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By A. Warczokand

The cleaning of copper smelting slag requires magnetite and cuprous oxide reduction. The slag reduction with coke, injected coal powder or bunker oil is strongly endothermic and requires heat generation by fuel combustion or the use of electric energy. The reduction of fayalitic slag with calcium carbide is slightly exothermic and the formed calcium silicate modifies the slag. Thus, the additional energy is required only for covering furnace heat losses. Results of crucible scale tests showed the rate of slag reduction approximately five times higher in comparison of the slag reduction with coke under the same conditions. It seems that the effect of exothermic reaction and slag modification with CaO at the reaction interface results in very high rate of slag reduction. Industrial scale tests carried out in the Anglo-American Chagres Smelter demonstrated the possibilities of effective reduction and cleaning of the slags from a flash smelter and Peirce-Smith converters in a Teniente Slag Cleaning Furnace. The slag reduction was carried out without any reductant or stirring gas injection, simply by calcium carbide charging through a furnace mouth, and was very fast.

Jan 1, 2007

By Cheng-Ting Chiang

Information integration and exchange for the entire building life cycle is one of the most important issues in the AEC industry. Although the Building Information Model (BIM) technology is widely utilized to address them, BIM is mainly concerned within the design and construction (D&C) phases. In the operation and maintenance (O&M) phases, however, the information integration and exchange issue becomes more complicated because software applications here require not only BIM but other information outside of the AEC domain, e.g., disaster mitigation. Nowadays, most BIM-related research focuses on the D&C phases and pays less concern on the O&M phases, hence there is a research need that can help seamlessly transfer the information between the D&C and O&M phases. In this research, a software framework using ontology was designed to deal with aforementioned problems. The BIM data from the D&C phases were used as a foundation to generate new models for different software applications for the O&M phases. The ontology technique was employed to assist the model transformation process between the original BIM and the models for applications. Finally, a disaster mitigation example was chosen to validate the framework, in order to make sure that the transformation process is comprehensive and useful from domain experts? perspective.

Aug 1, 2013

By J. Kolacz

"A new sensor based sorting system has been developed, providing a possibility for laboratory scale testing and further scale-up of the separation results to the industrial operation. The new system contains different sensors as: X-ray detectors, visible light cameras, NIR cameras, ultraviolet cameras and magnetic sensors, in the same sorting unit. The sorting unit allows advanced calibration options and fine-tuning of the installed sensors to achieve the best separation effect under controlled conditions. Finally, the processed material can be analysed and separated by the rejection mechanism, similarly to the industrial scale operation. At the same time, the process is carried out with limited amount of material allowing detailed statistical calculations for processed particles and all sensor types. The optimal settings and sensor types are specified for the industrial application.The paper describes the scale up of the results achieved for iron ore and coal, where the test work was first carried out using the new laboratory sorting system and where the industrial scale sorting system has been built, in the final stage. The industrial scale sorting results showed a very good correlation between the laboratory and full scale operation. Thanks to the detailed study carried out in the laboratory equipment, the settings of the sensors in the full scale operation provided much better separation efficiency. It was especially important to provide proper setting for the X-ray sensor data calculations, which can be very critical for achieving the best results. During the industrial scale sorting of coal, the input material had 40-55% rock particles as the direct source of ash in the coal stream. The optimal laboratory unit settings and transferring these settings to the industrial sorter, provided 98.8% efficiency for removing rock particles with only few % losses of coal."

Jan 1, 2016

By Scott Beer

What New Technologies Will Drive Economic Improvements? ??Historical ?1060?s: Mainframe Technologies ?1970?s: Mini Computing ?1980?s: Workstation Computing ?1990?s: Personal Computing ?2000?s: Network Computing Internet PDAs Cellular phones ??What?s the next technology improvement? ??What?s next for Mining?

May 1, 2009

By R. Ramirez

Atlantic Copper Refinery (Huelva, Spain) has operated the ISA permanent cathode technology since 1995. The current production rates are 260,000 t/y cathodes and 730 t/y anode slimes. These slimes undergo an atmospheric leaching in which their copper content is reduced from an average value of 24 % to 16 %. In June 2005 an optimization study of the leaching conditions was carried out aimed at lowering the copper content in the slimes to less than 8%. At the same time, a new mixer (Outukumpu Technology GLS-mixer) was installed in one of the three leaching reactors. As a result of the improvement of the leaching performance and to prevent the return of tellurium to the tankhouse, a cementation plant was commissioned in July 2005 to ensure a Te content below 50 ppm in the Cu-rich leachate. This paper describes the results of the improvement of the leaching conditions and the operation of the new tellurium removal plant.

