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Two-dimensional Finite Element Model (two-dimensional + finite_element_model)
Selected AbstractsAnalysis of shield tunnelINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2004W.Q. Ding Abstract This paper proposes a two-dimensional finite element model for the analysis of shield tunnels by taking into account the construction process which is divided into four stages. The soil is assumed to behave as an elasto-plastic medium whereas the shield is simulated by beam,joint discontinuous model in which curved beam elements and joint elements are used to model the segments and joints, respectively. As grout is usually injected to fill the gap between the lining and the soil, the property parameters of the grout are chosen in such a way that they can reflect the state of the grout at each stage. Furthermore, the contact condition between the soil and lining will change with the construction stage, and therefore, different stress-releasing coefficients are used to account for the changes. To assess the accuracy that can be attained by the method in solving practical problems, the shield tunnelling in the No. 7 Subway Line Project in Osaka, Japan, is used as a case history for our study. The numerical results are compared with those measured in the field. The results presented in the paper show that the proposed numerical procedure can be used to effectively estimate the deformation, stresses and moments experienced by the surrounding soils and the concrete lining segments. The analysis and method presented in this paper can be considered to be useful for other subway construction projects involving shield tunnelling in soft soils. Copyright © 2004 John Wiley & Sons, Ltd. [source] Modelling of paste flows subject to liquid phase migrationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2007M. J. Patel Abstract Particulate pastes undergoing extrusion can exhibit differential velocities between the solid and liquid phases, termed liquid phase migration (LPM). This is observed experimentally but understanding and predictive capacity for paste and extruder design is limited. Most models for LPM feature one-dimensional analyses. Here, a two-dimensional finite element model based on soil mechanics approaches (modified Cam-Clay) was developed where the liquid and the solids skeleton are treated separately. Adaptive remeshing routines were developed to overcome the significant mesh distortion arising from the large strains inherent in extrusion. Material data to evaluate the model's behaviour were taken from the literature. The predictive capacity of the model is evaluated for different ram velocities and die entry angles (smooth walls). Results are compared with experimental findings in the literature and good qualitative agreement is found. Key results are plots of pressure contributions and extrudate liquid fraction against ram displacement, and maps of permeability, liquid velocity and voids ratio. Pore liquid pressure always dominates extrusion pressure. The relationship between extrusion geometry, ram speed and LPM is complex. Overall, for a given geometry, higher ram speeds give less migration. Pastes flowing into conical entry dies give different voids ratio distributions and do not feature static zones. Copyright © 2007 John Wiley & Sons, Ltd. [source] Numerical approximation of a thermally driven interface using finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003P. Zhao Abstract A two-dimensional finite element model for dendritic solidification has been developed that is based on the direct solution of the energy equation over a fixed mesh. The model tracks the position of the sharp solid,liquid interface using a set of marker points placed on the interface. The simulations require calculation of the temperature gradients on both sides of the interface in the direction normal to it; at the interface the heat flux is discontinuous due to the release of latent heat during the solidification (melting) process. Two ways to calculate the temperature gradients at the interface, evaluating their interpolants at Gauss points, were proposed. Using known one- and two-dimensional solutions to stable solidification problems (the Stefan problem), it was shown that the method converges with second-order accuracy. When applied to the unstable solidification of a crystal into an undercooled liquid, it was found that the numerical solution is extremely sensitive to the mesh size and the type of approximation used to calculate the temperature gradients at the interface, i.e. different approximations and different meshes can yield different solutions. The cause of these difficulties is examined, the effect of different types of interpolation on the simulations is investigated, and the necessary criteria to ensure converged solutions are established. Copyright © 2003 John Wiley & Sons, Ltd. [source] Insulating effect of coals and organic rich shales: implications for topography-driven fluid flow, heat transport, and genesis of ore deposits in the Arkoma Basin and Ozark PlateauBASIN RESEARCH, Issue 2 2002J.A. Nunn ABSTRACT Sedimentary rocks rich in organic matter, such as coal and carbonaceous shales, are characterized by remarkably low thermal conductivities in the range of 0.2,1.0 W m,1 °C,1, lower by a factor of 2 or more than other common rock types. As a result of this natural insulating effect, temperature gradients in organic rich, fine-grained sediments may become elevated even with a typical continental basal heat flow of 60 mW m,2. Underlying rocks will attain higher temperatures and higher thermal maturities than would otherwise occur. A two-dimensional finite element model of fluid flow and heat transport has been used to study the insulating effect of low thermal conductivity carbonaceous sediments in an uplifted foreland basin. Topography-driven recharge is assumed to be the major driving force for regional groundwater flow. Our model section cuts through the Arkoma Basin to Ozark Plateau and terminates near the Missouri River, west of St. Louis. Fluid inclusions, organic maturation, and fission track evidence show that large areas of upper Cambrian rocks in southern Missouri have experienced high temperatures (100,140 °C) at shallow depths (< 1.5 km). Low thermal conductivity sediments, such as coal and organic rich mudstone were deposited over the Arkoma Basin and Ozark Plateau, as well as most of the mid-continent of North America, during the Late Palaeozoic. Much of these Late Palaeozoic sediments were subsequently removed by erosion. Our model results are consistent with high temperatures (100,130 °C) in the groundwater discharge region at shallow depths (< 1.5 km) even with a typical continental basal heat flow of 60 mW m,2. Higher heat energy retention in basin sediments and underlying basement rocks prior to basin-scale fluid flow and higher rates of advective heat transport along basal aquifers owing to lower fluid viscosity (more efficient heat transport) contribute to higher temperatures in the discharge region. Thermal insulation by organic rich sediments which traps heat transported by upward fluid advection is the dominant mechanism for elevated temperatures in the discharge region. This suggests localized formation of ore deposits within a basin-scale fluid flow system may be caused by the juxtaposition of upward fluid discharge with overlying areas of insulating organic rich sediments. The additional temperature increment contributed to underlying rocks by this insulating effect may help to explain anomalous thermal maturity of the Arkoma Basin and Ozark Plateau, reducing the need to call upon excessive burial or high basal heat flow (80,100 mW m,2) in the past. After subsequent uplift and erosion remove the insulating carbonaceous layer, the model slowly returns to a normal geothermal gradient of about 30 °C km,1. [source] | ||||||||||