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By Joseph A. Sopko

The first documented procedures for designing frozen earth structures are over 50 years old, implemented long before the introduction of the Finite Element Method (FEM). Since that time, the development of three-dimensional models has made the traditional and often over-conservative methods relatively obsolete. This paper discusses a new approach that is largely dependent on the analysis of internal stresses with the frozen structure and comparison to frozen soil laboratory tests. A specific design process is discussed related to initial field investigation, laboratory testing, structural and thermal analysis, and performance monitoring. The design results are compared to case histories in the field that verify the procedure. BACKGROUND One of the first documented methods to designing frozen earth retaining structures was by Sangar (1968). Methodical refinements were published by (Harris 1995) and published by the International Symposium on Ground Freezing in 2002 (Andersland et al. 1991). The structural design or thickness of the frozen mass was based on the unconfined compressive strength of the frozen soils. Two simple equations for determining the thickness of a frozen shaft are shown in Fig. 1 and the first two equations below.

Jan 1, 2019

By K. F. Unrug

In the paper a numerical modeling method is used for evaluation of a roof support system, which is commonly used in the US coal industry. The effectiveness of mechanical roof bolting with or without, header boards and steel straps are compared. This analysis takes into account the response of a shaly roof to changing environmental conditions in mines related to the seasonal changes in temperature and humidity of the intake air. Discussed are principles of roof support in coal mines and based on them a critical evaluation of header boards interaction with bolts and roof itself is carried out. Header boards create a soft inclusion within a much more stiffer system comprising bolt-rock. As an alternative to header boards, steel straps are analysed and corresponding results are presented. It is demonstrated that application of steel strap is beneficial from the stand point of stress distribution and maintaining tension on roof bolts. The laboratory investigations and modeling work previously undertaken by the authors, clearly indicate the detrimental effect of header boards on effectiveness of roof bolting. There are significant practical implications of the research considering that header boards are commonly used in mines. This practice has been probably originated from the wooden support used by mining in "pre-bolting era?, and it has stayed with coal mining based on tradition more than principles of engineering design. It is demonstrated that header board$ are detrimental and actually contribute to development of roof problems.

Jan 1, 1989

By W. Jomaa, V. Songmene, O. Mechri, Laval Université, P. Bocher, J. Levesque

"A 2D finite element modelling (FEM), based on pure Lagrangian approach, is developed for studying the serrated chip formation during high speed machining (HSM) of 7075-T651 alloy. The solution was achieved using a commercial software package, ABAQUS/Explicit v6.13. The Johnson-Cooke (JC) constitutive equation is used to describe the work material behaviour. Moreover, the JC damage equation is implemented into the FEM to take into account for the shear localization during the serrated chip formation. Modified Coulomb friction model has been used to characterize the sliding/sticking effects on the tool-chip interface with the friction coefficient and shear flow stress determined by force calibration and machining data, respectively. The proposed FEM is validated using experimental data obtained in HSM of 7075-T651. The FEM was able to predict accurately serrated chip morphology. The intensity of chip segmentation was found to increase with cutting speed.INTRODUCTIONHigh speed machining (HSM) is one of the most used processes for manufacturing aircraft parts with aluminum alloys. For aluminum alloys, the use of HSM increases metal removal rate and reduces the formation of built up edges and burrs. However, it was found that serrated (also named segmented or sawtooth chip) and discontinuous chips can be produced during HSM of some high strength aluminum alloys, such as 7075-T6 alloy (Rao & Shin, 2001). Many parameters were found to affect the segmented/discontinuous chip formation during the machining of aluminum alloys.There are two cases in which the serrated chip can forms: the first is when machining hardened materials (Morehead, Huang, & Luo, 2007), and the second, when machining ductile materials with a cutting speed higher than a critical value (Barry & Byrne, 2002). Different theories and models were developed in order to explain the formation mechanism of such kind of chips. According to Astakhov (2006), the segmented chip formation is attributed to variations in stress and plastic deformation states, and resulting temperatures on the cutting zone. Liyao et al. (2013) stated that the segmented chip formation was mainly attributable to adiabatic shear instability/catastrophic strain localization. Others (Vyas & Shaw, 1999) suggest that the fracture/crack propagation mechanism is at the root of chip generation."

