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Open pit mine plans define the complex strategy of displacement of ore and waste over the mine life. Various mixed integer linear programming (MILP) formulations have been used for production scheduling of open pit mines. The main problem with these models is the inability to solve real size mining problems. We present a mixed integer linear programming formulation for the open pit long-term production scheduling problem. To reduce the number of binary integer variables in the formulation, we aggregate blocks into larger units referred to as mining-cuts. We present a semi-supervised clustering algorithm which aggregates smaller blocks based on rock types and grade ranges into mining-cuts without introducing an error in the grade estimated values. The cluster-based aggregation algorithm is fully integrated into an MILP mine production scheduling prototype software. We have implemented, verified, and validated our models. The efficiency of the new platform is evaluated through iron ore mine case study.

Dec 6, 2010

By Aly M. Mohammad

The 12th and 14th Street Viaducts, which carry Route 139, are located west of the Holland Tunnel in Jersey City, New Jersey. The two viaducts, provide access to and from the Holland Tunnel (which connects New York City and New Jersey) and carry upwards of 50,0000 vehicles per day from Jersey City and New York City to points west. The New Jersey Department of Transportation (NJDOT) selected AECOM to perform design services including rehabilitation and seismic retrofit for the 12th Street and 14th Street Viaducts while maintaining traffic at all times. Building a new parallel bridge just north of the 14th Street Viaduct was essential in avoiding extremely costly traffic delays. Installation of the new foundation, in close proximity to the existing viaduct, required drilling through some of the existing timber piles supporting the bridge. As a result, the existing bridge was required to be reanalyzed for this new foundation configuration. This proposed structure consisted of 8 piers each supported on a single six (6) foot diameter drilled shaft. Currently this portion of the bridge structure has been constructed. The shafts were constructed with rock sockets that were five feet six inches (5?- 6??) in diameter and were extended 11.2 feet (3.4 meters) into rock. A 2300 ton Osterberg Load Test was performed on one production shaft to confirm the capacity of the shaft. The rock socket for the test shaft was in sandstone. This paper will present a description of the design methodology and construction methods adopted for the foundations. In addition, the paper will illustrate the Osterberg Load Test including: equipment used, number and locations of strain gages, and interpretation of results. Additionally, regarding the close proximity of the new foundation, the paper will present the type of equipment used to drill through the existing timber pile foundation while minimizing the impact on the integrity of the existing foundation. We will also present the method of analysis for analyzing the redistribution of load on the remaining piles. The results presented in this paper will assist the design engineer by providing a comparison between the geotechnical design assumptions and the actual measurements obtained by field measurements for this rock formation.

Jan 1, 2009

By Frank Chase

Longwall mining has gained the reputation as being the safest extraction method in underground coal mines. However, one of the most difficult tasks associated with longwall mining is moving the face once a panel is completed. Based on Mine Safety and Health Administration (MSHA) fatality reports since 1996, longwall face recovery operations have claimed the lives of 5 U.S. miners and have resulted in numerous injuries. Recovery operations can be hazardous because they involve moving large pieces of equipment in very confined spaces. They are also conducted in highly stressed ground conditions due to front abutment loads generated by panel extraction. Shield removal is the most hazardous operation during face recovery because miners are constantly exposed to the unpredictable gob edge. To protect the miners, one or more walking shields, cribbing and/or other supplemental roof and standing supports are typically employed as breaker line supports as each shield is removed. At the Harris No. 1 Mine in southern WV, mobile roof supports (MRS?s) have been used in lieu of traditional walking shields on 17 face moves since 1997. MRS?s are shield-like support units mounted on crawler tracks and are commonly used during room-and-pillar retreat mining operations. For longwall recovery, the two biggest advantages that MRS?s have over traditional walking shields are that they are remotely controlled and are highly maneuverable. MRS?s have contributed to safer shield recovery and shorter move times at the Harris No. 1 Mine. This paper will address both the safety and the operational issues associated with MRS usage during shield recovery. It will also discuss new developments, including the use of the inherently safer battery powered MRS?s, which have been recently certified by the Mine Safety and Health Administration.

