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By J. Gómez-Hernández, P. K. Kaiser

Abstract The process of stress-induced fracturing around underground excavations in brittle rock is associated with dilation or volume increase of the failed, fractured rock. Different attempts to account analytically for this dilation have been made within the framework of plasticity theory. This theory has been developed mostly for metals, strain-hardening materials or soils, but brittle failure of rock-like materials is characterized by strain-softening behaviour and the volume change is dominated by geometric factors, which may violate stability principles of plasticity. In this work a semi-empirical Rock Mass Bulking Model (RMBM) was developed, using as starting concepts: dilation angle, plastic strain rates, effective deformation modulus, effective Poisson's ratio, Griffith locus, and the definition of a bulking factor BF introduced by Kaiser et al. (1996). The model was calibrated in order to obtain bulking factors that are consistent with experimental data and case studies of measured bulking around underground excavations. Résumé La fracturation provoquée par le stress autour des excavations souterraines dans le minéral friable est associée à la dilatation ou à l’augmentation du volume de la roche en rupture. Dans le cadre de la théorie de la plasticité, différents essais ont été faits dans le but de trouver une justification analytique pour cette dilatation. Cette théorie a d’abord été élaborée pour les métaux, les matériaux ou les sols d’écrouissage, mais la rupture fragile de matériaux d’aspect rocheux est caractérisée par un comportement d’amollissement et le changement de volume est dominé par des facteurs géométriques, ce qui pourrait ne pas être conforme aux principes de stabilité de la plasticité. Dans le présent ouvrage, un Modèle semi-empirique de masse rocheuse a été élaboré, dont les concepts initiaux sont les suivants : angle de dilatation, vitesse de fluage plastique, module effectif de déformation, coefficient effectif de Poisson, locus de Griffith, et la définition d’un facteur de foisonnement FF apportée par Kaiser et al. (1996). Le modèle a été calibré afin d’obtenir des facteurs de foisonnement qui soient conformes aux données expérimentales et aux études de cas sur le foisonnement mesuré autour des excavations souterraines. Kurzfassung Der Prozess von Brüchen in unterirdischen Abgrabungen in sprödem Gestein ist mit der Ausweitung oder der Volumenzunahme des gebrochenen Gesteins verbunden. Verschiedene Versuche im Rahmen der Verformbarkeitstheorie haben versucht, diese Ausweitung analytisch festzustellen. Die Verformbarkeitstheorie wurde hauptsächlich für Metalle, kalthärtende Werkstoffe oder Böden entwickelt, da sprödes Versagen von Gestein ähnlichen Werkstoffen von kaltenhärtendem Materialverhalten gekennzeichtnet ist, und die Volumenveränderung von geometrischen Faktoren beherrscht wird, die die Stabilitätsprinzipien der Plastizität übertreten. In dieser Arbeit wurde ein halbempirisches Rock Mass Bulking Model (RMBM) (Modell für das Aufgehen der Gesteinsmasse), entwickelt, für das die folgenden Anfangsprinzipien benutzt wurden: Ausweitungswinkel, plastische Fliessensätze, wirksames Verformungsmodul, leistungsfähiges Poissons Verhältnis, die Griffith Ortskurve und die Bestimmung eines Aufgehensfaktor BF1 der von Kaiser et al. (1996) eingefürt wurde. Das Modell wurde so kalibriert, dass es die Aufgehenfaktoren erzielte, die mit den Vesuchsangaben und den Fallstudien von Aufgehensmessungen in unterirdischen Abgrabungen übereinstimmen.

Jan 1, 2003

By Danqing Gao, Brijes Mishra

Spatial variance of rock properties is an important characteristic of rock which addresses the heterogeneity of mechanical and physical properties and their effect on underground mining. Assessing spatial variance can be useful for both locating potential difficult grounds and performing reliability analysis in the mining support system. This study shows a microscale numerical model for rock material based on continuum mechanics. To consider the spatial correlation factor of mechanical properties in realistic rock mass, this study introduces a spatial correlation concept into the traditional type III extreme value distribution model. Based on the improved microscale random model, we conducted a series of numerical uniaxial compressive tests and one longwall mine model to investigate the progressive failure of rock. The results show that spatial correlation factor can significantly affect the load-deformation curves and fracture patterns. The spatial variance model was applied to a longwall mine that included several cutting sequences to observe the influence of the spatial variance on roof behavior. The cohesion and friction random fields induced failure that propagated randomly through the immediate roof in different entries. The results showed that the spatial variance provides an accurate prediction of erratic roof falls in coal mines.