Jan 1, 2007

By P. Rosario

"Current industry practice for HPGR assessment and sizing relies on conducting a series of tests using pilot-scale machines with roll diameters of 700 mm to 1000 mm. Substantial amounts of sample are required for such pilot test programs, typically 1 to 10 tonnes of the sample is needed depending on the level of study and complexity of the resource. Collection of large quantities of representative samples during the early stage development is challenging and expensive, thus significantly hinders the HPGR technology from being incorporated into early-stage designs. A robust and reliable laboratory test is therefore needed to allow a fair consideration of HPGR for early stage projects. With support from the Canadian Mineral Industry Research Organization (CAMIRO), the NBK Institute of Mining Engineering at the University of British Columbia (UBC) developed a suite of Piston Press bench-scale tests that correlated to pilot and full scale HPGR operating information (Davaanyam, 2015; Davaanyam et al, 2015; McClintock, 2018). The Piston Press Tests (PPTs) are capable of assessing the HPGR technology at the scoping, pre-economic analysis (PEA), and pre-feasibility (PFS) stages of project development. This paper will briefly describe the theory on which the PPTs are based, and then presents a case study conducted for a copper deposit to show how the PPTs are being used for scoping and pre-feasibility level studies. Specifically, the PPTs are being used to provide information for preliminary sizing and selection of an HPGR and to assess the effect of ore variability on HPGR performance. The results are also applied to developing HPGR circuit designs and can be incorporated in simulation so that optimum design parameters can be selected.INTRODUCTION It is widely accepted that high pressure grinding rolls (HPGRs) offer a viable energy-efficient solution for the modern comminution flowsheet design. Table 1 summarizes selected examples of HPGR applications in the hard rock mining industry. The main benefits of HPGRs are energy savings which leads to lower operating costs, and its stable operating characteristics that can better cope with variations in ore hardness when compared to the conventional SAG mill-based comminution circuits."

Jan 1, 2019

By T. E. Morimoto

Summary The Research Council of Alberta has made a series of tests with the cyclone washer to investigate the influence of the following operating variables: underflow apex diameter, .specific gravity of medium, pulp ratio, density distribution of the feed, and size analysis of the feed. The results obtained for all the variables studied, except size analysis of the feed, are included in this paper. The tests were made with smaller underflow apex diameters and lower specific gravity .suspensions than have been recommended by Cerchar for the sharpest separations. However, what is considered to be sufficiently good cleaning was accomplished with a suspension of 1.30 specific gravity and an underflow to overflow diameter ratio of 0.56. It was found that the sharpness of separation was not affected appreciably by variations in specific gravity of suspension or underflow apex diameter provided that the density of separation was within the normal range of washery operation. Cyclone performance was not too adversely affected by decreasing the pulp ratio. The minimum figure which gave reasonable separation was 4 to 1. The tests with various density distributions of feed revealed .that the degree of washing difficulty had no detrimental effect on the .sharpness of separation given by the cyclone. Introduction A major problem of the bituminous coal industry today is that of reducing the ash content of the finer sizes (minus 1/4-inch) of coal. This problem is particularly acute in Alberta, where, because of tectonic movement subsequent to deposition, the coals have been rendered friable, and bands of impurities have been intimately mixed with the clean material. As a consequence, most Alberta coals, as mined, contain a large proportion of fines and have a high inherent mineral-matter content. The advent of mechanized mining and stripping operations ?has further aggravated this problem.

Jan 1, 1952

By J. E. Dutrizac

Canada is currently the world's largest supplier of zinc concentrates and is also a major producer of zinc metal. This dominant position in the world's zinc market is a fairly recent circumstance and, in fact, the country's zinc industry was founded only in the early part of the twentieth century. By contrast, the American zinc industry was well established by the mid-nineteenth century, largely based on technology originally imported from the still older European practice. Initial attempts to create a viable Canadian zinc smelter were based on the traditional practice and were unsuccessful; success came only with new electrolytic technology, much of which was developed domestically. The purpose of this paper is to outline the early attempts to produce metallic zinc in Canada and to trace the gradual development of these first efforts into a viable zinc industry based on modern science and technology.