Jan 1, 2007

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 S. H. Lorain

This paper briefly describes the principal known commercial and near commercial deposits of gold-bearing gravel end the principal placer mining operations of Idaho County, Idaho. It is one of a series of similar papers on western mining districts. The data used in writing this paper were gathered during the summer of 1937. Information concerning gold-bearing gravels was obtained from prospectors and operators, while operators supplied most of the data on mining operations. No attempt was made actually to test the gravels. The principal object of the examination was to indicate placer areas worthy of further investigation by prospective operators.

Jan 1, 1938

By J Wei, A Yo, R Levy

Waste water reuse from municipal and industrial effluents is becoming increasingly important in many areas around the world. Water scarcity, local regulation and environmental impact are driving many industries like coal and copper mines to reuse the large volume of waste water they produce. For example, the Chinese coal industry generated about 4.2 billion tons of mine waste water in 2005 of which only approximately 30 per cent was reused. Coal energy represents 76.6 per cent of the total energy generated in China in 2007 and most of the coal-fired power plants are located in north-west of China, which is a water stressed area.The selection of mine waste water treatment process is challenging as the effluents typically contains high levels of organic compounds and salinity and their composition can vary significantly. In recent years there has been a growing interest in the integration of ultrafiltration (UF) and reverse osmosis (RO) membrane technologies for mine waste water treatment and reuse.In this paper, an overview of the design and performance of ultrafiltration and RO membranes applied for reuse of mine waste water are discussed. A study was carried out in two effluents treatment plants treating copper and coal mine waste water, which are located in Chile and China respectively. The following topics will be discussed to demonstrate the performance of an integrated membrane system in mine waste water reuse: The main challenges from copper mine waste water treatment: high level of chemical oxygen demand (COD); high level of total suspended solids (TSS); high salinity; high concentration of silica, sulfate, iron and other contaminants; and fluctuation of raw water quality. The main challenges from coal mine waste water treatment: high level of total dissolved solids, and waste water quality fluctuation. Design parameters for waste water treatment systems: Selection of pretreatment for dual-membrane system in the copper mine: Clarifier with coagulation and flocculation to remove high TSS; Dissolved Air Flotation (DAF) to remove non-settling solids; Media filtration to handle fine solids and particulate organics; Activated Carbon filters (ACF) to remove dissolved organics, colour and odours. Selection of UF and RO membranes and specific design of their recovery, flux, chemical dosage and cleaning regimes. Finally, the performance of UF and RO, including the main fouling factors and efficient cleaning procedures, will be presented and compared to the design parameters to demonstrate the efficiency and performance of the selected integrated membrane systems in each case.

Jan 1, 2009

By Edward L. McHugh, Charles Sabine, David G. Long

While less than 1% of reported mine accidents are associated with slope stability problems, slope failure accidents were responsible for about 15% of U.S. surface mine fatalities between 1995 and 2003. Small rockfalls, which may involve hand-sized rocks weighing only a few pounds, can cause fatal injuries to workers away from the protection of large machinery. Massive highwall failures containing a million cubic yards of material or more can be fatal even for heavy-equipment operators. As part of an ongoing study at the Spokane Research Laboratory, several remote sensing technologies are being evaluated as tools to assess slope stability and monitor slopes for hazards. An interferometric radar device capable of detecting very small displacements on slopes has been assembled and tested. Radar techniques can provide new tools to augment current methods for monitoring ground control hazards in mines.

