Modelling the large deformations in stratified media - the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models, However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright (C) 1999 John Wiley & Sons, Ltd.

Numerical modelling of double diffusion driven reactive flow transport in deformable fluid-saturated porous media with particular consideration of temperature-dependent chemical reaction rates

Numerical methods ave used to solve double diffusion driven reactive flow transport problems in deformable fluid-saturated porous media. in particular, thp temperature dependent reaction rate in the non-equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAG and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore-fluid flow, heat transfer and species transport/chemical reactions in deformable fluid-saturated porous media has been developed The coupled problem is divided into two subproblems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, if is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering.

Numerical modelling of chemical effects of magma solidification problems in porous rocks

The solidification of intruded magma in porous rocks can result in the following two consequences: (1) the heat release due to the solidification of the interface between the rock and intruded magma and (2) the mass release of the volatile fluids in the region where the intruded magma is solidified into the rock. Traditionally, the intruded magma solidification problem is treated as a moving interface (i.e. the solidification interface between the rock and intruded magma) problem to consider these consequences in conventional numerical methods. This paper presents an alternative new approach to simulate thermal and chemical consequences/effects of magma intrusion in geological systems, which are composed of porous rocks. In the proposed new approach and algorithm, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with the proposed mass source and physically equivalent heat source. The major advantage in using the proposed equivalent algorithm is that a fixed mesh of finite elements with a variable integration time-step can be employed to simulate the consequences and effects of the intruded magma solidification using the conventional finite element method. The correctness and usefulness of the proposed equivalent algorithm have been demonstrated by a benchmark magma solidification problem. Copyright (c) 2005 John Wiley & Sons, Ltd.

Predicting the mechanical behavior of amorphous polymeric materials under strain through multi-scale simulation

Polymeric materials have become the reference material for high reliability and performance applications. However, their performance in service conditions is difficult to predict, due in large part to their inherent complex morphology, which leads to non-linear and anisotropic behavior, highly dependent on the thermomechanical environment under which it is processed. In this work, a multiscale approach is proposed to investigate the mechanical properties of polymeric-based material under strain. To achieve a better understanding of phenomena occurring at the smaller scales, the coupling of a finite element method (FEM) and molecular dynamics (MD) modeling, in an iterative procedure, was employed, enabling the prediction of the macroscopic constitutive response. As the mechanical response can be related to the local microstructure, which in turn depends on the nano-scale structure, this multiscale approach computes the stress-strain relationship at every analysis point of the macro-structure by detailed modeling of the underlying micro- and meso-scale deformation phenomena. The proposed multiscale approach can enable prediction of properties at the macroscale while taking into consideration phenomena that occur at the mesoscale, thus offering an increased potential accuracy compared to traditional methods.

Determination of stresses around a cylindrical single pile caused by horizontal movements of soils with the finitive element method

This study was carried out with the aim of modeling in 2D, in plain strain, the movement of a soft cohesive soil around a pile, in order to enable the determination of stresses resulting along the pile, per unit length. The problem in study fits into the large deformations problem and can be due to landslide, be close of depth excavations, to be near of zones where big loads are applied in the soil, etc. In this study is used an constitutive Elasto-Plastic model with the failure criterion of Mohr-Coulomb to model the soil behavior. The analysis is developed considering the soil in undrained conditions. To the modeling is used the finite element program PLAXIS, which use the Updated Lagrangian - Finite Element Method (UL-FEM). In this work, special attention is given to the soil-pile interaction, where is presented with some detail the formulation of the interface elements and some studies for a better understand of his behavior. It is developed a 2-D model that simulates the effect of depth allowing the study of his influence in the stress distribution around the pile. The results obtained give an important base about how behaves the movement of the soil around a pile, about how work the finite element program PLAXIS and how is the stress distribution around the pile. The analysis demonstrate that the soil-structure interaction modeled with the UL-FEM and interface elements is more appropriate to small deformations problems.

