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By D. Kruse, M. Sanaei

"3D finite element models of the Segmentally Lined Shaft (SLS) structure are simulated as means of numerical analyses of the system’s structural behavior. Top-down constructed rings, comprised of precast concrete segments, create a large diameter, relatively shallow underground space that can be utilized for various applications. To further investigate the effects of soil conditions and different loadings on the shaft structure, the FE model was run under various boundary conditions. Simulations include a) effects of various soil layers on the SLS, including a circumferential boundary of modified ground, b) effects of various soil layers on the SLS without any ground modification, c) Seismic analysis of the SLS with ground modification and d) Seismic analysis of the SLS without any ground modification. Comparing the analyses outcomes emphasizes the significance of the inclusion of the ground modification boundary in the structural performance of the SLS. INTRODUCTION TO SLS Underground structures are classically built rectangular in shape, which normally requires a two-step construction process beginning with installation of temporary shoring to support earth loads during the excavation, followed by the construction of the permanent structure. Attractive and practical alternatives are circular shafts referred to as segmentally lined shafts (SLS). The structure consists of a stacked series of rings formed from an assemblage of precast concrete segments. Top-down constructed systems of large diameter, relatively shallow SLS structures provide both temporary earth support during excavation and permanent structural support for many civil and building applications. The circular shafts sustain the lateral earth pressure mainly through hoop-stress mechanism, resulting in improved stability and structural efficiency. Cylindrical shell structures with large diameter to wall thickness ratios are prone to buckling under external pressure. In typical designs of small diameter shafts and tunnel linings with small diameter to wall thickness ratios, nonlinear buckling analysis (i.e., nonlinear geometric analysis) is usually not considered, since the buckling capacities for those structures are much higher than typical pressures encountered at their design depths. With an economically viable wall thickness, buckling becomes a critical issue, which should be addressed, for circular shafts with very large diameters. In the design and construction of the SLS, the stability of the structure can be improved by modifying the soil surrounding the circumference of the shaft to a limited thickness and to about 10 ft below the finished shaft structure. This thick wall of soil mixed with cement creates a composite integrated structure while serving additional purposes such as ground control and ground water seepage cutoff."

Jan 1, 2016

By W. G. Pariseau

Recent advances in rock-mass mechanics and computational technology now allow for the stability analysis of excavations in "wet" mines where mining-induced changes in rock mass deformation and fluid flow are coupled and time dependent. In addition to water pressure and flow in jointed, possibly porous, rock masses, all of the usual dry-mine parameters, including the premining stress state and rock-mass properties, are taken into account. Finite-element analyses of shafts and tunnels, as circular, elliptical, rectangular and arched-rectangular hole shapes excavated in an initially stressed and pressurized rock mass, indicate that the usual guidelines for optimum shape and orientation of single openings apply. Here, optimum means maximizing the minimum wall safety factor or, equivalently, minimizing the peak stress concentration. The results also show that failure originates in elements at the wall and the minimum safety factor at the wall in the wet case is always less than the dry case, regardless of drainage time allowed.

Jan 1, 1997

By W. G. Pariseau

Recent advances in rock mass mechanics and computational technology now allow for stability analysis of excavations in "wet" mines where mining-induced changes in rock mass deformation and fluid flow are coupled and time-dependent. All the usual dry mine parameters including the premining stress state and rock mass properties are taken into account, in addition to water pressure and flow in jointed, possibly porous, rock masses. Finite element analyses of shafts and tunnels as circular, elliptical, rectangular and arched-rectangular hole shapes excavated in an initially stressed and pressurized rock mass indicate that the usual guidelines for optimum shape and orientation of single openings apply. Here, optimum means maximizing the minimum wall safety factor, or equivalently, minimizing the peak stress concentration. The results also show that failure originates in elements at the wall and that the minimum safety factor at the wall in the wet case is always less than the dry case regardless of drainage time allowed.

