Homogeneous equilibrium model for geomechanical multi-material flow with compressible constituents

Multi-material flow generally describes a situation where several distinct materials separated by sharp material interfaces undergo large deformations. In order to model such flow situations in the context of geomechanics and geotechnical engineering, a theoretical framework is presented which introduces a possible two-phase coupled saturated granular material behavior among the different materials. This is achieved by extending the technique of local volume averaging to a hierarchy of three spatial scales, based on a product of two indicator functions. A homogeneous equilibrium mixture model is subsequently derived for an example flow consisting of bulk solid, bulk fluid, and undrained granular material with compressible constituents. The closure relations are provided at the macroscale, including those describing granular behavior covering the full frictional-collisional flow regime and bulk material volume fraction evolution. The paper discusses the advantages and restrictions of the proposed mixture model and addresses its application and full-scale numerical implementation.DFG, FOR 1136, Modellierung von geotechnischen Herstellungsvorgängen mit ganzheitlicher Erfassung des Spannungs-Verformungs-Verhaltens im Boden (GeoTech)DFG, SA 310/26-1, Numerische Modellierung der Herstellung von RüttelinjektionspfählenDFG, SA 310/26-2, Numerische Modellierung der Herstellung von Rüttelinjektionspfähle

Explicitly coupled consolidation analysis using piecewise constant pressure

The paper describes an explicit coupling procedure for efficient consolidation analysis. Each time step is divided into a flow step followed by a drained mechanical step. The flow step keeps the total mean stress increment fixed and solves a diffusion problem based on piecewise constant pressure data. The procedure can be added to purely mechanical finite element codes and does not require a fully coupled element type. Details on discretization and implementation are provided as well as results of numerical tests

Entwicklung und experimentelle Validierung einer allgemeinen Lagrange‐Euler (ALE) Methode für Bodenmechanik

Large deformation problems in soil mechanics and geotechnical engineering can hardly be addressed by the traditional Lagrangian finite element method because the material and mesh motions coincide. This paper presents an arbitrary Lagrangian‐Eulerian (ALE) method in which the computational mesh is regarded as an independent reference domain to keep mesh quality acceptable throughout the calculation. The relative velocity between the material and the mesh introduces additional complexity which is treated by a Lagrange‐plus‐remap strategy in conjunction with efficient algorithms. Because thorough validation plays a crucial role, experimental model testing concerned with penetration into sand have been carried out and back‐analyzed by using the ALE method.Bodenmechanische und geotechnische Problemstellungen mit großen Verformungen können mit der traditionellen Lagrange'schen Finite Elemente Methode kaum gelöst werden, weil hierbei die Bewegung des Netzes der des Materials entspricht. Dieser Beitrag präsentiert eine allgemeine Lagrange‐Euler (ALE) Methode, bei der das Netz als unabhängiges Referenzgebiet betrachtet wird, um die Qualität des Netzes während der gesamten Berechnung aufrecht zu erhalten. Der sich aus der Relativgeschwindigkeit zwischen Material und Netz ergebende Zuwachs an Komplexität wird mittels einer Lagrange‐plus‐Remap Strategie und effizienten Algorithmen behandelt. Weil die sorgfältige Validierung eine wichtige Rolle spielt, wurden experimentelle Modellversuche zur Penetration in Sand durchgeführt und mit Hilfe der ALE Methode nachgerechnet

Numerical evaluation of the soil behavior during impact driving of pipe-piles

During the impact driving of pipe-piles, the soil is influenced in different ways including the void ratio, stress distribution, and plugging formation. Such effects may play an important role in structural design criteria such as the pile’s lateral support provided by the soil. Hence, this work is focused on investigating the change in the mechanical characteristics of the soil during impact driving using an advanced numerical analysis tool which is validated against an experiment. The investigation includes the pile penetration behavior, plugging formulation inside the pile, and the change of the lateral stress in the soil during the pile installation. The proposed numerical model is shown to provide similar results compared to experimental measurements. The void ratio of the soil is influenced due to pile driving up to a lateral and vertical distance of 2D and 1D, respectively, where D is the pile diameter. Compared to the initial void ratio, the soil inside the pile experienced loosening about 20% while the soil outside is densified about 30% during driving. Moreover, the induced lateral stress inside is more than the one outside the pile, indicating the formation of plugging. Compared to the initial lateral stress state, the pile installation increased the lateral stress up to four times inside and two times outside the pile. Based on the findings of this work, the effects of driving on soil mechanical properties are not minimal and may affect the pile performance including the lateral resistance of the pile. By using the numerical approaches such as one in this study, the evaluation of the various effects on the soil due to pile driving and gaining a better understanding of the such complex problems are possible