Jan 1, 2016

By B. MohammadSadeghi, S. Bakhshivash, M. Haghshenas, F. Rahimi

"Constrained groove pressing (CGP), as a severe plastic deformation (SPD) technique, is one of the applicable methods for sheet metal forming capable of producing ultra-fine grained materials (UFGMs). In CGP, processing and die design parameters can significantly affect the deformation response of sheet metal specimen. Having said this, in the present research the effects of die design variables and processing parameters (i.e. shear angle and friction) on the deformation behaviour of an Al-Mg-Si Alloy are studied thoroughly. Finite element analysis (FEA), was used to evaluate the effectiveness of mentioned parameters on the deformation homogeneity, strain distribution and pressing load variations. Also, mechanical properties of the deformed sample in term of micro-hardness was analyzed. It is observed that with increasing the shear angle, effective stress, strain and pressing load are enhanced. Moreover, by increasing the coefficient of friction, pressing load enhances. The color coded micro-hardness measurement showed a good agreement with the strain distribution obtained from FEA (higher hardness for the zones associated with higher shear plastic strain values).INTRODUCTIONWork hardening results in enhanced mechanical properties upon cycles of deformation (Hosford & Caddell, 2007). However, the formability of the processed products are affected by work hardening reducing the possibility of processing in subsequent deformation cycles. Therefore, many industrial processes cannot be performed on sheet metals to produce products with desired mechanical and physical properties (Valiev, Islamgaliev, & Alexandrov, 2000). Severe plastic deformation (SPD) is an effective grain refining technique which can impose large plastic strains through cold working on a metallic specimen (Bisadi, Rastgou, Payganeh, Zeynali, & Ghahremani, 2010). SPD techniques are mainly categorized into three types; sheet, bulk and tube forming. Among SPD sheet forming methods, Constrained Groove Pressing (CGP) (Shin, Park, Kim, & Park, 2002), Accumulative Roll Bonding (ARB) (Saito, Tsuji, Utsunomiya, Sakai, & Hong, 1998) and Repetitive Corrugation and Straightening (RCS) (Zhu, Lowe, Jiang, & Huang, 2001) possess potential applications in manufacturing industries."

Jan 1, 2016

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 Y. L. Su, R. Stefanko, Y. J. Wang

This chapter describes a new approach to the solution of stress distribution around underground openings utilizing the finite element method and employing stochastically simulated rock properties. It is well-known from extensive laboratory tests that the properties of rocks, e.g., Young's modulus and Poisson's ratio, are not single-valued but form some distribution. If the scatter of test data is attributed to the variability of the rock itself rather than due to an inadequacy in test procedure, then stress solutions have to consider these variations. Utilizing this basic philosophy, the present study was initiated. A long circular opening subjected to plane strain in a hydrostatic stress field was chosen as a specific example to illustrate this approach. The technique adopted in solving stress distributions was based on the finite element method. This method is essentially a generalization of standard structural analysis procedures in which the continuum is idealized as an assemblage of "elements," interconnected at a finite number of nodal points. It is capable therefore of handling different material properties for individual elements in the model, if desired. In this study, each individual element was assumed to be isotropic, homogeneous, and elastic. However, values for Young's modulus and Poisson's ratio were randomly varied from element to element according to an assumed frequency distribution.

Jan 1, 1970

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 Evans U. Jegbefume

A plane strain two-dimensional finite element model employing the method of negative reaction loading has been used to model roof collapse and subsidence resulting from the underground gasification of coal in regions of soft overburden such as that found in Texas. The model included dry zones of rock around the cavity. Roof collapse was included by considering the final state of stress in the elements and removing those that had undergone tensile failure. The two-dimensional plane strain model was extended to include thermal loading and thermal softening of the roof rock. Roof collapse initiation and growth of the cavity were modelled by examining the portion of the rock immediately above the cavity under thermal and hydrostatic load. The model was extended to include linear creep using the method of incremental strains. The overburden was modelled as a generalized Kelvin material.

Jan 1, 1982

By K. Fotoohi

This paper presents a basic, and yet practical, three-dimensional finite element model that was developed by the authors for stress/stability analysis of mine structures. While the code is linear elastic at this stage, it has some practical features that make it an attractive tool for mine design. Such features include: simulation of mine backfill support, mining induced strain energy calculation, powerful out-of-core frontal solver and failure analysis by Mohr-Coulomb or Hoek-Brown failure criteria. Model development criteria are discussed, and the potential application of the model to mining is demonstrated by design examples.