Jan 1, 1995

By W. G. Pariseau

Conventional barrier pillars in underground coal mines are intended to protect mains and sub-main entries for relatively long periods of time. Inter-panel barrier pillars that may be used in especially deep coal mines, say, below 800 m (2,400 ft), are intended to protect longwall panel faces and adjacent panel entries for the life of nearby panels. Barrier pillar failures have serious consequences, especially when failure is sudden and catastrophic. Design of barrier pillars is thus of considerable importance to safety and efficiency of operations. Locally, failure occurs at the limit to elasticity when stress tends to exceed strength. Strength of rock is stress dependent, so an analysis of stress is central to rational design of barrier pillars. There are several approaches to stress analysis for coal mine pillar design that range from the simplified but popular tributary area method including variations that use empirical definitions of the tributary area (volume) to more sophisticated numerical methods such as the boundary element method and the finite element method. Despite ease of use, empirical methods are limited and always suspect when applied to conditions beyond their scope of definition, while boundary element methods do not generally include pillars in the solution domain. The finite element method is not so restricted and thus is a natural choice for conventional and inter-panel barrier pillar safety analyses. Caving of roof strata certainly affects the distribution of stress about longwall faces and nearby barrier pillars. Conventional wisdom that considers roof strata to respond as cantilever beams indicates the longer the span the greater are loads on longwall faces and face supports. Failure of roof beams, caving, shortens spans and relieves face and support loads. The same view is applicable to barrier pillars in that long roof spans outside of barrier pillars leads to higher pillar loads than short spans. Hence, caving should be beneficial to barrier pillar safety. However, the benefit may be small depending on the extent of caving and only in the form of a slight reduction in overburden weight transmitted to the barrier pillar, especially in case of inter-panel barrier pillars. FINITE ELEMENT MODEL Finite element models for stress analysis in rock mechanics are formulated in consideration of physical laws, kinematics, and material laws. These models meet the essential requirements for equilibrium of stress, satisfy strain displacements relations, and in a general sense, relate stress to strain through material laws, often referred to as constitutive relations. The last may be complex and replete with nonlinearities. A de facto engineering material law is the elastic model in the form of Hooke?s law for linear, homogeneous materials that may be anisotropic. A limit to elasticity is imposed by strength in the form of a failure criterion or yield function that accommodates triaxial stress states. Examples used in rock mechanics are the well-known Mohr-Coulomb (MC)criterion, the popular Hoek-Brown (HB) criterion, and the Drucker-Prager (DP) criterion. The first is linear in stress, while the second is nonlinear. Both do not include any effect of the intermediate principal stress. The last is also linear in stress but includes the intermediate principal stress. All show an increase in the major principal stress at failure with confining pressure. In the UT2/3 finite element programs, the failure criterion Y is a nonlinear, anisotropic form and is also the plastic potential [1]: [YJI=+ 11NYJI=+- (1) ] where N is an exponent, usually 2, and J2 and I1 are nonlinear anisotropic forms of the second invariant of deviatoric stress and the first invariant of principal stress. The form (1) reduces to DP when N=1and isotropy prevails. When Y = 1, the limit to elasticity is reached and plastic deformation is possible. The material constants that enter (1) are all computed from unconfined compressive, tensile, and, in case of anisotropy, shear strengths. These latter strengths may be estimated from conventional laboratory test data. Of course, joints in field-scale rock masses induce different values. How different is often a matter of conjecture. For comparative studies, laboratory rock properties seem adequate. Inelastic, that is, plastic behavior occurs with strain beyond the elastic limit. Strain hardening, ideal plasticity, and strain softening are possibilities. Ideally brittle behavior with complete loss of strength is an extreme form of strain softening [2]. Caving may also be considered as strain softening with a less drastic reduction of material properties. As intact roof strata fail, fall, and form a rubble pile below, a new material is formed with greatly reduced elastic moduli and strengths, say, 1/100th of the original intact moduli and strengths. From another viewpoint, caving is simply a natural cut and fill process. Input for stress analysis by the finite element method includes: 1. Preexcavation stress state 2. Geology (stratigraphic column) 3. Structure (major faults, joint sets) 4. Elastic moduli 5. Strengths, and specific gravities of each rock type 6. Excavation sequence Output from an analysis includes distributions of: 1. Stress 2. Strain 3. Displacement 4. Local factor of safety (element fs) The last is defined as the ratio of strength to stress and in view of the failure criterion (1), is the ratio [fsJstrengthJstress=] where the numerator is the maximum possible value and the denominator is the actual value of the square root of the second invariant of deviatoric stress. This invariant is a measure of shear stress intensity but also reduces to uniaxial tensile and compressive strengths as the case may be. An fs greater than 1 indicates an elastic state of element stress; a value of 1 indicates the limit to