The use of the boundary element method in the analysis of single lap joints

The most common techniques for stress analysis/strength prediction of adhesive joints involve analytical or numerical methods such as the Finite Element Method (FEM). However, the Boundary Element Method (BEM) is an alternative numerical technique that has been successfully applied for the solution of a wide variety of engineering problems. This work evaluates the applicability of the boundary elem ent code BEASY as a design tool to analyze adhesive joints. The linearity of peak shear and peel stresses with the applied displacement is studied and compared between BEASY and the analytical model of Frostig et al., considering a bonded single-lap joint under tensile loading. The BEM results are also compared with FEM in terms of stress distributions. To evaluate the mesh convergence of BEASY, the influence of the mesh refinement on peak shear and peel stress distributions is assessed. Joint stress predictions are carried out numerically in BEASY and ABAQUS®, and analytically by the models of Volkersen, Goland, and Reissner and Frostig et al. The failure loads for each model are compared with experimental results. The preparation, processing, and mesh creation times are compared for all models. BEASY results presented a good agreement with the conventional methods.

Masonry macro-block analysis

The structural analysis involves the definition of the model and selection of the analysis type. The model should represent the stiffness, the mass and the loads of the structure. The structures can be represented using simplified models, such as the lumped mass models, and advanced models resorting the Finite Element Method (FEM) and Discrete Element Method (DEM). Depending on the characteristics of the structure, different types of analysis can be used such as limit analysis, linear and non-linear static analysis and linear and non-linear dynamic analysis. Unreinforced masonry structures present low tensile strength and the linear analyses seem to not be adequate for assessing their structural behaviour. On the other hand, the static and dynamic non-linear analyses are complex, since they involve large time computational requirements and advanced knowledge of the practitioner. The non-linear analysis requires advanced knowledge on the material properties, analysis tools and interpretation of results. The limit analysis with macro-blocks can be assumed as a more practical method in the estimation of maximum load capacity of structure. Furthermore, the limit analysis require a reduced number of parameters, which is an advantage for the assessment of ancient and historical masonry structures, due to the difficult in obtaining reliable data.

Limits on the validity of infinite length assumptions for modelling shallow landslides

The infinite slope method is widely used as the geotechnical component of geomorphic and landscape evolution models. Its assumption that shallow landslides are infinitely long (in a downslope direction) is usually considered valid for natural landslides on the basis that they are generally long relative to their depth. However, this is rarely justified, because the critical length/depth (L/H) ratio below which edge effects become important is unknown. We establish this critical L/H ratio by benchmarking infinite slope stability predictions against finite element predictions for a set of synthetic two-dimensional slopes, assuming that the difference between the predictions is due to error in the infinite slope method. We test the infinite slope method for six different L/H ratios to find the critical ratio at which its predictions fall within 5% of those from the finite element method. We repeat these tests for 5000 synthetic slopes with a range of failure plane depths, pore water pressures, friction angles, soil cohesions, soil unit weights and slope angles characteristic of natural slopes. We find that: (1) infinite slope stability predictions are consistently too conservative for small L/H ratios; (2) the predictions always converge to within 5% of the finite element benchmarks by a L/H ratio of 25 (i.e. the infinite slope assumption is reasonable for landslides 25 times longer than they are deep); but (3) they can converge at much lower ratios depending on slope properties, particularly for low cohesion soils. The implication for catchment scale stability models is that the infinite length assumption is reasonable if their grid resolution is coarse (e.g. >25?m). However, it may also be valid even at much finer grid resolutions (e.g. 1?m), because spatial organization in the predicted pore water pressure field reduces the probability of short landslides and minimizes the risk that predicted landslides will have L/H ratios less than 25. Copyright (c) 2012 John Wiley & Sons, Ltd.

