Dynamic Analysis of Geotechnical Problems by Arbitrary Lagrangian-Eulerian Method

Dynamic Analysis of Geotechnical Problems by Arbitrary
Lagrangian-Eulerian Method
M. Nazem and J.P. Carter
Centre for Geotechnical and Materials Modelling, School of Engineering, The University of Newcastle, Newcastle,
NSW, Australia
Keywords: ALE method, dynamic analysis, finite element
ABSTRACT: In this paper, an Arbitrary Lagrangian-Eulerian (ALE) method is addressed to solve dynamic
problems involving large deformation. This ALE method is based upon the operator split technique in which the
material displacements and mesh displacements are uncoupled. Special issues such as time-stepping, mesh
refinement, dynamic equilibrium checks and remapping of state variables are briefly explained. The ALE method
and the Updated-Lagrangian (UL) method are then used to analyse a rigid footing to examine the significance of
inertia effects and large deformation on the predicted footing response. The results show the efficiency of the
ALE method for solving dynamic geotechnical problems involving large deformations.
1 Introduction
In many geotechnical problems, it is vital to consider the geometrical nonlinearity caused by large deformation in
order to capture a more realistic behaviour. The solutions so obtained will then be more accurate and reliable,
which should ultimately lead to cheaper and safer design. For example, highway embankments built on very soft
clay deposits can undergo settlements in the order of 1 to 10 metres without undergoing a conventional bearing
capacity failure. Such large movements warrant a large deformation approach in the analysis of the embankment
behaviour. Another example is the installation of displacements piles which are essential components of the
foundations of many offshore platforms. During installation, significant changes of geometry occur that should not
be neglected in an analysis of the effects of pile installation. The Arbitrary Lagrangian-Eulerian (ALE) method,
being well established in fluid mechanics and solid mechanics, has been shown to be robust and efficient in
solving static geotechnical problems involving large deformations (see, for example, Nazem et al., 2006) as well
as time-dependant consolidation problems (see Nazem et al., 2007).
There is also a wide range of geotechnical problems where dynamic loads are applied to soil in which the effects
of inertia forces should not be neglected. For example, in problems such as dynamic compaction and rapid
penetration of objects into soil, the propagation of a stress wave through the ground usually involves large stress
and strain amplitudes. These problems also involve large deformations. One possible and robust way to solve
dynamic problems involving large deformation is to take advantage of the ALE method. In this paper, an ALE
method based on the operator-split technique for solving dynamic geotechnical problems is presented and some
of its key aspects are briefly explained. The performance and capability of the method are demonstrated by
analysing a rigid footing under statically as well as dynamically applied vertical pressure. The effect of rapid
loading on the behaviour of the footing is also demonstrated by performing several small deformation and large
deformation analyses.
2 Finite element formulation


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