Jul 20, 2020

By Danqing Gao, Brijes Mishra

Heterogeneity in rock formation affects both rock behavior and strength. Spatial variance of rock properties is an important characteristic of rock that addresses the heterogeneity of mechanical and physical properties and their effects on underground mining. Assessing spatial variance can be useful for locating potential difficult grounds and for performing reliability analysis in the mining support system. This study presents a spatially correlated, random model to investigate the influence of rock heterogeneity on rock strength and failure propagation. A random field database with specific spatial correlation was created for each physical-mechanical property using laboratory data and the extreme value stochastic model in MATLAB. Based on the improved microscale random model, we considered one three-dimensional numerical model to study a mine operating in the Pittsburgh seam. The influence of random field data on entry roof was investigated. The realistic random field database added two scale-measured parameters from horizontal and vertical directions to control the spatial correlation length. A number of cutting sequences were also considered in order to identify the effect of spatial variance on roof behavior. The results show that spatial variance provides an accurate prediction of erratic roof falls in coal mines.

By Sidney L. Hansen

This report was written because of concerns of the possible error involved when stopping leakage is incorrectly assumed to be turbulent. It is common practice to use turbulent flow to characterize each airway branch for computer models of mine ventilation circuits. This report addresses computer methods to accurately model air-leakage paths. A graphical method is described for deriving the equations of leakage through stoppings. The significance of modeling leakage according to the proper flow regime (turbulent or laminar) is demonstrated by the following method. A hypothetical mine was developed to represent present-day conditions. The stoppings of the mine were chosen to leak according to laminar flow properties. The mine was represented by constructing two base models. One base model used turbulent leakage equations for each stopping, while allowing the corresponding resistances to vary. The other base model used the correct laminar leakage equations and held corresponding resistances constant. The mine circuit was then expanded to demonstrate future development. The expanded portion was designed with stoppings that were identical to those in the base mine. The mine in the future state was represented by two projection models. Each projection model was an extended version of its associated base model; one used turbulent leakage equations and one used laminar leakage equations for stoppings. The laminar projection was theoretically correct and is used as a basis for comparison of differences in airflow quantities. Rather than modeling every leakage path for stoppings, a more practical approach is also discussed. A good level of accuracy is maintained by combining leakage paths if the proper flow equations are used. This method was used on the hypothetical mine projection and the flows were very similar to the theoretical values.

Jan 1, 1989

By Shoma Sinha, Nirmal K. Sinha

Deformation in a material at any temperature is known to consist of two major components - a reversible (elastic) part and an irreversible part (often called plastic). What is not universally known is the fact that at high temperatures greater than about 0.4Tm, where Tm, is the melting point in Kelvin, the reversible part includes not only elastic but also a delayed elastic (recoverable but time dependent) component. A very simple computational model is presented here for a constant-strain stress relaxation test (SRT) on the basis of a three-component constant-stress rheological equation derived from strain relaxation and recovery test (SRRT) data. It is shown that the rapid stress reduction during the early periods of relaxation when the stresses are high is governed primarily by delayed elasticity irrespective of the imposed strain level. This is in contradiction to the popular concept prevailing today. The asymptotic approach to a quasi-stable stress rate at longer times and lower stresses is, however, controlled by viscous flow (power-law creep). The validity of the theory is examined by comparing the predictions with experimental results obtained for a titanium-base alloy Ti-6246 at 0.45Tm.

Jan 1, 2004

By V. K. Kalyani

The present paper discusses a three layer feed forward artificial neural network (ANN) model, trained using the error back propagation algorithm, has been established to simulate the column flotation circuit used for beneficiation of Sillimanite. Parameters such as superficial air velocity, wash water rate, froth height, % solid, feed velocity, sodium silicate and oleic cid are considered as process operating variables and % yield of Sillimanite is the output of the experiment. The results from the ANN modeling, involving the non linear relationship between inputs and outputs, indicate good agreement with experimental observations. The network model validates the experimentally observed trends. The optimal model parameters in terms of network weights have been estimated and can be used for computing parameters of the process over wide-ranging experimental conditions.