Three-dimensional hydrodynamic numerical modelling of fold nappe formation, basement-cover deformation and slab detachment with applications to the helvetic nappe system (W Switzerland)

Many three-dimensional (3-D) structures in rock, which formed during the deformation of the Earth's crust and lithosphere, are controlled by a difference in mechanical strength between rock units and are often the result of a geometrical instability. Such structures are, for example, folds, pinch-and-swell structures (due to necking) or cuspate-lobate structures (mullions). These struc-tures occur from the centimeter to the kilometer scale and the related deformation processes con-trol the formation of, for example, fold-and-thrust belts and extensional sedimentary basins or the deformation of the basement-cover interface. The 2-D deformation processes causing these structures are relatively well studied, however, several processes during large-strain 3-D defor-mation are still incompletely understood. One of these 3-D processes is the lateral propagation of these structures, such as fold and cusp propagation in a direction orthogonal to the shortening direction or neck propagation in direction orthogonal to the extension direction. Especially, we are interested in fold nappes which are recumbent folds with amplitudes usually exceeding 10 km and they have been presumably formed by ductile shearing. They often exhibit a constant sense of shearing and a non-linear increase of shear strain towards their overturned limb. The fold axes of the Morcles fold nappe in western Switzerland plunges to the ENE whereas the fold axes in the more eastern Doldenhorn nappe plunges to the WSW. These opposite plunge direc-tions characterize the Rawil depression (Wildstrubel depression). The Morcles nappe is mainly the result of layer parallel contraction and shearing. During the compression the massive lime-stones were more competent than the surrounding marls and shales, which led to the buckling characteristics of the Morcles nappe, especially in the north-dipping normal limb. The Dolden-horn nappe exhibits only a minor overturned fold limb. There are still no 3-D numerical studies which investigate the fundamental dynamics of the formation of the large-scale 3-D structure including the Morcles and Doldenhorn nappes and the related Rawil depression. We study the 3-D evolution of geometrical instabilities and fold nappe formation with numerical simulations based on the finite element method (FEM). Simulating geometrical instabilities caused by sharp variations of mechanical strength between rock units requires a numerical algorithm that can accurately resolve material interfaces for large differences in material properties (e.g. between limestone and shale) and for large deformations. Therefore, our FE algorithm combines a nu-merical contour-line technique and a deformable Lagrangian mesh with re-meshing. With this combined method it is possible to accurately follow the initial material contours with the FE mesh and to accurately resolve the geometrical instabilities. The algorithm can simulate 3-D de-formation for a visco-elastic rheology. The viscous rheology is described by a power-law flow law. The code is used to study the 3-D fold nappe formation, the lateral propagation of folding and also the lateral propagation of cusps due to initial half graben geometry. Thereby, the small initial geometrical perturbations for folding and necking are exactly followed by the FE mesh, whereas the initial large perturbation describing a half graben is defined by a contour line inter-secting the finite elements. Further, the 3-D algorithm is applied to 3-D viscous nacking during slab detachment. The results from various simulations are compared with 2-D resulats and a 1-D analytical solution. -- On retrouve beaucoup de structures en 3 dimensions (3-D) dans les roches qui ont pour origines une déformation de la lithosphère terrestre. Ces structures sont par exemple des plis, des boudins (pinch-and-swell) ou des