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Possibilities and limitations of the Prevost model for the modelling of cohesionless
soil cyclic behaviour.
Possibilités et limitations du modèle de Prévost pour la modélisation du comportement cyclique
des sols sans cohésion.
Cerfontaine B.
1,2
, Charlier R.
1
, Collin F.
1
1
University of Liège, Department of Architecture, Geology and Constructions, Geotechnical Engineering Division, Chemin
des chevreuils, 1, B52/3, 4000 Liège, Belgium
2
FRIA, F.R.S.-FNRS, National Fund for Scientific Research, 1000, Bruxelles, Belgium
ABSTRACT: The Prevost’s model is currently used to model cyclic behaviour of soils especially in earthquake engineering. The
original model is able to capture the main features of cyclic behaviour: pore pressure build up and plastic deformation accumulation.
But accurate modelling of laboratory tests requires improvements. Enhanced models exist but require a lot of parameters that make
them cumbersome for practical purpose. A suction caisson, part of a tripod offshore foundation for wind turbines is modelled.
Possibilities of the Prevost’s model are highlighted compared with a classical Drucker-prager model.
RÉSUMÉ : Le modèle de Prévost est couramment utilisé pour modéliser le comportement cyclique des sols, notamment dans
l’ingénierie sismique. Le modèle original permet la représentation des caractéristiques principales de ce genre de comportement : une
accumulation des pressions d’eau et déformations plastiques. Cependant, la représentation précise d’essais de laboratoire nécessite des
modifications du modèle. Ces améliorations existent mais au prix d’un grand nombre de paramètres additionnels, ce qui rend malaisée
son utilisation en pratique. Un caisson à succion, partie d’une fondation tripode d’éolienne offshore a été modélisé. Le sol est
représenté alternativement par un modèle classique de Drucker-Prager puis par le modèle de Prevost afin de souligner les apports de
celui-ci.
KEYWORDS: soil mechanics ; cyclic behaviour ; foundations ; constitutive behaviour
1 INTRODUCTION
Modelling the cyclic behaviour of soils is a crucial issue for
earthquake engineering as well as for designing offshore wind
turbines. This topic of interest is still an ongoing domain
(Houlsby, et al., 2005). Despite its drawbacks, the Prevost’s
model, based on nested surfaces and non-associated plasticity is
able to capture hysteretic behaviour of soils under cyclic
loading.
1.1
Definitions
The sign convention of soil mechanics is applied, compressive
stresses and strains are positive. The Macauley brackets
〈 〉
are
defined according to:
〈f〉 = 0,
< 0
f,
≥ 0
(1)
‘:’ indicates a dot product between two tensors (in bold
characters) of the same order: for example
: =
∙
in
index notation. If
′
is the effective (Cauchy) stress tensor and
= 1 3⁄ ∙
:
is the mean effective stress, then the deviatoric
stress tensor (
) is defined through
= ′
− p
∙
(2)
where
is the identity tensor.
1.2
Constitutive equations
The Prevost’s model lies within the framework of elasto-
plasticity. Constitutive equations are written in incremental
form. The equation below links the effective stress rate
′
to the
elastic deformation rate
−
′
= ∶ (
−
)
(3)
where
is the isotropic fourth-order tensor of elastic
coefficients. The plastic rate of deformation
is defined
through
= ⋅ 〈L〉
(4)
where
is a symmetric second order tensor, defining a plastic
potential. The plastic loading function is a scalar that depicts the
amount of plastic deformation and is defined in the following
L= 1 H
'
⋅Q:σ
′
(5)
where
is a second-order tensor defining the unit outer normal
to the yield surface and
′
the plastic modulus associated to this
surface. This normal tensor can be decomposed into its
deviatoric and dilationnal parts as
=
+ Q" ⋅
(6)
1.3
Yield functions
The model is made of conical nested surfaces in principal stress
space (Prevost, 1985). Their apex are fixed at the origin of axes
but could be translated on the hydrostatic axis to take a small
cohesion into account (for numerical purpose). The i-th surface
is defined through
f
≡
⋅ − p′ ⋅
∶ − p′ ⋅
− M
⋅ (
)
= 0
(7)
where
is a kinematic deviatoric stress tensor defining the
coordinates of the yield surface centre in deviatoric space and
M
is a material parameter denoting the aperture of the cone.