Jan 1, 1999

By M. H. ElMaghraby

This paper describes the development and validation of a strategy for vibration-based online detection of faults in a particular class of machinery commonly found in industry. This machinery is defined by two basic characteristics that preclude it from the application of standard online condition monitoring approaches. The first characteristic is that the machine is in a constant state of transient operation, thus making it difficult to differentiate between changes in transducer measurements that are due to variable duty and those that are due to machine malfunction or fault. The second characteristic is the fact that the machinery involves multiple sub systems that are subject to identical and simultaneous loading, operating environments and duty cycles. An example of such machinery is a system of multiple hydraulic pumps driving a common load. The monitoring strategy presented here employs an anomaly detection scheme together with methods of signal processing and feature extraction that exploit the parallel duty arrangements of this equipment. Preliminary data is collected from a pair or motor-gearbox assemblies used in a material haulage system in the mining industry. Testing and validation was performed on a mechatronic test bench with both healthy and faulted components. Experiments were carried out to investigate how various configurations of the system were able to detect different types of faults. The results indicate that this approach is effective and merits further investigation.

May 1, 2013

By Gobbs C., J. Lam

"The Eagle East project, accessed from the existing and operating Eagle Mine in the Upper Peninsula of Michigan, is an underground base metal project currently in execution by Lundin. This paper will provide an update on several aspects of ventilation including use of a twin-decline access, innovative airflow crossover arrangement and construction ventilation methodology. Integration into existing mine ventilation systems including construction methodology will also be covered. Performance benchmarks and lessons learned are discussed across these topics.INTRODUCTIONLundin has owned and operated the Eagle Mine since 2013. This hard rock underground mine is located in the upper peninsula of Michigan, USA. High-grade nickel ore is mined using sublevel open stoping mining methods and trucked to surface via haul ramp. The mine, having been in production for four years, is nearing the completion of the initial orebody. A satellite orebody 2,000 meters East of the current workings and approximately 900 meters below surface, was identified that could extend operations until 2023. In 2016, Lundin approved the Eagle East project and construction began in 2017 (Lundin Mining Corporation, 2017).Due to proximity to the existing mine, Eagle East will be both accessed and serviced from the existing Eagle Mine. Ventilation at the Eagle Mine uses two fresh air intakes with direct fired combustion heaters; one at the mine portal feeding fresh air into the ramp and one at a fresh air raise located near the Eagle deposit. The primary ventilation circuit is powered on the exhaust air side, with two 700 hp exhaust fans located at a single return air raise. Underground, fresh air is distributed through the main access decline and fresh air raise (FAR) to the production levels and controlled with mechanical regulators on the exhaust side. The exhaust air is collected through return air raises with a collector/transfer drift on 250 Level and then to the surface through a return air raise (RAR)."

Jan 1, 2019

By F. Calizaya, S. Bhattacharyya

"This study presents the results of a set of sound level measurements carried out in three underground mines where auxiliary fans are used regularly. Sound levels as high as 100 dB(A) by the workings and 115 dB(A) by the fans were measured in these mines. These levels are quite high even for intermittent noise. Ventilation layouts and best practices used to overcome potential problems related to overexposure to fan noise in underground hard-rock mines are presented here. Factors such as fan type, rotational speed, and silencer-duct arrangements and their effects on noise attenuation are discussed. INTRODUCTION Auxiliary fans are used in hard-rock mines extensively. They are used to ventilate development headings, crusher rooms, conveyor transfer points, and underground shops. They are also used in developing long tunnels and ramps. Depending on the flow requirements and space restrictions, single or double stage axial fans with rigid or flexible ducts are used. Usually, they are high pressure (3.75 kPa) fans with flow rates ranging from 7.1 m3/s to 30 m3/s. The input power varies from 15 kW to 113 kW (Mutama, 2004; O’Connor, 2008). Typically, a 113 kW fan can produce sound levels as high a 113 dB(A) (Howes, 2005). Silencers are often omitted for cost reduction purposes or when used, they are not well maintained. Furthermore, silencers provide limited attenuation depending on their length and type. Typically, the sound attenuation ranges from 10 dB(A) for a 1 × D silencer to 14 dB(A) for a 2 × D silencer, where D is the fan diameter. In a mine, the silencer is subject to wear and tear, especially when the silencer is used in harsh environments. The interior lining can get clogged and the acoustic fill can get covered by dust and diesel soot, thus reducing the silencer performance. Periodic cleaning of the interior casing can increase the attenuation capacity of a silencer by 6 to 9 dB(A) (Dabson & Acuña, 2017). However, this requires a special silencer design in which the inner cartridge can be removed, the sound absorbing material replaced, the inner casing cleaned and the whole set retrofitted. A number of techniques can be used to reduce auxiliary fan noise in underground mines. These range from selecting the right fan for the job to installing adequate silencers. The choice depends on the air quantity requirement at the working place, cross-sectional area of the opening, duct diameter, fan type (axial or centrifugal) and local restrictions. Auxiliary ventilation layouts and best practices used to overcome potential problems related to overexposure to fan noise in underground hard rock mines are presented here. Factors such as fan type, rotational speed, duct diameter, and silencer-duct arrangements and their effects on noise attenuation are discussed."

