how the supports interact with the ground conditions, hence measurement of the ground reaction curve. In order to obtain this information, pumpable roof supports were instrumented to measure support loading. Roof deformation and roof-to-floor convergence measurements in the vicinity of the instrumented supports were also made. The experimental parameters for the installation were the support spacing and water¬to-solids ratio of the grout, which controls the grout strength and ultimately the maximum capacity of the support. The study clearly shows that at this mine a 24-inch diameter support is fully capable of providing adequate ground control under depths of cover of 750 ft as only 50 pct of the available support capacity was utilized outby the longwall face. It was also shown that the 2.00 to 1 water¬solids ratio, despite providing a slightly softer support response, is sufficient for maintaining the same degree of roof control provided by the traditional 1.75 to 1 grout mix. The 10-ft spacing of the supports did not cause any ground control problems outby the face. However, inby the face the performance of the support is degraded once the peak capacity of the supports is exceeded. It appears that the large load shedding behavior, which is characteristic of this support following peak loading, allows the immediate roof to separate. When this happens, the support is unable to regain control of the roof in time to prevent failure of the immediate roof beam.

Jan 1, 2003

By Alan Peacock

Shield supports have been in use in the USA underground mines since 1975, and their development in the intervening time has been progressive and inovative. Specialized techniques are used to optimize their performance in a particular application and to design the component parts.

Jan 1, 1981