By Thomas M. Barczak

Roof support technology for longwall tailgates has changed dramatically during the past decade. Filling tailgates with conventional wood cribs is becoming the exception rather than the rule. Modern engineered timber support systems and a host of other alternative support products provide far greater capacity as well as stiffer response, thereby allowing the supports to resist roof movement with much less displacement than the soft wood cribbing used in the past. For these reasons, these products can provide superior roof control. In addition, the material handling requirements for support installation have now become a major consideration in the support design and selection process. Products such as conventional wood cribbing that require piece-meal construction of bulky, heavy components have diminished, while prop-type supports and products that can be installed with machinery and pumpable support technologies have grown in use resulting in fewer injuries to mine workers. Now, the opportunity exists to provide the safest, most cost effective support system, through engineering design rather than by trial and error and to optimize the use of the support system chosen. Yet this is rarely done. The key to accomplishing this task is to understand the interaction of the support system with the ground conditions at the installation site. A major focus of the paper is to conceptualize the support and interaction through the use of a ground reaction curve which relates the support resistance to the convergence of the longwall tailgate. The goal of any roof support design is to control the ground deformations and maintain the structural integrity of damaged or broken ground to the extent possible to provide a stable mine opening. In general, deformations will be a function of the stress environment and inherent strength of the surrounding rock mass. However, if the deformations are intimately linked to the stress changes such that the deformation can be controlled by the load resistance or reinforcement provided by a roof support system, then the loading behavior can be described as load-controlled. Conversely, if the deformation occurs irrespective of the installed support (assuming practical limitations), then the loading behavior is described as displacement-controlled. In this case, the deformation can be considered irresistible from a practical standpoint. In this context, the nature of the loading has significant consequences on the support design requirements. Finally, examples using the NIOSH Support Technology Optimization Program (STOP) to develop design criteria using ground reaction data from underground studies and ways to include uncontrolled convergence as part of the design criteria for standing roof supports will also be discussed.

By K. G. Thorne, L. J. Cabri, L. R. Fyffe, D. R. Lentz, D. Hoy

"Mineralization at the Main zone of the Clarence Stream gold deposit in southwestern New Brunswick occurs within a parallel series of quartz veins that occupy a NE-trending, steeply north-dipping, brittle-ductile shear zone related to the nearby terrane-bounding Sawyer Brook fault. This deformation zone cuts volcaniclastic sedimentary and volcanic rocks of the Silurian Waweig Formation, and is intruded by mantle-derived East Branch Brook gabbroic dikes and a number of felsic dikes. Intermittent shear-zone reactivation during local magmatic activity induced heterogeneous deformation and alteration of the country rocks and dikes. The terminal phase of shearing is associated with narrow pegmatite-aplite dikes that grade laterally into granophyric granite, and into an auriferous quartz vein. Gold, aurostibite, and gold-antimony intergrowths, predominantly with vein quartz, are associated with a low ƒO2 sulfide mineral assemblage (pyrrhotite, arsenopyrite, and berthierite) that has a sulfur isotopic signature consistent with a magmatic source. Gold saturation and deposition occurred episodically between 300° and 360°C at low activity of sulfur, predominantly in response to pressure reduction during brittle failure combined with the effects of decreasing temperature and sulfidation reactions during fluid-wall-rock interaction. Geochronological studies demonstrate that the timing of the emplacement of the pegmatite-aplite dikes and associated auriferous veins overlap with that of the Early Devonian Magaguadavic granite. Moreover, the composition of the dikes is consistent with their derivation from this granite as late fractionates. The Main zone of the Clarence Stream deposit is therefore interpreted to be intrusion-related, with the Magaguadavic granite being the ultimate source of the gold-bearing fluids. La minéralisation de la zone principale du gisement aurifère de Clarence Stream dans le sud-ouest du Nouveau Brunswick occupe une série de veines de quartz parallèles dans une zone de cisaillement fragile-ductile de direction NE et à pendage abrupt vers le nord apparentée à la faille de Sawyer Brook avoisinante qui délimite deux terranes. Cette zone de déformation recoupe les roches volcaniclastiques et volcaniques de la Formation de Waweig d’âge Silurien et est recoupée par les dykes de gabbro d’East Branch Brook, d’origine mantellique, ainsi que par divers dykes felsiques. La réactivation intermittente de la zone de cisaillement durant l’activité magmatique locale a entraîné la déformation et l’altération hétérogènes des dykes et de l’encaissant. La phase finale du cisaillement est associée à de minces dykes d’aplite-pegmatite qui passent latéralement à des granites granophyriques, puis à des veines de quartz aurifères. L’or, l’aurostibite et les intercroissances d’or et d’antimoine principalement associées aux veines de quartz sont associés à un assemblage minéral de sulfures à faible ƒO2 (pyrrhotite, arsénopyrite et berthierite) présentant une signature isotopique du souffre compatible avec une source magmatique. La saturation en or et la précipitation a eu lieu épisodiquement entre 300° et 350°C dans des conditions de faible activité de souffre, principalement en réponse à la baisse de pression durant la rupture fragile ainsi qu’aux effets de la baisse de température et aux réactions de sulfuration durant l’interaction entre le fluide et l’encaissant. Les études géochronologiques indiquent que l’âge de la mise en place des dykes de pegmatite-aplite et des veines aurifères qui leur sont associées coïncide avec le granite de Magaguadavic, d’âge Dévonien Précoce. De plus, la composition des dykes est compatible avec une origine provenant de ce granite sous la forme de phases fractionnées tardives. Le gisement principale (Main zone) de Clarence Stream est ainsi considéré comme étant associé aux intrusions, le granite de Magaguadavic étant la source ultime des fluides aurifères."