mullions (cuspate-lobate) et sont présentés de l'échelle centimétrique à kilométrique. Mécaniquement, ces structures peuvent être expliquées par une différence de résistance entre les différentes unités de roches et sont généralement le fruit d'une instabilité géométrique. Ces différences mécaniques entre les unités contrôlent non seulement les types de structures rencontrées, mais également le type de déformation (thick skin, thin skin) et le style tectonique (bassin d'avant pays, chaîne d'avant pays). Les processus de la déformation en deux dimensions (2-D) formant ces structures sont relativement bien compris. Cependant, lorsque l'on ajoute la troisiéme dimension, plusieurs processus ne sont pas complètement compris lors de la déformation à large échelle. L'un de ces processus est la propagation latérale des structures, par exemple la propagation de plis ou de mullions dans la direction perpendiculaire à l'axe de com-pression, ou la propagation des zones d'amincissement des boudins perpendiculairement à la direction d'extension. Nous sommes particulièrement intéressés les nappes de plis qui sont des nappes de charriage en forme de plis couché d'une amplitude plurikilométrique et étant formées par cisaillement ductile. La plupart du temps, elles exposent un sens de cisaillement constant et une augmentation non linéaire de la déformation vers la base du flanc inverse. Un exemple connu de nappes de plis est le domaine Helvétique dans les Alpes de l'ouest. Une de ces nap-pes est la Nappe de Morcles dont l'axe de pli plonge E-NE tandis que de l'autre côté de la dépression du Rawil (ou dépression du Wildstrubel), la nappe du Doldenhorn (équivalent de la nappe de Morcles) possède un axe de pli plongeant O-SO. La forme particulière de ces nappes est due à l'alternance de couches calcaires mécaniquement résistantes et de couches mécanique-ment faibles constituées de schistes et de marnes. Ces différences mécaniques dans les couches permettent d'expliquer les plissements internes à la nappe, particulièrement dans le flanc inver-se de la nappe de Morcles. Il faut également noter que le développement du flanc inverse des nappes n'est pas le même des deux côtés de la dépression de Rawil. Ainsi la nappe de Morcles possède un important flanc inverse alors que la nappe du Doldenhorn en est presque dépour-vue. A l'heure actuelle, aucune étude numérique en 3-D n'a été menée afin de comprendre la dynamique fondamentale de la formation des nappes de Morcles et du Doldenhorn ainsi que la formation de la dépression de Rawil. Ce travail propose la première analyse de l'évolution 3-D des instabilités géométriques et de la formation des nappes de plis en utilisant des simulations numériques. Notre modèle est basé sur la méthode des éléments finis (FEM) qui permet de ré-soudre avec précision les interfaces entre deux matériaux ayant des propriétés mécaniques très différentes (par exemple entre les couches calcaires et les couches marneuses). De plus nous utilisons un maillage lagrangien déformable avec une fonction de re-meshing (production d'un nouveau maillage). Grâce à cette méthode combinée il nous est possible de suivre avec précisi-on les interfaces matérielles et de résoudre avec précision les instabilités géométriques lors de la déformation de matériaux visco-élastiques décrit par une rhéologie non linéaire (n>1). Nous uti-lisons cet algorithme afin de comprendre la formation des nappes de plis, la propagation latérale du plissement ainsi que la propagation latérale des structures de type mullions causé par une va-riation latérale de la géométrie (p.ex graben). De plus l'algorithme est utilisé pour comprendre la dynamique 3-D de l'amincissement visqueux et de la rupture de la plaque descendante en zone de subduction. Les résultats obtenus sont comparés à des modèles 2-D et à la solution analytique 1-D. -- Viele drei dimensionale (3-D) Strukturen, die in Gesteinen vorkommen und durch die Verfor-mung der Erdkruste und Litosphäre entstanden sind werden von den unterschiedlichen