Jan 1, 2006

By André C. Zingano

The domino effect in a violent pillar collapse occurs due to the redistribution of stress in the remaining pillars near the collapse, and this stress transfer occurs in the immediate and main roofs. The remaining pillars do not have enough load capacity to support this overstress and also fail, and the domino effect propagates further to the entire panel. The domino effect does not occur only due to low load capacity of the pillars, but also the roof rock mass quality, because the stress is transferred by the roof. In high competent roof without discontinuity (fault), like massive sandstone seam, the deformation of the roof is the cause of pillar collapse extension and propagation. Depending on how close it is approaching the collapse limit; the immediate and main roofs behave differently. When it is close to the collapse limit roof convergence and pillars compression occur. Conversely when it is far from the collapse limit divergence and pillars decompression occur. This is called the arc-effect. This paper studies this behavior of the roof (immediate and main roofs) using numerical modeling to simulate the roof deformation and stress distribution in the roof and pillars. This simulation represents the progression of pillar collapse and shows the zone of convergence and divergence of the roof, and also the effect of this behavior on pillar confinement. Two-dimensional plain strain model was applied to simulate the arc-effect. The simulation results were compared to those of the instrumentation that was installed before the collapse. Keywords: pillar collapse, room and pillar, numerical modeling

Jan 1, 2005

By Tiruttani Munikamal, Suresh Sundarraj

"A numerical model of the induction hardening process of steel cranks has been developed and the predicted results of temperature and phase distribution during this solid state phase transformation process are verified with experimental data from the literature. This heat treatment process involves heating the crank to the austenitic temperature range followed by rapid quenching in water to harden the surface of the crank. The model has been developed using ABAQUS, commercial FEA software. The formation of martensite, pearlite, and retained austenite phases are modeled and implemented through a user defined function in ABAQUS. A sensitivity study on the various process parameters affecting the amount of phase distribution has been carried out.IntroductionThe type of surface and sub-surface microstructure as well as the residual stresses that are present in a component after manufacturing, significantly affects it fatigue performance. The wear resistance of the automotive components such as crankshaft, gears, camshaft and bearings depends on the surface hardness. In order to achieve the surface hardness, these steel components are subjected to a type of quench hardening heat treatment process. There are several heat treatment processes available for the industrial application to improve the mechanical properties of the final part. Case hardening using induction heating is one of the widely used industrial techniques for improving the surface microstructure of a steel component. It consists of two stages i.e. induction heating cycle, followed by quenching in a fluid medium (usually water or oil)"

Jan 1, 2012

By Sadough vanini Ali

Charpy impact energy of functionally graded steels produced by electroslag remelting in crack divider configuration has been modeled in various strain rates. It has been well known that majority of materials indicate different behaviors under different strain rates and temperatures. Therefore, modifying the elastic-plastic model considering the effects of strain rates and temperature gives us an acceptable prediction of these composites behaviors in impact test. In this investigation, graded steel was divided in to several layers in which the layers have the same strains under the impact. Constitutive equation describing the flow stress variations as a function of strain rates and temperatures, have been used to express the stressstrain behavior of layers. The parameter values of constitutive equation determined for all the layers via using the boundary conditions based on composite graded behaviors which were the characterized ferrite, austenite, bainite and martensitte phases. Consequently by applying the rule of phase mixtures and ascribing the impact energy of each layer to the area of stress-strain curve of the same layer, the whole impact energy of composite is the sum of layers impact energy with considering the layers volume fraction.