Jan 1, 2009

By K. C. Viveros, R. R. Ambriz, C. García, F. De Villèle, A. Talha, D. Jaramillo

Cold hole expansion on base metal, weld metal and heat affected zone of 6061-T6 aluminum alloy welds was simulated by means of finite element method. Three dimensional compact test models with a previous fatigue crack length with a relation of ??= a/W = 0.3, were used to analyze the hole expansion process. Considering the local mechanical properties for each zone of the welded joint, the optimal expansion degree (1.64 to 2.46 %) was determined. The residual stress field, through thickness, after the expansion process in all welding zones, were correlated with the crack opening displacement obtained by finite element analysis. It was observed, that compressive residual stress fields for a post-expansion, in different crack lengths, provided a crack closure mechanism for base metal, weld metal and heat affected zone. Contrary, the crack remained open when residual stresses are positive. The results are given as tangential stresses versus distance from the edge of the cold expansion and crack opening displacement as a function of applied load.

Jan 1, 2014

By A. S. Usmani

The flow associated with the pouring of molten metal into moulds has been modelled on the basis of certain simplifying assumptions. A finite element based Navier-Stokes equation solver has been used to analyse the flow. The velocities obtained from the Navier-Stokes equation solver are used to advect a pseudo-concentration function for modelling the fluid front. A simple problem with a known analytical solution is solved first to test the model. Subsequently, several more examples with varied geometrical configurations are modelled, including one with curved flow boundaries.

Jan 1, 1992

By Francois E. Heuze

Excavation of large rock caverns is a stepwise process. Whether one uses a heading and bench method or a multiple drift system, the use of excavation steps enables one to introduce the reinforcement, such as bolts or shotcrete, at the earliest possible stage. Knowing the spatial distribution and properties of rock materials and geological discontinuities, the cavern geometry and its reinforcement must be optimized. The finite element method of analysis is a powerful tool for such optimization. However, the models are only as good as their ability to account realistically for the physical attributes of the prototype and for the excavation sequence. They must include the following: - ability to model an incremental construction process. Thus requires the use of "Restart" procedures where displacements and stresses from a previous equilibrium are saved for the next step. - ability to model non-linear rock material behavior; in particular, the post-peak behavior of the rock which retains a residual strength when con-fined. The stability of many under-ground structures rests with the "broken" rock carrying significant loads. - ability to account for the non-linear behavior of geological discontinuities. These are two-fold. First, up to peak, non smooth rock joints will dilate. In a confined situation, dilation will increase joint strength by a consider-able amount (Obert, et al, Brady, 1971, Heuze,1978a), Then, beyond the peak, the joint also retains residual strength.

Jan 1, 1978

By Daniel W. H. Su

The ability to predict the effects of longwall mining on topography and surface structures is important for any coal company in making permit applications and anticipating potential mining problems. The sophisticated finite element model described and evaluated in this paper is based upon five years of underground and surface observations and evolutionary development of modeling techniques and attributes. The model provides a very powerful tool to address subsidence and other ground control questions. The model can be used to calculate post-mining stress and strain conditions at any horizon between the mine and the ground surface. This holds the promise of assisting in the prediction of mining-related hydrological effects.