mechani-schen Eigenschaften der Gesteinseinheiten kontrolliert und sind häufig das Resulat von geome-trischen Istabilitäten. Zu diesen strukturen zählen zum Beispiel Falten, Pich-and-swell Struktu-ren oder sogenannte Cusbate-Lobate Strukturen (auch Mullions). Diese Strukturen kommen in verschiedenen Grössenordungen vor und können Masse von einigen Zentimeter bis zu einigen Kilometer aufweisen. Die mit der Entstehung dieser Strukturen verbundenen Prozesse kontrol-lieren die Entstehung von Gerbirgen und Sediment-Becken sowie die Verformung des Kontaktes zwischen Grundgebirge und Stedimenten. Die zwei dimensionalen (2-D) Verformungs-Prozesse die zu den genannten Strukturen führen sind bereits sehr gut untersucht. Einige Prozesse wäh-rend starker 3-D Verformung sind hingegen noch unvollständig verstanden. Einer dieser 3-D Prozesse ist die seitliche Fortpflanzung der beschriebenen Strukturen, so wie die seitliche Fort-pflanzung von Falten und Cusbate-Lobate Strukturen senkrecht zur Verkürzungsrichtung und die seitliche Fortpflanzung von Pinch-and-Swell Strukturen othogonal zur Streckungsrichtung. Insbesondere interessieren wir uns für Faltendecken, liegende Falten mit Amplituden von mehr als 10 km. Faltendecken entstehen vermutlich durch duktile Verscherung. Sie zeigen oft einen konstanten Scherungssinn und eine nicht-lineare zunahme der Scherverformung am überkipp-ten Schenkel. Die Faltenachsen der Morcles Decke in der Westschweiz fallen Richtung ONO während die Faltenachsen der östicher gelegenen Doldenhorn Decke gegen WSW einfallen. Diese entgegengesetzten Einfallrichtungen charakterisieren die Rawil Depression (Wildstrubel Depression). Die Morcles Decke ist überwiegend das Resultat von Verkürzung und Scherung parallel zu den Sedimentlagen. Während der Verkürzung verhielt sich der massive Kalkstein kompetenter als der Umliegende Mergel und Schiefer, was zur Verfaltetung Morcles Decke führ-te, vorallem in gegen Norden eifallenden überkippten Schenkel. Die Doldenhorn Decke weist dagegen einen viel kleineren überkippten Schenkel und eine stärkere Lokalisierung der Verfor-mung auf. Bis heute gibt es keine 3-D numerischen Studien, die die fundamentale Dynamik der Entstehung von grossen stark verformten 3-D Strukturen wie den Morcles und Doldenhorn Decken sowie der damit verbudenen Rawil Depression untersuchen. Wir betrachten die 3-D Ent-wicklung von geometrischen Instabilitäten sowie die Entstehung fon Faltendecken mit Hilfe von numerischen Simulationen basiert auf der Finite Elemente Methode (FEM). Die Simulation von geometrischen Instabilitäten, die aufgrund von Änderungen der Materialeigenschaften zwischen verschiedenen Gesteinseinheiten entstehen, erfortert einen numerischen Algorithmus, der in der Lage ist die Materialgrenzen mit starkem Kontrast der Materialeigenschaften (zum Beispiel zwi-schen Kalksteineinheiten und Mergel) für starke Verfomung genau aufzulösen. Um dem gerecht zu werden kombiniert unser FE Algorithmus eine numerische Contour-Linien-Technik und ein deformierbares Lagranges Netz mit Re-meshing. Mit dieser kombinierten Methode ist es mög-lich den anfänglichen Materialgrenzen mit dem FE Netz genau zu folgen und die geometrischen Instabilitäten genügend aufzulösen. Der Algorithmus ist in der Lage visko-elastische 3-D Ver-formung zu rechnen, wobei die viskose Rheologie mit Hilfe eines power-law Fliessgesetzes beschrieben wird. Mit dem numerischen Algorithmus untersuchen wir die Entstehung von 3-D Faltendecken, die seitliche Fortpflanzung der Faltung sowie der Cusbate-Lobate Strukturen die sich durch die Verkürzung eines mit Sediment gefüllten Halbgraben bilden. Dabei werden die anfänglichen geometrischen Instabilitäten der Faltung exakt mit dem FE Netz aufgelöst wäh-rend die Materialgranzen des Halbgrabens die Finiten Elemente durchschneidet. Desweiteren wird der 3-D Algorithmus auf die Einschnürung während der 3-D viskosen Plattenablösung und Subduktion angewandt. Die 3-D Resultate werden mit 2-D Ergebnissen und einer 1-D analyti-schen Lösung verglichen.