Oct 1, 2011

By S. Sundarraj

The morphological transition between columnar and equiaxed structures is an important solidification phenomenon frequently observed in castings, especially complex parts with varying cross-section, The mechanical properties and the occurrence of defects such as hot tears are strongly dependent on the structure formed in the casting. Hence, it is important to understand the conditions leading to columnar or equiaxed structures. Although extensive work has been done in modeling solidification systems, almost all of the existing models are based on the assumption that the structure formed in the casting is either purely columnar or purely equiaxed. Prediction of the columnar-equiaxed transition (CET) requires a solidification model which accounts for the formation of both columnar and equiaxed structures, along with related microscopic and macroscopic solidification phenomena. In this paper a CET model is presented which: (i) takes account of both columnar and equiaxed structures, (ii) accounts for macroscopic heat transfer coupled with microscopic phenomena such as nucleation, growth and microsegregation, (iii) satisfies solute conservation, and (iv) is easy to implement in commercial finite element and finite difference software. The proposed model predictions of CET have been validated with available experimental results for a uni-directional solidification of an aluminum-copper alloy. A sensitivity analysis has also been carried out to determine the effects of various parameters on the CET model predictions. The model is being extended to other alloy systems and more complex geometries. This work will be published in due course.

Jan 1, 1996

By M. Abdollahi, M. R. Khalesi, Y. Kianinia, A. Khodadadi Darban

High cyanide consumption during the processing of gold ores with high sulphide minerals can make the typical cyanidation uneconomic. Also cyanide is a toxic material and environmental concerns of cyanide compounds are serious. Optimization of cyanide consumption requires a methodology to estimate the amount of exposed cyanicides, the kinetic of their dissolution and estimation of formation of cyanide complexes which consume the free cyanide. In this paper, a methodology to estimate cyanide consumption by modeling the minerals and gold leaching kinetic based on a liberation model and speciation of all possible cyanide related species in the solution is presented. The results showed that this methodology could successfully estimate the cyanide consumption based on mineralogical data with very lower number of parameters compared to empirical models present in the literature, while it offers the prediction of formation of all cyanide complexes which could be used for optimization purposes.

Jan 1, 2017

By Mohsen Mohammadi, Edward Cyr

"To date, several studies have been performed on the static mechanical properties of SLM-AlSi10Mg alloy. There have also been more recent studies on the relation between scan strategy, texture, and mechanical properties of SLM metals and composites. However, there is a huge knowledge gap in the available literature regarding texture and mechanical behavior of SLM-AlSi10Mg alloy under high strain rates. Therefore, in this study, dynamic mechanical behavior of AlSi10Mg_200C alloy manufactured by DMLS technique was investigated at high strain rates ranging from 900/s to 1700/s using Split Hopkinson Pressure Bar. Texture using X-ray diffraction technique of the initial samples were measured. The yield strength, peak flow stress, and ductility increased in all samples with increase of strain rate. TEM studies have also revealed evidence of continuous dynamic recrystallization in grains after 900/s–1700/s strain-rate tests. A Taylor polycrystal crystal plasticity constitutive model was then developed to capture and predict the texture evolution and mechanical response under dynamic loading, using plastic work as a critical parameter for the onset of recrystallization.INTRODUCTION Additive manufacturing (AM) powder techniques are among the fastest advancing breakthroughs in manufacturing in recent years, defined by a bottom-up layer by layer process of joining with energy input from lasers or electron beam (Herzog et al., 2016; Gibson et al., 2015). Among alloys fabricated by SLM, AlSi10Mg is of high interest to industry and academia due to its low density, high specific strength and excellent corrosion resistance, making this alloy a viable contender for aerospace, automotive, and marine applications. Circumstances such as car crash or bird aircraft strike hazards subject potential additively manufactured AlSi10Mg parts to impact loadings. This drives an interest in understanding and predicting dynamic behaviour of these alloys. AlSi10Mg is the AM counterpart of A360 die-cast aluminum, which possess hypoeutectic microstructure (Li et al., 2015). Up to the present time, many studies have presented the mechanical properties of SLM-AlSi10Mg alloy. The mechanical properties and microstructure of AlSi10Mg produced by selective laser melting (SLM) or DMLS techniques can be controlled using different parameters, such as feedstock powder (Asgari et al., 2017), and process parameters (Olakanmi et al., 2015). The microstructure and mechanical properties of AlSi10Mg can also be controlled using post heat treatment after SLM process Li et al., 2016). The mechanical properties of SLM-AlSi10Mg are sensitive to strain rate and can both change under quasi-static (Rosenthal et al., 2017) and high strain rates (Asgari et al., 2018). However, a significant knowledge gap in available literature regarding modeling these behaviours, and especially micromechanical modeling of dynamic behaviour."