Jan 1, 2008

By G. L. Oldright, Virgil Miller

"This paper is the tenth 4 of a series on smelting in the lead blast furnace, and the fifth 5 on modifications brought about by the introduction of richer charges.ACKNOWLEDGMENTSAll of the data on handling rich charges in lead smelting given in this recent set of five articles describing the results of a cooperative study by the United States Bureau of Mines and the University of Utah were obtained through the courtesy and with the cooperation of the staff of the Bunker Hill & Sullivan Mining & Concentrating Co. at Kellogg, Idaho. The authors acknowledge with appreciation the assistance given by Stanly A. Easton, vice.-president and general manager, F. M. Smith, smelter director, and A. F. Beasley, smelter superintendent, whose generosity, sympathy, and assistance made it possible to obtain this information for the mining industry.GENERAL DISCUSSIONWhen the charge has been dropped into the lead blast furnace, it is out of control of the operator to the extent that, whatever the material is, it must practically all be melted and run out of the blast furnace. The necessary uniformity of mixture to produce slags of regular composition and the choice of the slag—forming ingredients and products to be formed can be made only before the charge to dropped.It was found (R.I. 3096) at Kellogg, where the charge is mostly sinter, that the ratio of the slag—forming ingredients taken from each tuyere was nearly constant, in contrast to the irregular composition of slags taken similarly from a furnace whose charge consisted of ingredients differing greatly in chemical and physical nature, including size. If the charge consists almost entirely of sinter, the blast furnace should then operate more uniformly."

Aug 1, 1932

By X. Zhou

In this study, the cyclonic static microbubble flotation column (FCSMC) was investigated for fluorite beneficiation. The structure and principle of the specially designed column are described. Fluorite samples from the tungsten separation tailings of the Shizhuyuan Mine, Chenzhou, Hunan Province, P.R. China, were tested using a small-scale continuous flotation test unit, and concentrates with a fluorite grade higher than 98% were obtained. One rougher and three cleaner stages in the FCSMC achieved the same separation performance as one rougher and eight cleaners in conventional flotation cells. This greatly simplified the flotation circuit and reduced operating costs.