Non-linear analysis of laminated metal matrix composites by an integrated micro/macro-mechanical model

The present paper describes an integrated micro/macro mechanical study of the elastic-viscoplastic behavior of unidirectional metal matrix composites (MMC). The micromechanical analysis of the elastic moduli is based on the Composites Cylinder Assemblage model (CCA) with comparisons also draw with a Representative Unit Cell (RUC) technique. These "homogenization" techniques are later incorporated into the Vanishing Fiber Diameter (VFD) model and a new formulation is proposed. The concept of a smeared element procedure is employed in conjunction with two different versions of the Bodner and Partom elastic-viscoplastic constitutive model for the associated macroscopic analysis. The formulations developed are also compared against experimental and analytical results available in the literature.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Ein Beitrag zur realitätsnahen Modellierung und Analyse von stahlfaserverstärkten Stahlbeton- und Stahlbetonflächentragwerken

Das Werkstoffverhalten von stahlfaserfreiem bzw. stahlfaserverstärktem Stahlbeton unter biaxialle Druck- Zugbeanspruchung wurde experimentell und theoretisch untersucht. Die Basis der experimentellen Untersuchungen waren zahlreiche Versuche, die in der Vergangenheit an faserfreiem Stahlbetonscheiben zur Bestimmung des Werkstoffverhaltens von gerissenem Stahlbeton im ebenen Spannungszustand durchgeführt wurden. Bei diesen Untersuchungen wurde festgestellt, dass infolge einer Querzugbeanspruchung eine Abminderung der biaxialen Druckfestigkeit entsteht. Unter Berücksichtigung dieser Erkenntnisse sind zur Verbesserung der Werkstoffeigenschaften des Betons, Stahlbetonscheiben aus stahlfaserverstärktem Beton hergestellt worden. Die aus der Literatur bekannten Werkstoffmodelle für Beton sowie Stahlbeton, im ungerissenen und gerissenen Zustand wurden hinsichtlich der in der Vergangenheit ermittelten Materialeigenschaften des Betons bzw. Stahlbetons unter proportionalen sowie nichtproportionalen äußeren Belastungen erklärt und kritisch untersucht. In den frischen Beton wurden Stahlfasern hinzugegeben. Dadurch konnte die Festigkeits- und die Materialsteifigkeitsabminderung infolge Rissbildung, die zur Schädigung des Verbundwerkstoffs Beton führt, reduziert werden. Man konnte sehen, dass der Druckfestigkeitsabminderungsfaktor und insbesondere die zur maximal aufnehmbaren Zylinderdruckfestigkeit gehörende Stauchung, durch Zugabe von Stahlfasern besser begrenzt wird. Die experimentelle Untersuchungen wurden an sechs faserfreien und sieben stahlfaserverstärkten Stahlbetonscheiben unter Druck-Zugbelastung zur Bestimmung des Verhaltens des gerissenen faserfreien und stahlfaserverstärkten Stahlbetons durchgeführt. Die aus eigenen Versuchen ermittelten Materialeigenschaften des Betons, des stahlfaserverstärkten Betons und Stahlbetons im gerissenen Zustand wurden dargelegt und diskutiert. Bei der Rissbildung des quasi- spröden Werkstoffs Beton und dem stahlfaserverstärkten Beton wurde neben dem plastischen Fließen, auch die Abnahme des Elastizitätsmoduls festgestellt. Die Abminderung der aufnehmbaren Festigkeit und der zugehörigen Verzerrung lässt sich nicht mit der klassischen Fließtheorie der Plastizität ohne Modifizierung des Verfestigungsgesetzes erfassen. Es wurden auf elasto-plastischen Werkstoffmodellen basierende konstitutive Beziehungen für den faserfreien sowie den stahlfaserverstärkten Beton vorgeschlagen. Darüber hinaus wurde in der vorliegenden Arbeit eine auf dem elasto-plastischen Werkstoffmodell basierende konstitutive Beziehung für Beton und den stahlfaser-verstärkten Beton im gerissenen Zustand formuliert. Die formulierten Werkstoffmodelle wurden mittels dem in einer modularen Form aufgebauten nichtlinearen Finite Elemente Programm DIANA zu numerischen Untersuchungen an ausgewählten experimentell untersuchten Flächentragwerken, wie scheibenartigen-, plattenartigen- und Schalentragwerken aus faserfreiem sowie stahlfaserverstärktem Beton verwendet. Das entwickelte elasto-plastische Modell ermöglichte durch eine modifizierte effektive Spannungs-Verzerrungs-Beziehung für das Verfestigungsmodell, nicht nur die Erfassung des plastischen Fließens sondern auch die Berücksichtigung der Schädigung der Elastizitätsmodule infolge Mikrorissen sowie Makrorissen im Hauptzugspannungs-Hauptdruckspannungs-Bereich. Es wurde bei den numerischen Untersuchungen zur Ermittlung des Last-Verformungsverhaltens von scheibenartigen, plattenartigen- und Schalentragwerken aus faserfreiem und stahlfaserverstärktem Stahlbeton, im Vergleich mit den aus Versuchen ermittelten Ergebnissen, eine gute Übereinstimmung festgestellt.