Jan 1, 2019

By John Taylor

"The Highvale Mine in Alberta is owned by TransAlta Utilities Corpora/ion and operated by Mana/fa Coal Lid. It is the largest coal mine in Canada and in 1982 supplied 8.6 million 1onnes of sub-bituminous ""B"" coal to TransAlta's Sundance Ceneraling Plan/. Annual produclion is scheduled to increase in 1983 when the firs/ unit of the new Keephil/s Generating Plant comes on stream and is expec/ed to exceed 11 million tonnes by 1985 when the second unit is commissioned. Coal is mined from several pits in a multi-seam operation. Comprehensive maintenance, drainage and environmental programs form a major part of the operation.IntroductionThe Highvale Mine is located eighty kilometres west of Edmonton, Alberta on the south shore of Lake Wabamun (Fig. I). The mine is owned by TransAlta Utilities Corporation (T.A.U.) and is operated by Manalta Coal Ltd. In 1982, 8.6 million tonnes of coal were supplied to T.A.U.'s 2100 MW Sundance Generating Plant, making it the largest producing coal mine in Canada. By 1985, with two 375 MW units on line at T.A. U .'s new Keephills Generating Plant, annual production is estimated to exceed eleven million tonnes. The generating plants accept crushed unwashed coal from the mine via the coal handling plant system conveyor belts. The coal is classified as sub-bituminous ""B"" and has an average heating capacity of 18.6 MJ I kg.HistoryPrior to 1943 only small scale mining took place in the Highvale area. Between 1943 and 1961 two strip mining companies, Mount Royal Collieries and Continental Collieries operated on the present mine site. Both operations excavated coal along the south shore of Lake Wabamun."

Jan 1, 1985

By Robert B. Parsons

"There is a widespread concern that certain of Finance Minister Michael Wilson's Tax Reform proposals will likely lead to a significant decline in flow through funding after 1988. This does not bode well for the junior exploration sector, which relies heavily on flow-through to finance exploration programs. The exploration industry is actively pursuing various solutions to the problems posed by Tax Reform, in order to ensure that flow-through has a future.IntroductionWhile the proposals contained in Finance Minister Michael Wilson's Tax Reform White Paper may not be as far-reaching as some people had expected, nevertheless the combination of the existing tax rules and proposed new rules offers sufficient complexity to keep pencils sharpened for many months. After having had an opportunity to study Tax Reform since June 18, 1987, the sharpened pencils are suggesting that the White Paper is not without its shortcomings and pitfalls. Insofar as the mineral exploration industry is affected, there is widespread concern that adoption of certain Tax Reform proposals could spell near disaster for mineral exploration in Canada. More specifically, there seems to be a consensus among the industry, as well as some federal and provincial government officials, that the announced phase-out of the ""mining exploration depletion allowance"" (MEDA) would reduce the appeal of flow-through shares to the point where only a fraction of exploration funding would be financed in the future by flow-through."

Jan 1, 1987

By Neillm Alastair S.

"This paper looks at what has happened in the past decade in the rare earth industry, particularly for those companies outside China trying to develop alternative projects to the Chinese dominated supply chain. The rare earth industry has gone through a metamorphosis over the past decade. The industry was basically unknown outside China until overnight it became the next hot topic on the financial streets of Canada and Australia. Suddenly various junior miners shifted from uranium and other out-of-favor commodities to rare earths as funds were easy to access from an investment community that did not understand the complexities of the space. The initial funding was done on traditional junior mining metrics of grade and deposit size. This has morphed over time to:1) Lights versus heavies2) Making a concentrate3) The importance of separation4) Off-take agreementsAt the peak of the market frenzy certain flagship operations were built using the “Not Made in China” moniker. Unfortunately certain errors were made during implementation, which are finally coming to the surface and making the rest of the pack wondering what will happen next. A review and update of some of the mistakes made and lessons learned will be discussed.BACKGROUNDAbout ten years ago awareness started to form around the rare earth industry and various groups recognized that because of the closure of Molycorp, Mountain Pass, and the dominance of China, there was a risk of uncertainty of reliable supply. This was not news for those active in the industry like Rhodia (now Solvay), the Japanese, South Koreans and other key consumers but to others it was like a light went on and rare earths became the new “.com” trend for investment banks, investors and some mining companies looking for the next hot topic.In the late 1990’s Molycorp accounted for around 20-25% of the world’s supply of rare earths, mostly lights (La, Ce, Pr and Nd), with small amounts of heavies from other sources. Then environmental issues forced the closure of the operation at Mountain Pass. Within six months China had increased production to plug the gap in supply. Around that time China was developing a strategy to leverage their position in rare earths and implemented a series of regulations to increase the value added component of rare earths inside China."