Jan 1, 2018

By Walter C. Labys

This paper reports on recent modeling efforts to analyze the eastern U.S. steam coal market with a cross-sectional econometric as well as a quadratic programming approach. The background to coal modeling is examined first. The particular aspect of the steam coal market to be modeled are then presented and the corresponding coal model described. Both empirical results and rigorous mathematic pertubation analysis are presented. Conclusions are then drawn regarding potential modeling applications in the policy area.

Jan 1, 1979

By Susan A. Fredholm, Randolph E. Kirchain, Elsa A. Olivetti, Jeremy R. Gregory, Jeffrey B. Dahmus

"A general model for evaluating the economic and environmental performance of electronics recycling systems is developed. This model comprehends the three main functions in a recycling system – collection, processing, and system management – and aims to enable quantification of the impact of context and system architecture on the economic and environmental performance of electronics recycling systems. Such a model can be used both to evaluate and improve existing electronics recycling systems, as well as to design and implement new systems. A case study, based loosely on Maine, is presented to show the utility of such a model.IntroductionAs recycling systems for complex durable goods (CDGs), and in particular for waste electronics, become more widespread, understanding the economic and environmental performance of such systems becomes critical, both to enable improvement of existing systems and to inform the design of new systems. However, with the range of possible system architectures and the important role of locational characteristics (context), understanding the determinants of system performance is challenging [1]. To address this issue, a modeling framework to project the economic and environmental performance of CDG recycling systems, based on contextual and architectural characteristics, has been developed.The modeling framework presented here comprehends the three main functions – collection, processing, and system management – which are common to most recycling systems. These three functions are modeled using a variety of modeling techniques and serve as a bridge between inputs related to system context and system architecture, and outputs related to economic and environmental performance. The models developed here are intentionally meant to be both broad, in order to address entire recycling systems, and general, such that many different systems, both real and hypothetical, can be analyzed."

Jan 1, 2008

By Liming Yuan

Barometric pressure changes affect air density, leading to change in the mass of the gas in the gob. When the barometric pressure decreases, the volume of gas in the gob expands, while the volume of gas contracts when the barometric pressure increases, causing the gob to breathe out and in. Although the concept of gob ?breathing? is simple, its effect on spontaneous heating of coal in the gob area is not clear. In this study, computational fluid dynamics (CFD) simulations were conducted to model the spontaneous heating of coal in longwall gob area under measured barometric pressure changes. A single longwall panel using a bleederless ventilation system was simulated. If there is no barometric pressure change, the intake airflow rate is equal to the return airflow rate. When the barometric pressure changes, these two airflow rates are no longer equal, and the difference between the two airflow rates represents the airflow rate the gob breathes in and out. The effect of inflow and outflow of gas on the potential spontaneous heating in the gob was investigated using the CFD model developed in our previous study. The effect of barometric pressure changes on the spontaneous heating was found to be dependent on the gob permeability and the coal oxidation rate. The effect of barometric pressure changes on oxygen concentrations in the gob was also examined.

Jan 1, 2010

By Liming Yuan, A. C. Smith

Barometric pressure changes affect air density, leading to change in the mass of the gas in the gob. When the barometric pressure decreases, the volume of gas in the gob expands, while the volume of gas contracts when the barometric pressure increases, a process which causes the gob to “breathe” out and in. Although the concept of gob “breathing” is simple, its effect on spontaneous heating of coal in the gob area is not clear. In this study, computational fluid dynamic (CFD) simulations were conducted to model the spontaneous heating of coal in the longwall gob area under measured barometric pressure changes. A single longwall panel using a bleederless ventilation system was simulated. If there is no barometric pressure change, the intake airflow rate is equal to the return airflow rate. When the barometric pressure changes, these two airflow rates are no longer equal, and the difference between the two airflow rates represents the airflow rate the gob breathes in and out. The effect of inflow and outflow of gas on the potential spontaneous heating in the gob was investigated using the CFD model developed in our previous study. The effect of barometric pressure changes on the spontaneous heating was found to be dependent on the gob permeability and the coal oxidation rate. The effect of barometric pressure changes on oxygen concentrations in the gob was also examined.