Jan 1, 2007

By M. R. TECK, N. Rudd, L. K. Thomas, D. L. Katz

The authors are to be congratulated for presenting the first comprehensive paper on the theory and practice of threshold pressure determination in connection with underground gas storage. It is of particular value since most previous experimental work on this subject has been proprietary to the commercial laboratories engaged in such testing and to their clients. This dlscussion is presented in amplification of the subject paper, not in criticism, and is based upon our experience with approximately 5,000 threshold pressure determinations. Our comments are directed primarily to the experimental procedures as described by Thomas et al. It should be noted that, while clay mineral-rich lithologies are the most common caprock materials, the samples used (Table 1) include low permeability sandstones and carbonates, but do not include shales or other formations in which clav minerals exert a dominant effect. While our experience on samples analogous to those investigated by the authors generally confirms their findings, we have found that even more rigorous experimental conditions must be imposed where clay minerals are the controlling factor. These additional conditions result from the well-known molecular character of the clay minerals themselves in which water is interlaminated with, and bonded to, silicate sheets, thus becoming an essential component of the molecule. In many clay minerals the character of the intersheet bonding, and thus the dimension of the lattice, is strongly affected by variations in the identity and concentration of cations present in the intersilicate water. On a supermolecular scale, adsorbed water films on particle or "flakes" of shale provide much of the cohesive force necessary to maintain mechanical strength. The thickness of these films is variable and inversely proportional to intergranular pressure within the dimensional limits involved in caprock investigation. The thickness of the intersilicate water layers may also be subject to pressure under some conditions. These considerations are reflected in several necessary modifications of the experimental procedures described by the authors. Two of these are, in our judgment and experience, of such importance that they cast real doubt on the validity of data obtained on argillaceous materials without their application. The very careful resaturation procedures proposed by the authors should give good results in connection with the relatively "inert" lithologies used in their experiments. Our experience suggests, however, that they would create more problems than they would eliminate if applied to argillaceous materials. 1. Drying of the sample at the temperature and for the duration indicated by the authors not only will dessicate the sample with consequent shrinkage cracking, parting along bedding planes, and even total disassociation in the case of fissile shales, but it may also alter the character of the clay minerals themselves — in some cases irreversibly. 2. Prolonged evacuation to 2 microns Hg further dessicates the sample and is even more effective in reducing the intersilicate water content. 3. Resaturation with water differing in pH or chemical content from that existing originally in the sample also serves to alter the nature of the sample, particularly its structure and strength. 4. Our experience has been that, even with the thorough precautions proposed by the authors, complete resaturation of very fine grained materials is rarely obtained. Yet our experience confirms the

Jan 1, 1969

By Louis Donolo

New buildings in today's urban environment, especially in down-town areas, invariably involve the construction of multiple level basements. Used for parking, storage and commercial space, these underground structures normally extend 30 to 50' and more below grade and, to make optimum use of expensive land, they usually occupy the full site right up to street/sidewalk and property lines. SOIL SUPPORT SOLUTIONS Building these basements requires vertical excavation, and consequently, a temporary soil support system which will eventually be replaced by the permanent foundation walls of the structure.

Jan 1, 1987

By K. M. Mohamed, R. K. Zipf

The shear strength properties of generic cement foam material and cement foam/concrete interfaces were examined at three testing scales. In laboratory direct shear tests on specimens with average shearing area of 0.006 m2 (10 in.2), the cement foam material had average peak and residual shear strengths of 0.88 MPa (128 psi) and 0.39 MPa (56 psi), respectively. Depending on the concrete strength, the cement foam/concrete interfaces had peak and residual shear strengths ranging from 0.71 to 0.81 MPa (103 to 117 psi) and from 0.27 to 0.29 MPa (39 to 42 psi), respectively. In laboratory direct double shear tests on specimens with average shearing area of 0.084 m2 (130 in.2), the cement foam/concrete interfaces had average peak and residual shear strengths of 0.17 to 0.30 MPa (25 to 44 psi) and of 0.11 to 0.23 MPa (16 to 33 psi), respectively. In large shear tests of simulated cement foam seals with the Mine Roof Simulator (MRS) test frame, cement foam/concrete interfaces with shearing area of 1.486 m2 (2,304 in.2) had average shear strengths of about 0.08 and 0.16 MPa (11 and 23 psi) along the roof and floor interfaces, respectively. The average shear strength through the cement foam material was 0.38 MPa (55.3 psi). Finite element analysis of the large seal tests and the back analysis of the shear strength of full-scale cement foam seals conducted at the NIOSH Lake Lynn Laboratory confirmed shear strength of about 0.14 MPa (20 psi) along the seal/rock interfaces. The study concluded that the structural analysis of cement foam seals should be based on their residual shear strength determined from small laboratoryscale tests of the cement foam/concrete or rock interface and not be based on their peak strength.