Jan 1, 1986

By Youliang He

Twin-roll casting is an integrated casting and rolling process that involves the continuous solidification of a melt and the plastic deformation of the solidified metal between two rotating rolls. Computer modeling is a valuable tool to help engineers understand the metallurgical process during twin-roll casting. However, commercially available software can only model either the fluid flow/heat transfer of the melt or the plastic deformation of the solid, but not both. In this study, an object-oriented finite element program was developed to simulate the steady-state fluid flow, solidification and plastic deformation of an A7,31 magnesium alloy in a horizontal twin-roll caster. The melt, the mush zone and the solid were treated as a generalized Newtonian flow in an Eulerian reference frame and different constitutive equations were employed to describe the material behaviours. The effect of operational parameters on the solidification process was discussed based on the simulation results.

Jan 1, 2010

The paper describes a practical methodology based on numerical modelling for the prediction of progressive failure of underground mine stopes with cable bolt support. A case study of the 40-761 stope at Kidd Creek Mine, Timmins, Ontario is presented. The stope was mined by blasthole open stoping in 1986 as a lead stope within a mining block between 36-1 and 38-2 levels. Initially designed to peak at 38-2 level, the stope back caved upwards approximately 40m towards 36-1 level. Cable bolts were installed above the stope from 36-1 level after caving had begun. The stope eventually stopped to cave when the falling rock mass encountered a sufficiently high cable density. The paper provides details of the geomechanical data and modelling results of the case study. Numerical modelling is carried out using a finite element package known as e-z tools which has, among other things, a special cable/rockbolt simulation capability.

Jan 1, 1994

By I. Mc Dougall

Finite element models were generated of two submerged arc furnaces of different geometries. A 48MW circular furnace and a 68MW 6-in-line rectangular furnace were studied. The electrodes, raw material, slag and molten metal were included in the model. ANSYS/Multiphysics was used to predict the current density distribution in the electrodes, raw material, slag and molten metal as a result of the three phase AC current. The effect of the electrode immersion on the current path was studied. The ?proximity effect? caused a pronounced asymmetry in the electrode currents in the circular furnace, whilst the electrode currents in the rectangular furnace exhibited radial symmetry. The current distribution in the melt in both furnaces indicated that the bulk of the current flows between phases. The current density is greatest between electrodes. Results were compared to qualitatively similar published work, operating experience and results of furnace dig-outs.

Jan 1, 2007

By F. Fournier Dit Chabert, F. Tancret, J. François Castagné, R. Le Gall

During the repair of turbine blades by a laser cladding process, it is observed that interdendritic cracking occurs in the heat affected zone (HAZ). Auger electron spectroscopy, performed on sample broken at high temperature, reveals interfacial sulfur segregation, which is known to be one of the main causes of microcraking in the HAZ during welding processes. Moreover, thermal gradients generated by the process are responsible for important thermomechanical stresses. In the present work, the finite element code Comsol Multiphysics is used to simulate the laser cladding process in order to determine both the thermal field and, using an elastoplastic law, the stress field inside the component. The originality is that the temperature history calculated in the thermomechanical model is extracted then injected in a segregation model in order to calculate the local segregation behavior. This model can be eventually used to predict the risk of cracking as a function of process parameters and alloy chemistry.

Jan 1, 2006

By Richard K. Komarek, Antonios Zavaliangos, Roman T. Dec

Current industrial compacting and briquetting practices are largely based on trial-and¬error techniques. This paper introduces a two dimensional finite element model of compacting/briquetting process in the roller press. Compared with other modeling techniques used in the past, finite element method offers the most versatile approach because it incorporates adequate information about powder behavior, geometry and frictional conditions and offers predictions for the density distribution, velocity field, stress distribution, roll force, roll torque and other important process variables. More over, when the model includes elasticity, it offers predictions on the internal stress state in the briquet after its exit from the pressing zone. This enables to perform realistic computer experiments which are helpful for establishing the pressing system design, forming cavity geometry and process conditions necessary to produce compacted or briquetted product with the desired properties.

