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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 M. Cepak, K. Donovan, W. G. Pariseau

This paper examines the difficulties of applying the finite element (FE) method of analysis to quantitative design of cable bolt systems. Cable bolt systems are in general use for ground control in VCR (Vertical Crater Retreat) topes throughout the world. However, despite their widespread use and importance, design of cable bolt systems is highly subjective. Two difficulties with the FE approach are examined: (i) the use of standard elements with a high aspect ratio (slender elements) to represent bolts, and (ii) the influence of cable bolts on hanging wall stability of a VCR study stope. Analysis results indicate that the use of slender elements for bolts is practical in large scale finite element analyses of VCR stopes. There are significant advantages in this approach to the engineering design of cable bolt systems in underground mining.

Jan 1, 1984

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 R. S. Sandhu, S. H. Advani, J. K. Lee, B. L. Aboustit

A comprehensive finite element formulation for thermo-elastic consolidation based on a general variational principle is presented Sample one dimensional problems associated with isothermal consolidation, heat conduct ion, and thermo-elastic consolidation are presented. In addition, evaluations of thermo-elastic consolidation for an underground coal conversion field site are conducted.

Jan 1, 1982

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 I. S. Laitinen

Outokumpu Technology has recently introduced new technology in both copper electrorefining and electrowinning. This technology includes, among other things, a new permanent cathode (Outokumpu Permanent Cathode) and new busbar technology (Outokumpu Double Contact System). The new technology has already been tested in commercial scale cells. To get a better understanding of the busbar system a multiphysical simulation model of the electrowinning and electrorefining cells was developed. A mathematical model of electrical conduction and heat transfer in a copper electrolysis cell was developed from partial differential equations. The model was expanded to a cell group including seven electrolysis cells connected electrically in series. The model was solved numerically using the finite element method (FEM). Using the model, different intercell busbar systems were simulated. Typical electrical disturbances, like loose contacts between cathodes and the main busbar and short circuits between electrodes, were included in the simulation. The results of the simulation runs with conclusions are presented in this paper.

Jan 1, 2007

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 D Frantzos

Pressure time histories were recorded for low density ammonium nitrate/fuel oil, detonated in long heavy walled steel cannons of various bores. These were shell used in a finite element model of a horizontally layered limestone rock mass to predict the crack propagation limits in presplit blasting for a range of borehole diameters. Apart from showing very good agreement with field results, the model clearly demonstrated the strong dependence of the results on the pressure-time curve. The important elements were the peak pressure, the rise time to it and its duration. Control of these characteristics offers the possible future production of more ideally suited pressure-time profiles for the optimization of crack propagation distances and borehole spacings for various ground conditions. Also the results to date provide the basis for investigating the characteristics of the explosives presently used in presplit blasting, and finding ways to modify them with the purpose of optimizing the field results.

Jan 1, 1987

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

By S. Behera, K. Dey

This paper presents a methodology for finite element (FE) modelling to analyse the total deformation of rockmass under blast-load, with a focus on predicting backbreak that may occur during surface blasting operations. Backbreak can result from improper use of explosive energy, leading to damage beyond the excavation zone and jeopardizing operational safety and productivity. The paper highlights the impacts of backbreak on bench stability, excavator operation, drilling operation, flyrock generation, and improper fragmentation and boulder formation in surface blasting. However, prior estimation of extent of rock breakage zone can provide an idea to formulate the blast design to control the backbreak. While vibration-based prediction models are commonly used to estimate backbreak, they require physical blasting experimentation. To overcome this limitation, the paper describes the development of a FE model using ANSYS Explicit dynamics, which simulates rock blasting and calculates the total deformation of the rockmass. The rockmass deformation is modelled using Drucker-Prager (D-P) strength model with the Jones-Wilkins-Lee (JWL) equation of state for the explosives. The accuracy of the FE model is evaluated through physical experiments, and the results are compared with the vibration models. The FE model demonstrates close proximity to physical observations as well as vibration model result in predicting backbreak, thereby offering a promising alternative to vibration-based prediction models. The primary objective of the study is to predict the response of the insitu rockmass to explosive blast loading and determine the effective rock breakage zone.

Jan 1, 2024

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 P. K. Currie, J. V. Walters

Solution mining of magnesium salts (Carnallite and Bischofite) is taking place near Veendam, in the northeast Netherlands. The magnesium salts are used for the production of magnesia sinter, used as a base material for the manufacture of refractory bricks for furnaces. This paper gives, first, an introduction to the operational procedure followed in Veendam, with the emphasis on some of the unique aspects, and then discusses rock-mechanical aspects of the cavity behaviour. The creep behaviour of magnesium salts is described, and Finite Element calculations on cavity stability and potential surface subsidence are discussed.

Jan 1, 1985