Numerical evaluation of the pipe-pile buckling during vibratory driving in sand

The buckling of steel pipe piles during vibratory driving is numerically studied using the Multi-Material Arbitrary Lagrangian-Eulerian (MMALE) method. This method handles the large soil deformations that occur during pile driving and other geotechnical installation processes. The Mohr-Coulomb and an elastic-perfectly plastic material model are used to model the soil and the pile mechanical behavior, respectively. The result of a small-scale pile driving experiment is used to validate the numerical model. The penetration trend agrees well with the experimental measurements. Thereafter, four case scenarios and their possible effects on pile buckling, namely the presence of heterogeneity in the soil (a rigid boulder inside the soil) and the existence of geometrical imperfection modes in the pile (ovality, out-of-straightness, flatness) are investigated. This study shows that a combination of local and global buckling initiates at the pile tip and the pile shaft, respectively. During the initiation of buckling, a decrease in the penetration rate of the pile is observed compared to the case where no or minimal buckling occurs. It is shown that a less portion of the driving energy is spent on the pile penetration and the rest is spent on other phenomena such as buckling, resulting in less pile penetration. The cross section of the pile tip after buckling takes a form of a “peanut”, yet with a different geometry for each case. In cases where the model was initially symmetric, an asymmetric shape in cross section of the pile tip was obtained at the final stage which can be attributed to complex soil-structure interaction. The results of the numerical approach provide promising results to be used as an evaluation tool to reach reliable predictions in pile installation practice

Lagrange-Euler Formulierungen in der Bodenmechanik

Bodenmechanische und geotechnische Problemstellungen werden häufig durch große Materialverformungen und andere damit einhergehende Phänomene gekennzeichnet. Bei deren Modellierung stoßen die klassische Bodenmechanik und die traditionelle Finite Elemente Methode basierend auf der Lagrange Formulierung an ihre Grenzen. In dem Beitrag werden die kontinuumsmechanischen Grundlagen einer verallgemeinerten Lagrange-Euler Formulierung vorgestellt. Anschließend werden ihre unterschiedlichen Ausprägungen im Rahmen der numerischen Umsetzung anhand von Anwendungsbeispielen diskutiert sowie das Potential dieser Simulationsmethoden in der Bodenmechanik und Geotechnik aufgezeigt.DFG, 76838227, Numerische Modellierung der Herstellung von Rüttelinjektionspfähle

Differential geometry applied to continuum mechanics

Die Differentialgeometrie bietet den geeigneten Hintergrund, um die Kontinuumsmechanik mit einer einheitlichen und mathematisch präzisen Terminologie darzulegen und zu diskutieren. Ausgehend von einem Rückblick auf die lineare Geometrie in affinen Punkträumen führt die Arbeit in die moderne Differentialgeometrie auf Mannigfaltigkeiten unter Berücksichtigung der folgenden Themen ein: Topologie, Tensoralgebra, Bündel und Tensorfelder, Äußere Algebra sowie Differential- und Integralkalküle. Die erarbeiteten Werkzeuge werden anschließend auf grundlegende Themen der Kontinuumsmechanik angewendet. Insbesondere wird die Kinematik eines materiellen Körpers und die Massenbilanz vom geometrischen Standpunkt heraus formuliert, das Prinzip der Objektivität von Tensoren und von Materialgleichungen wird untersucht, und es wird der Unterschied zwischen der Lagrange'schen und der Euler'schen Formulierung auf klärende Weise dargestellt. Desweiteren skizziert die Arbeit eine verallgemeinerte Arbitrary Lagrangian-Eulerian (ALE) Formulierung der Kontinuumsmechanik auf differenzierbaren Mannigfaltigkeiten. Als wesentlicher Bestandteil ermöglicht dabei die eingeführte Gittermannigfaltigkeit eine konsistente Beschreibung der Beziehungen zwischen dem materiellen Körper, dem umgebenden Raum und dem beliebigen Referenzgebiet der ALE Formulierung. Nicht zuletzt besteht die Zielsetzung der Arbeit darin, wichtige Formeln und grundlegende Ergebnisse auf den behandelten Gebieten teilweise auch mit vollständigem Beweis zusammenzustellen. Sofern es zweckmäßig erscheint, werden Punktargumente und der Wechsel der Bezugspunkte in den Gleichungen hervorgehoben. Außerdem wird je nach Bedarf sowohl die Komponentenschreibweise, als auch die direkte oder absolute Schreibweise von Tensoren angewendet und dadurch ein eingleisiges Vorgehen vermieden. Gedruckte Version im Shaker Verlag [http://www.shaker.de/Online-Gesamtkatalog/Details.asp?ISBN=978-3-8322-8154-0] erschienen.Differential geometry provides the suitable background to present and discuss continuum mechanics with an integrative and mathematically precise terminology. By starting with a review of linear geometry in affine point spaces, the paper introduces modern differential geometry on manifolds including the following topics: topology, tensor algebra, bundles and tensor fields, exterior algebra, differential and integral calculi. The tools worked out are applied subsequently to basic topics of continuum mechanics. In particular, kinematics of a material body and balance of mass are formulated by applying the geometric terminology, the principles of objectivity and material frame indifference of constitutive equations are examined, and a clear distinction of the Lagrangian formulation from the Eulerian formulation is drawn. Moreover, the paper outlines a generalized Arbitrary Lagrangian-Eulerian (ALE) formulation of continuum mechanics on differentiable manifolds. As an essential part, the grid manifold introduced therein facilitates a consistent description of the relations between the material body, the ambient space and the arbitrary reference domain of the ALE formulation. Not least, the objective of the paper is to provide a compilation of important formulae and basic results -some of them with a full proof- frequently used by the community. If practical, point arguments and changes in points within equations will be clearly indicated, and component and direct (or absolute) tensor notation will be applied as needed, avoiding a single-track approach to the subject. Printed Version available from Shaker Verlag [http://www.shaker.de/Online-Gesamtkatalog/Details.asp?ISBN=978-3-8322-8154-0]