Jan 1, 2004

By C. Arson

"Optimizing hydraulic fracture injection parameters in order to maximize hydrocarbon extraction and to avoid extensive borehole spalling is still an open issue. In this paper, the Differential Stress Induced Damage (DSID) model is employed to simulate the anisotropic damage distribution around pressurized boreholes drilled in fractured shale. The loading path is purely mechanical: excavation and fluid injection are simulated by stress relaxation followed by pressurization. We investigate the effect of pre-existing fracture orientation, in-situ stress and injection pressure on the propagation of anisotropic damage during pressurization. Finite Element results indicate that (1) damage initiates and develops when the ratio of two in-situ stress component deviates from 1, and the magnitude of damage is proportional to this stress deviation; (2) For a given in-situ stress field, damage initiates for a certain threshold of injection pressure, and the damage zone extends as the injection pressure increases; (3) A pre-existing fracture only affects the damage zone locally; the orientation of that fracture does not affect the damaged zone, which is controlled by in situ stress and injection pressure.INTRODUCTIONHydraulic fracturing is used to increase shale permeability and to enhance hydrocarbon extraction. In order to maximize the extraction ratio and to avoid wellbore spalling and clogging during fluid injection, the parameters related to injection for each particular site need to be optimized. Therefore, it is necessary to clearly understand how shale responses upon excavation and pressurization.It is well known that breakouts grow in the direction of minimum compression and that plastic deformation around wellbores tends to arrest breakouts (Zoback et al., 1985). Laboratory acoustic emission tests revealed that fractures propagate along the direction of maximum compression stress, and fractures (breakouts) are surrounded by the Excavation Damaged Zone (EDZ), in which rock properties are weakened by the presence of micro cracks (Eberhardt et al., 1999; Martino et al., 2004). The anisotropy from orientated foliations and cracks may influence the development and propagation of fractures and breakouts (Everitt et al., 2004). Sonic televiewer logs proved that during hydraulic fracturing, fluid injection further alters the stress distribution (Evans et al., 2005). Shale natural fabric strongly affects the evolution of the EDZ around boreholes."

Jan 1, 2015

By K. Pietruszka

The article presents the concept of the application of the Finite Element Method (FEM) and ABAQUS software in the global monitoring of changes in the rock mass and on the surface of the area, as a result of backfilling the workings. Waste materials applied for stabilizing old mining workings can have a strong influence on the rock mass and surface. According to the regulations, this process should be carefully monitored, especially in terms of the safety of surface structures and rock mass stability. The article presents the concept of an analytic and graphic presentation of the results of the measurements of old workings, applying the Finite Element Method and ABAQUS software in model studies. The main purpose of such interpretation of the geodetic observations results is the application of methods providing wide possibilities to present the geometry of workings, their changes and the influence of the rock mass and surface.

Jan 1, 2008

By A. F. Giamei, F. Landis, M. O. Duffy, R. J. Mador

"The directional solidification of complex advanced gas turbine airfoils must be carried out without the nucleation of undesirable grains and with minimal shrinkage. Such problems are typically eliminated by using a number of mold design and process iterations. A more efficient approach is envisioned where a solidification model is generated and utilized to accelerate process development. Towards this end, the directional solidification (DS) of simple geometrical shapes in a crystal grower apparatus has been simulated with MARC finite element nonlinear thermal analyses.The finite element models of cylindrical (2D) and rectangular (3D) cross-section bars in the DS environment are presented. Temperature dependent properties, the impact of latent heat of fusion and a time-dependent radiation boundary condition constitute the more salient features of the MARC models. Solidification zone thermal behavior is predicted during the withdrawal transient for the specific case of nickel based superalloys grown in ceramic shell molds. Comparisons of analytical results with experiments demonstrate notable prediction accuracy. INTRODUCTIONSingle crystal and uni-directional crystal turbine blades require tightly controlled conditions if metallurgically and mechanically acceptable parts are to be produced. Gated blade geometry and process parameters must be precisely determined if incorrect grain structure, orientation and shrinkage are to be avoided. Since purely experimental development programs designed to evaluate these parameters can be excessively costly and time-consuming, an effort combining engineering analysis and verification by experiment has been initiated at Pratt & Whitney. Comparison of analytical predictions and measured data for geometries simpler than a turbine blade, namely cylindrical and rectangular bars, comprised the initial stage of this effort. Subsequent tasks involve modeling geometries of increasing complexity and ultimately the simulation of the directional solidification of the turbine blade, shown schematically in Figure 1. This paper summarizes the results of the initial stage of the effort."