Jan 1, 1998

By Wilson Blake

A mathematical model based on the finite element method of stress analysis has been used to describe the behavior of the western wall of the Kimbley Pit as its slope was steepened from 45 degrees to 57 degrees. Theoretical stress changes because of slope modification are slight except at the toe of the modified slope. Magnitudes of stress created are small when compared with the strength of a competent rock. Resulting displacement patterns point out the need for determining the in situ state of stress at a site prior to excavation or modification. A comparison of model results with field measurements shows that, in general, the model has described the measured behavior of the west wall of the Kimbley Pit remarkably well.

Jan 1, 1968

By Shad M. Sargand, Glenn A. Hazen, A M. M Jayasuriya

Various types of waves originate from a blast source to propagate through rock/soil media away from the blast. Input vibration to a structure depends on the soil-structure interaction which varies with the dynamic properties at the intersection as well as the stress and strain levels developed from the vibration of the structure-ground system. Hence it is important to study such effects on the response of a structure due to blast loads and this knowledge can be used in the design and control of blasts that are carried out close to buildings, highways and other structures.

Jan 1, 1994

By B. Q. Li, H. C. de Groh, X. Lu

"A fully 3-D, transient finite element model is developed to represent the magnetic damping effects on complex fluid flow, heat transfer and electromagnetic field distributions in a metallic melt. The model development is based on our in-house finite element code for the fluid flow, heat transfer and electromagnetic field calculations. The numerical model is tested against numerical and experimental results for water as reported in literature. Various numerical simulations are carried out for the melt convection and temperature distribution with and without the presence of a transverse magnetic field. Numerical results show that magnetic damping can be effectively applied to stabilize melt flow, reduce turbulence and flow levels in the melt and over a certain threshold value a higher magnetic field resulted in a greater reduction in velocity. Also, for the study of melt flow instability, a long enough running time is needed to ensure the final fluid flow recirculation pattern. Moreover, numerical results suggest that there seems to exist a threshold value of applied magnetic field, above which magnetic damping becomes possible and below which the convection in the melt is actually enhanced.1. INTRODUCTIONThe imposition of a DC magnetic field on a moving, electrically conducting fluid, such as molten metal or semiconductor melt, produces an opposing Lorentz force that results in a reduction of flow velocity in the liquid. This effect has been explored in both the semiconductor and metals industries to control natural convection and/or surface tension induced Marangoni convection as well as thermally induced flow instability during solidification processing of these melts [1-6]. A mathematical model can be of great use in developing both fundamental understanding of the fluid-magnetic field interactions in these magnetically-assisted processing systems and basic guidelines for process design, control and optimization.This paper presents a 3-D mathematical model for magnetically damped fluid flow and heat transfer in a melt cavity, which is useful for interpreting results for unidirectional solidification processes at slow solidification rate, and some preliminary results concerning the magnetic damping effects on the flow instability in the melt. The model development is based on the finite element solution of the Navier-Stokes equations, energy equations and equations for induced electric field. The model is tested against reported results and is then applied to study the fluid flow and thermal distribution in the metallic melt with and without an external magnetic field."

Jan 1, 1999

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

Surface subsidence induced by multiple-panel coal extraction was calculated with finite element stress analysis. The use of nonlinear material behavior and GAP elements, which provide a realistic representation of shearing along existing planes of weakness, allows the finite element program to accurately reproduce observed subsidence profiles. A reduction factor of 1/6 is applied to the measured rock strength and modulus for use in the finite element model. The models satisfactorily predict a significant change in maximum subsidence and subsidence profile associated with an increase from subcritical to near critical panel width. Modeled shearing along planes of weakness is in good agreement with available time domain reflectometry field observations and is demon¬strated to have a very profound effect on the maximum subsidence and the shape of the subsidence profile. When both material nonlinearity and planes of weakness are incorporated, the finite element model appears to possess great potential for accurately predicting surface subsidence and subsurface strata deformation in environments where little subsidence information is available.

Jan 1, 1990

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