Jan 1, 2016

By Philip M. J. Gray

"The real cost of conversion from ore to semi-fabricated non-ferrous metals has been increasing for many years. Consumer resistance and improved knowledge and techniques now available justify investment in revolutionary as well as evolutionary methods of extraction. Metallurgical factors in current practice which preordain high production costs are identified as: smelters' demand for clean minerals, use of processes with low intensity of working per unit of reactor volume, use of low-velocity reactions, use of long reactor retention times relative to the speed of reactions, dilution of values in solution and commitment to electric power as a source of energy.Six new types of flowsheet are proposed for processing from ore to metal, composed of steps which are economic to construct and maintain and making maximum direct use of fossil fuel and the energy content of minerals. The basic knowledge and technology for developing these flowsheets exists. It is very tentatively suggested that these routes might reduce the capital and production cost for conversion of ore to metal by 30-50%."

Jan 1, 1980

By N. Erarslan, M. Ghamgosar

The size of rock fragments depends on the nature of the loading applied the strength of the minerals and the texture of the rock. Research in the literature demonstrates that there is a distinct difference in the rock fracturing process for static and cyclic loading. The tensile strength of brittle rocks is also one of the most significant parameters influencing the rock fracturing process and the propagation of micro-fractures on the crushing, blasting and cutting of rock. The Brazilian indirect tensile test, one of the methods approved by the International Society for Rock Mechanics (ISRM), has been used to determine rock fracture behaviour under different cyclic loading modes. In this study, the dimensions of Brisbane Tuff specimens have been selected according to the method outlined by the ISRM. The main aim of this study is to evaluate the effect of cyclic loading amplitude and frequency on the Fracture Process Zone (FPZ) at the micro-, meso- and macro-scales. The post-failure behaviour of the Brisbane Tuff specimens was obtained under cyclic loading with frequencies varied from 1 to 10 Hz. The amplitude was varied from 10% of Ultimate Tensile Strength (UTS) up to 80% UTS. Laboratory investigations of rock fragment size revealed that different loading frequencies and amplitudes produce different FPZ dimensions. Multivariate Analysis of Variance (MANOVA) results demonstrated that the FPZ dimension is relatively sensitive to the frequency change. Fragment size analysis showed that the FPZ is a consequence of the initiation, propagation and coalescence of micro-fractures and depends on the nature of the loading. Laboratory evidence showed that the FPZ dimension, for the cyclic tests performed on Brisbane tuff, is ranged from 0.07 to 20 mm. The achievement of this study highlights a key finding in the understanding of fracture patterns and propagation models in the FPZ under cyclic loading, which is the dominate mechanical action in the oscillator disc cutter (ODC).

Jan 1, 2015

By J. T. Vehkala, S. S. Kerr, D. E. Robertson

"Since the late 1970s, extensive work has been carried out at Placer Dome Inc. 's Dome Mine to develop new mining methods and equipment to improve the productivity of narrow vein mining (Mining Magazine, Oct. 1986, pp. 308-317; Mar. 1988, pp. 176-/79). This work has been focused on mining veintype deposits varying from 0.9 m to 1.5 m in width using open stoping and cut-and-fill mining methods.In 1989, the Dome Mine entered into a contract with Ram Raising Ltd., a joint venture company of Angus Martin and I.S. Redpath Ltd., to develop and mine a narrow vein test stope using an Alimak Raise Climber. Early results have been favourable, indicating that Alimak methods can be used successfully to mine narrow vein are.HistoryThe Dome Mine, which has been in continuous operation since 1910, is located in South Porcupine, part of the city of Timmins, Ontario. The mine is wholly-owned and operated by Placer Dome Inc. and is part of Placer Dome Inc.'s international stable of of 19 mines."