Jan 1, 2014

By Lance A. Roberts

Micropiles are commonly utilized for applications other than foundation retrofit. In bridges, for example, micropiles can serve as the permanent foundation elements or can be used in temporary support applications. In this paper, a case study on the use of micropiles for the 18th Street Expressway Bridge rehabilitation/repair project in Kansas City, Kansas is presented. In the project, micropiles were utilized for support of six temporary jacking structures, which allowed the bridge to be lifted while repairs were completed. A group of six micropiles was required to support each jacking structure. The required compressive service load per micropile was approximately 300 kips (1300 kN) and the settlement of the micropiles under the service load was to be limited to 0.5 in. (12.7 mm). Two field compression tests were conducted as part of the project. The field load test data was integrated within a soil-structure interaction capacity approach in order to analyze and permit the shortening of the design bond length for the production micropiles.

Jan 1, 2009

By N. Merriam

This report describes Koppelman's work to develop the K-Fuel® Series C Process used to dry and stabilize Powder River Basin coal. It also contains summaries of the results of bench-scale and pilot plant tests conducted to prove the Series C Process. The process is being used by the KFx-Thermo Ecotek partnership for a 500,000 ton per year commercial plant that has been constructed near Gillette, Wyoming. The plant is presently undergoing shakedown.

Feb 24, 1997

Researchers from the National Institute for Occupational Safety and Health (NIOSH) are developing a coal pillar rib rating (CPRR) technique to measure the integrity of coal ribs. The CPRR characterizes the rib composition and evaluates its impact on the inherent stability of the coal ribs. The CPRR utilizes four parameters: rib homogeneity, bedding condition, face cleat orientation with respect to entry direction, and rib height. All these parameters are measurable in the field. A rib data collecting procedure and a simple sheet to calculate the CPRR were developed.

Jan 7, 2020

By Michael Day, Paul Kos, Scott Brinton

A hydrogeologic characterization and impact analysis was performed for a proposed quarry at the Hitch Rack Ranch located in the Little Turkey Creek watershed southwest of Colorado Springs, Colorado. Continuous multiple channel tubing, nested piezometers, stream flow measurements, and mapping of known seeps were used to define the three-dimensional potentiometric distribution and areas of groundwater recharge and discharge. Water balance considerations, mass balance calculations, and potentiometric response to earth tides and barometric fluctuations confirmed that the granite fracture system in the ridge area of the proposed quarry has an extremely low bulk hydraulic conductivity resulting in minimal groundwater discharge to sustain the baseflow of Little Turkey Creek. The Little Turkey Creek valley forms the major conduit for groundwater flow exiting from the upper part of watershed underlain by granite. This conclusion has significant implications with respect to mine planning to minimize projected impacts to the hydrologic system and preserve this recharge component to downgradient Denver Basin sedimentary deposits.

By L. D. Patts, J. D. Noll, S. E. Mischler, G. H. Schnakenberg

In this study, we evaluated the ambient diesel particulate matter (DPM) concentrations (at the intakes and exhausts of the mine) as the entire vehicle fleet of a stone mine switched from using 35% biodiesel to using a water emulsified fuel (PuriNOx). Elemental carbon (EC) was reduced by 45% when a PuriNOx blend containing 10% water replaced 35% biodiesel and by 57% when a PuriNOx blend containing 20% water was used. Other factors such as engine duty cycle and production changes could potentially cause some day-to-day EC fluctuations, and no direct comparison to commonly used dieselfuels (No. 1 or No. 2) was achieved. Therefore, a second study was performed in a controlled “isolatedzone” environment to fametal mine, comparing PuriNOxto No.1 diesel fuel in a load haul dump vehicle. The EC fraction of the DPM was reduced by about 71% when the PuriNOx blend containing 10% water was used and by about 85% when the PuriNOx blend containing 20% water was employed. This study did not determine how the water emulsified fuel would affect the engine or power.

By J. M. Pei

In this paper, the nonlinear finite element analysis is used to study the support system of a tunnel which is designed to pass through deep-embeded stratum. The rock mass is rather intact, though a section of tunnel will pass through the weak belt. Under the influence of the high ground stress, the condition of stability and the form of support become complicate. This paper, talcing into account the nonlinear properties of rock mass and the Interaction between rock, and support, makes a comparison between the two kinds of soft and rigid support systems, and analysed the changes of their bearing forces.

Jan 1, 2010