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Finite Element Modelling of D-wall Supported Excavations
Modèle elément finis d’excavations soutenues par parois moulée
Everaars M.J.C., Peters M.G.J.M.
Grontmij Nederland BV
ABSTRACT: Two different methods of Finite Element Modelling (FEM) of diaphragm walls are explained. Both methods are
applied in state of the art geotechnical practice and comprise beam elements (Method 1) and elasto-plastic volume elements (Method
2). Selection of the appropriate method is not clear in advance and depends upon project specific requirements. In this paper the
selection process is illustrated based on two cases. The first case is a large infrastructural railway project through the historical city
centre of Delft, The Netherlands. The second case is an underground expansion project of the Drents Museum in Assen, The
Netherlands.
RÉSUMÉ : Cet article détaille deux modèles de parois moulées à l’aide de la méthode des éléments finis (FEM). Les deux méthodes
suivent les derniers développements en géotechnique utilisant des éléments de poutre (Méthode 1) et des volume élasto-plastiques
(Méthode 2). La méthode appropriée s’est avérée dépendante des besoins spécifiques pour un projet donné. Le processus de sélection
est décrit dans cet article à l’aide de deux exemples. Le premier est un projet d’infrastructure ferroviaire de grande envergure dans le
centre historique de la ville de Delft, Pays-Bas. Le second porte sur un projet d’agrandissement souterrain du musée Drents à Assen,
Pays-Bas.
KEYWORDS: Deep excavations, Diaphragm wall, Jet grout wall, Tunneling, Finite element modelling.
1 INTRODUCTION
Practical Finite Element Modelling (FEM) is important in
geotechnical design of excavations. It is a powerful tool were
excavations are located in urban areas. In those areas the impact
on the environment is high. Application of FEM plays a role in
risk and damage control. Where space is scarce, underground
structures, such as tunnels and basements, often support
buildings. Other assignments may involve construction close to
existing historical buildings. Staged construction of such
structures and the impact to their environment can be analysed
in all-embracing calculation models.
This paper discusses two cases of D-wall supported
excavations. Attention is paid to practical modelling
approaches. In FEM D-walls may be modelled as elasto-plastic
beam elements, or as linear elastic, non-porous volume
elements. Both methods of D-wall modelling are appropriate.
However a distinct selection can not be made in advance. The
selection depends on project specific functional conditions.
What information shall be delivered by the model? Is the D-wall
vertically loaded, or does it only retain? What are the
environmental conditions? Should soil deformations between
the excavation and adjacent buildings be minimised? Or, are
structural connections required, between for example D-wall
and floors, in order to model the behaviour of the total
underground construction?
For two cases the selection of the modelling approach is
discussed. The first case is the design of a railway tunnel
through the historical city centre of Delft, The Netherlands.
Here the elasto-plastic beam elements are applied. The other
case concerns the underground expansion of the Drents
Museum in Assen, The Netherlands. For the design of the
expansion of the Drents Museum the linear elastic, non-porous
volume elements were applied to model a jet grout wall. Both
projects cannot be compared by means of soil conditions or
nature of the proposed developments. The cases are used to
provide background for discussion of benefits and
disadvantages of both methods.
Selection and application of modelling methodologies and
the application of calculation results in the design may provide
the reader information to support the selection of the elastic
beam elements, or the linear elastic volume elements for other
projects.
2 FEM MODELLING OF DIAPRAGHM WALLS – 2
METODS
For design purposes two methods are commonly applied for
finite element modelling of diaphragm wall supported
excavations (CUR 231, 2010). This section explains the two
methods in detail. Advantages and disadvantages are provided
that may contribute to pre-selection of the model that fits best to
the specific project features. The two models can be described
as follows:
Method 1: elastic (or elasto-plastic) beam element;
Method 2: linear elastic or Mohr Coulomb, non-porous
volume element.
Modelling diaphragm wall as beam element (Method 1)
requires input parameters such as w (kN/m
2
), EI (kNm
2
/m), EA
(kN/m), n (-), R
inter
(-), M
pl
(kNm/m) and N
pl
(kN/m). The latter
two parameters apply to the elastoplastic model. Current
generation of user friendly FEM software (Plaxis) do not
comprise material models simulating concrete behaviour. The
properties of the diaphragm walls should be varied manually.
Where the bending moment exceeds the cracking limit the
Young’s modulus (E
uncracked
, MPa) should be reduced (generally
to E
cracked
, 10,0 MPa to 12,5 MPa). Diaphragm walls have high
weights and often a bearing function. In order to model such
features in FEM a “fixed-end-anchor” (spring element) should
be defined at the bottom of the diaphragm wall beam. The
vertical spring stiffness of this fixed-end-anchor can be fitted to