Jan 1, 1990

By Dennis Z. F. Mraz

"Because rock salt and pot ash formations contain particles capable of elastic deformation, the material has usually been compared with various rheological models containing elastic elements. Extensive laboratory testing of salt and potash samples resulted in various theoretical conclusions based on conditions quite different from those in a deep mine. It is felt that sufficient data have now been collected from underground measurements and observations to demonstrate the inelastic behaviour of salt masses in a deep mine. The conditions in deep salt strata can be defined as near hydrostatic, because the acting pressures are very high compared to the negligible elastic limit of the salt. The pressure field and creep around the single opening is a function of its shape, size and age. The same factors, together with extraction, determine the behaviour of the mining a rea. The application of the correct analytical method in mine design can significantly improve the excavation techniques and predetermine the long-term behaviour of openings."

Jan 1, 1973

By Sakellariou M., Ferentinou M.

Determination of the nonlinear behavior of multivariate dynamic systems often presents a challenging and demanding task. Therefore, complex geomechanics systems are an ideal area for the application of intelligent methods. Often the physical problem is controlled by nonlinear equations, conveying to the use of neural networks. Hudson, (1992a), aiming at efficient engineering modelling and design, introduced and developed Rock Engineering Systems (RES) approach, through the implementation of generic interaction matrix GIM. This approach has been used for a wide variety of rock engineering and other problems, resulting in many case studies available, which illustrate the application of RES to rock engineering problems. Considering the spectrum of the coding methods for the Generic Interaction Matrix, we suggest an objective coding approach. Among the five proposed coding GIM methods, the coding method according to the slope of Pi and Pj relation is relatively accurate, but it might be difficult or impossible to establish or estimate the exact relation of Pi vs Pj for most of the variables involved within a rock engineering system. Self organising maps, are a special type of unsupervised artificial neural networks, which can learn from complex, multidimensional data, and transform them to visually decipherable clusters. The proposed, coding of the GIM, is performed through the combined use of scatter plots produced through, (SOM), and the coding according Pi vs Pj slope. Naghadehi et al., (2013) constructed a database of worldwide experience, in open-pit mine slope stability, the selection of the principal factors was based on Hudson (1992a) who proposed an ‘atlas’ of factors affecting the stability of rock slopes. Slope classification was performed according to status of stability. The rating of the GIM matrix was completed, coupling scatter matrix produced by SOM training, and Pi vs Pj slope plot. Results refer to the identification of clusters, according to status of stability within the original multivariate data set, and the rating of the principal factors according to the dominance and interaction intensity within the open pit mines RES.

Jan 1, 2015

By Debasis Deb, Ankur Narang, G. P. Raja Sekhar, Kamal C. Das

"The stability of underground structures made (especially) in jointed rock mass is of the utmost important to designers, engineers and operators. Rock bolting is generally being practised to reinforce excavation walls and roofs by minimizing the movement of rock joints. This study proposes a new analytical model for the prediction of displacements, axial load and shear stress of a fully grouted rock bolt intersected by single or multiple rock joint(s). The governing equations for rock bolt are derived based on the assumption that shear force generated by slippage along the bolt-grout interface has a linear relationship with respect to the relative displacement at the interface. The proposed model is novel compared to the existing literature in the sense that it accounts for rock kinematics as an enriched sum of a continuous part (elastic) and a discontunous (jump) part due to the presence of joint planes. The complete solution of the bolt displacement, axial load and shear stress is derived as a function of the rock displacements, and, it comprises of Heaviside and/or Dirac delta functions in the solution space due to the jump at the intersection point(s) of bolt(s) and joint(s).Our novel solution is able to predict the elastic behavior of a grouted bolt, subjected to opening of the joint planes in pull-out test and also in excavated tunnel. These two cases also serve as benchmarks for grouted rock bolts with multiple joints and can be used for validation of numerical and experimental models. Further, the solution is applied to analyze the behaviour of grouted rock bolt as well as cable bolt installed in circular tunnel, with variations in rock joint(s) opening displacement, shear stiffness in the boltgrout interface and locations of the joint planes. Results indicate that for a specified grout stiffness, the maximum axial load developed in the bolt for discontinuous distribution of rock mass displacement is significantly higher than that of the continuous distribution of rock displacement. This paper provides an analytical interpretation of bolt beaviour considering multiple joint planes with variable joint opening displacements. The results obtained via the analytical method are in line with the corresponding investigation done by other authors. Thus, our analytical treatment can be used to understand bolt behaviour in realistic situations."

Jan 1, 2015