Jan 1, 2010

By Gabriel Walton, Sankhaneel Sinha

"Rib failures are a major hazard in underground mining. When pillars are subjected to loading, extensile cracks are generated parallel to the excavation boundary, which can manifest as rib falls. A common mitigation measure is to install supports, especially bolts, normal to the rib surface. The type and spatial distribution of these supports along the pillar is often based on experience rather than comprehensive analysis. Since conducting field experiments is often impractical and expensive, a convenient alternative is to perform 3D numerical modeling. In this study, FLAC3D has been used to capture the interaction of rib bolts and the failure processes governing the stability of pillars. An associated goal is to determine whether, at all, a continuum software is capable of modeling the effect of supports. The modeling involved two important steps: selection of a proper constitutive model, and, explicit simulation of rock bolts. Based on precursory work in the last decade, an S-shaped strength criterion was chosen that can describe the tensile fracture mechanism of rock at low confinement and shear failure mechanism of rock at high confinement. The built-in pile structural element in FLAC3D is a simplified representation of the complete bolt system. Hence, the different components of a rock bolt (i.e., steel, grout, steel-grout interface, and grout-rock interface) have been explicitly modeled within the rock mass and then tested for its ability to replicate the ground-support interaction behavior. INTRODUCTION Rib failure-related hazards and injuries have plagued the mining industry for decades (Mohamed et al., 2016; Iannacchione and Prosser, 1998). In highly stressed environments, excavation parallel cracks are the primary initiators of skin instability. In absence of any support, this failure can indirectly destabilize the excavation by increasing the exposed span of intersections and roadways. Over the last two decades, there have been numerous injuries (fatal and non-fatal) due to rib failures in underground coal/non-coal mines."

Jan 1, 2017

By Mick Lownds, Ruilin Yang

The potential advantages of electronic detonators with accurate timing have been increasingly recognized by the blasting community. However, in comparative blasts the results with pyrotechnic timing are sometimes comparable to those from electronic timing. Statistical variation in blast results is a plausible cause of these observations.

Jan 1, 2011

By Marianella Perez, Williams Calderón, Gonzalo Montes-Atenas

The lack of fresh water sources, particularly in the Northern part of Chile, has driven the mine sites to search for new and sustainable paths to obtain water resources to run minerals processing operations. Among them, the use of seawater in concentrators appears as an interesting solution to this problem. However, the presence of seawater will have an impact onto the operation, not only because it will enhance corrosion reactions in the equipment installed in a plant, but also because it may affect how particles will effectively be processed across the numerous unit operations existing in the mine site. Among such unit operations, the grinding stage is a highly regarded as it defines the success of the separation of valuable minerals from gangue material in the froth flotation operation. Then, one important aspect to be addressed is to understand how the presence of seawater will affect the different mechanisms acting during the operation of a ball mill. The aim of this research work is to assess the effect of changing the aqueous matrix from process water to seawater in ball mills onto the mill performance. The methodology considered the use of Fluent® software and its capabilities to run numerical simulations with heterogeneous media. On one hand, from the data analysis, it is possible to infer that breakability mechanisms should not be significantly affected. On the other hand, the high ionic strength of the matrix should impact importantly particle transport mechanisms within the mill. Particularly, when transporting finer particles. Rheology results were in agreement with previous published research studies suggesting the suspensions to behave as Newtonian, Dilatant o Pseudo-plastic fluid depending on the amount of fine particles present in the grinding media. The latter will result in changes in the residence time of particles in the mill producing overgrinding or an excess in the circulating loads.

Jan 1, 2014

By Alaina B. Hanlon

Keywords: Undercooling, Convection, Dendrites, Stainless Steel, Levitation Certain Fe-Cr-Ni stainless steel alloys solidify from an undercooled melt by a two-step process in which the metastable ferrite phase forms first followed by the stable austenite phase. Recent experiments have shown that the lifetime of the metastable phase is strongly influenced by flow within the molten sample. The current research will provide insight to why flow affects the metastable phase. This new understanding will lead to the use of convection to control microstructural evolution in spray-forming of stainless steels. Simulations using a commercial computational fluid dynamics package, FIDAP, yield a range of convective flow velocities that cause mechanical damage to the dendrites which is compared to experimental results. If the convective velocities are great enough that the dendrites bend, then low angle boundaries form at the points of collision. These result in high energy sites that could serve as nuclei for the stable phase.

Jan 1, 2005