Use of fused airborne scanning laser altimetry and digital map data for urban flood modelling

Flood modelling of urban areas is still at an early stage, partly because until recently topographic data of sufficiently high resolution and accuracy have been lacking in urban areas. However, Digital Surface Models (DSMs) generated from airborne scanning laser altimetry (LiDAR) having sub-metre spatial resolution have now become available, and these are able to represent the complexities of urban topography. The paper describes the development of a LiDAR post-processor for urban flood modelling based on the fusion of LiDAR and digital map data. The map data are used in conjunction with LiDAR data to identify different object types in urban areas, though pattern recognition techniques are also employed. Post-processing produces a Digital Terrain Model (DTM) for use as model bathymetry, and also a friction parameter map for use in estimating spatially-distributed friction coefficients. In vegetated areas, friction is estimated from LiDAR-derived vegetation height, and (unlike most vegetation removal software) the method copes with short vegetation less than ~1m high, which may occupy a substantial fraction of even an urban floodplain. The DTM and friction parameter map may also be used to help to generate an unstructured mesh of a vegetated urban floodplain for use by a 2D finite element model. The mesh is decomposed to reflect floodplain features having different frictional properties to their surroundings, including urban features such as buildings and roads as well as taller vegetation features such as trees and hedges. This allows a more accurate estimation of local friction. The method produces a substantial node density due to the small dimensions of many urban features.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

Uses of airborne scanning laser altimetry for river flood modelling and coastal geomorphology

Two ongoing projects at ESSC that involve the development of new techniques for extracting information from airborne LiDAR data and combining this information with environmental models will be discussed. The first project in conjunction with Bristol University is aiming to improve 2-D river flood flow models by using remote sensing to provide distributed data for model calibration and validation. Airborne LiDAR can provide such models with a dense and accurate floodplain topography together with vegetation heights for parameterisation of model friction. The vegetation height data can be used to specify a friction factor at each node of a model’s finite element mesh. A LiDAR range image segmenter has been developed which converts a LiDAR image into separate raster maps of surface topography and vegetation height for use in the model. Satellite and airborne SAR data have been used to measure flood extent remotely in order to validate the modelled flood extent. Methods have also been developed for improving the models by decomposing the model’s finite element mesh to reflect floodplain features such as hedges and trees having different frictional properties to their surroundings. Originally developed for rural floodplains, the segmenter is currently being extended to provide DEMs and friction parameter maps for urban floods, by fusing the LiDAR data with digital map data. The second project is concerned with the extraction of tidal channel networks from LiDAR. These networks are important features of the inter-tidal zone, and play a key role in tidal propagation and in the evolution of salt-marshes and tidal flats. The study of their morphology is currently an active area of research, and a number of theories related to networks have been developed which require validation using dense and extensive observations of network forms and cross-sections. The conventional method of measuring networks is cumbersome and subjective, involving manual digitisation of aerial photographs in conjunction with field measurement of channel depths and widths for selected parts of the network. A semi-automatic technique has been developed to extract networks from LiDAR data of the inter-tidal zone. A multi-level knowledge-based approach has been implemented, whereby low level algorithms first extract channel fragments based mainly on image properties then a high level processing stage improves the network using domain knowledge. The approach adopted at low level uses multi-scale edge detection to detect channel edges, then associates adjacent anti-parallel edges together to form channels. The higher level processing includes a channel repair mechanism.