Jan 1, 1986

By M Oldenburg, P J. Digby, L Nilsson

A constitutive model for the simulation of fracture and fragmentation processes in rapidly loaded rocks is studied. The model was included in a wave propagation finite element code. The results obtained from two different configurations of explosive charge and reflecting surfaces in a plane strain problem were studied. The evolution of the time-dependent fracture pattern is presented.

Jan 1, 1985

By O. E. Wheeler

The term "finite element analysis" is heard and seen in print a great deal these days; a few words on what precisely it is are in order. In the broadest sense, finite element analysis is an application of an idea developed by a nineteenth century mathematician named Rayleigh. His basic idea was to decompose any problem in mathematical physics into a large number of simpler problems, solve the simpler problems, and then put those solutions together to form an approximation to the solution of the original problem. The scheme works nicely because of two features: first, much of the difficulty in solving practical problems of mathematical physics stems from irregularities in the boundaries and the simpler problems can be chosen with regular boundaries and second the smaller problems are solved for small physical areas where simple approximations of the solution do not differ much from the true solution. In the narrower sense, in which we are now interested, finite element analysis is a technique of using imaginary simple structural elements to construct analytical models of real structures. A direct parallel with the Rayleigh approach exists since the "finite elements" have simple boundaries and are restricted to simple behavior within a single element. Although the correspondence between Rayleigh's ideas and finite element analysis is now widely recognized, the computational tool, as it has developed over the last thirty years, comes not from the discipline of physics but rather from that of structural engineering. It is interesting that it came not from the traditional research community, the universities, but instead from working

Jan 1, 1974

By H. Stigzelius

FINLAND'S recent mining history is both dramatic and pitiful in its shifting fortunes, dominated as it has been, by the country's proximity to the border zone of opposing dictatorships and social traditions; Fascism to the south, Communism to the east, and Democracy to the west. After 108 years under Russia's more or less harsh rule, Finland gained its democratic independence during the 1917 revolutionary strife in Russia with the official help of Germany and spontaneous help of other neighbors. The young nation was attacked by Russia in 1939 and again in 1941. It is common knowledge how the Finns fought with everything they had and everything they could get against their overwhelming adversary, and how by force of circumstances they landed in the Axis camp in 1941. Finland has never been known as a mining country in the same way as near-by Sweden, whose abundant iron and copper smelters during long periods so greatly contributed to the nation's welfare. Its largely barren, Archaean-granite geology long seemed forbidding. Some mining was done, to be sure; copper and tin at Pitkaranta near the Russian border, and lead and copper at Orijarvi. But towards the end of the last century the absence of a single producing mine cast a pessimistic shadow of truth over the Finnish poet Runeberg's words, that

Jan 1, 1946

By V. Vahatalo, E. Hakapaa, H. Tanner

Recently modernized, the surface plant of the Outokumpu mine in Finland incorporates a number of ideas meriting close scrutiny from this side of the Atlantic. The mining methods make extensive use of concrete in some unusual ways. Design of the headframe and surface plant represents the latest thinking of European engineers and includes an integral Koepe hoist. The deposit is in eastern Finland, province of North Karelia, 30 miles west northwest of Joensuu and at 60'44' N, latitude. Pyrrhotite, pyrite, chalcopyrite, and sphalerite mineralization occurs in a shear zone in quartzite near a body of serpentinite. Two lenses have a total length over 12.000 ft, with remaining reserves of the 3 to 4 pct Cu ore estimated at about 15 million metric tons.

Jul 1, 1955