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A large deformation finite element analysis solution for modelling dense sand
Solution d'analyse par éléments finis d’une large déformation pour la modélisation de sable dense
Li X.
1,2
, Hu Y.
1
, White D.
1
1
University of Western Australian, Perth, Australia
2
Beijing Jiaotong University, China
ABSTRACT: To capture the softening behaviour of dense sand, an extended Mohr-Coulomb model was developed using a critical state
framework. The model extends Bolton’s correlations to capture dilatancy and peak strength, and is compatible with the remeshing and
remapping strategies used in large deformation finite element analysis. This model is initially being used to simulate the behaviour of sand
layers during foundation and spudcan penetration into uniform and stratified soils, but is applicable to a variety of problems that cannot be
accurately simulated using conventional M-C plasticity alone.
RÉSUMÉ : Pour attraper le comportement s’adoucissant de sable, un modèle de Mohr-Coulomb étendu a été développé en utilisant un cadre
critique d’état. Le modèle étend les corrélations de Bolton pour capturer la dilatance et la résistance de pic, et est compatible avec les
stratégies de remaillage et remappage. Ce modèle est initialement utilisé pour simuler le comportement des couches de sable lors de la
pénétration du caisson vers les sols feuilletés. Donc, il sera applicable à une variété de problèmes qui ne sont pas bien capturées en utilisant la
plasticité M-C conventionnel.
KEYWORDS: Critical state; Large deformation analysis; Remeshing and mapping algorithm; Dilation; Shear band; Biaxial test.
1 INTRODUCTION
Sand can display dilation and strain-softening during shearing under
certain stress and relative density conditions. There are numerous
constitutive models developed to capture these characteristics
(Manzari and Dafalias 1997; Li et al. 1999). However, to be able to
implement such a constitutive model into finite element software
for large deformation analysis, a relatively simple model is essential
with the minimum of control variables involved. This is to ensure
that the large deformation analysis can be kept stable.
Large deformation of sand has not been analysed widely since
large deformation doesn’t occur in general when a conventional
foundation is placed on sand. However, when foundations – such as
the spudcan foundations beneath offshore drilling rigs – are placed
on sand overlying clay in offshore design, it is more likely for the
sand layer to experience large deformation (Yu et al. 2010).
Although large deformation of layered soils has been studied
extensively for stiff clay over soft clay soils using large deformation
FE analysis (LDFE) and centrifuge tests, fewer LDFE studies for
sand over clay conditions have been executed since to date no
suitable modelling approach exists for efficient simulation of the
large strain behaviour of sand.
This paper describes an investigation into the dependency of
bearing capacity on the large strain shearing characteristics of sand.
An extended Mohr-Coulomb (MC) model was developed, which
features strain-dependent hardening and softening using a critical
state framework. The model uses state dependent dilatancy and
friction angles. The controlling relations have been calibrated for a
number of well-characterised sands, demonstrating that the model is
a practical approach that can capture the specific responses of
particular soils. The model was implemented in LDFE analysis (Hu
and Randolph 1998a, 1998b) using the remeshing and interpolation
technique with small strain model (RITSS).
The results of LDFE/RITSS with the extended MC model show
that the volumetric and softening behaviour of sand has a
significant influence on the penetration resistance of foundations
during large penetration. When a shear band forms in sand, its
dilatancy angle reaches zero and the sand finds the critical state. For
foundations on uniform sand, this model shows how the variation in
the bearing capacity factors N
q
and N
is linked to density and
initial stress state, as well as the fundamental strength property, the
critical state friction angle.
The extended CSMC model coupled with LDFE shows great
potential to capture sand behaviour through large deformations in a
simple and efficient computational framework.
2 CRITICAL STATE MOHR-COULOMB (CSMC) MODEL
2.1 State dependent dilatancy angle and friction angle
Using the critical state concept, Been and Jefferies (1985) proposed
a state parameter,
to identify the current soil density state and to
predict the subsequent shearing behaviour. The state parameter,
is defined as:
c
e e
(1)
where
e
is the current void ratio;
e
c
is the critical state void ratio at
current stress. The state parameter
can be used to indicate the
current volume change tendency of the sand and be linked to the
dilation angle (Jefferies 1993; Manzari and Dafalias 1997; Li et al.
1999; Li 2002).
Been and Jefferies (1985) reported that both the peak friction
angle
p
and dilatancy angle
decrease with increasing
. This
idea also can be extended to loose sand where negative dilatancy
(or contraction) occurs. A simple single parameter relation can be
written as:
tan
A
(2)
where
A
is a constant and is suggested as 1.2 (Li et al. 2013). The
parameter A serves as a scale factor to the dilatancy angle, and it
influences dilatancy angle in both the negative and positive regions
of the state parameter
, i.e. both dense and loose sands.
For a better fit to experimental data, a three-parameter relation
can be written as:
s ( )
tan
(1 exp
)
n
ign m
A
(3)
where m, n are constants; n is a parameter controlling the curve
shape; m is a parameter majorly influenced the curve shape with
positive state parameter, i.e. loose sand.
Bolton (1986) linked peak friction and dilation angles by:
p
c
a
(4)
where
c
is critical friction angle;
a
is a constant. However, the
value of
a
varies with soil stress condition and soil type (Li et al.
2003). Thus, the energy equation proposed by (Taylor 1948) is
preferred here:
tan tan tan
c
(5)
Combining Eqs. 3 and 5, the relation between the mobilized friction
angle and soil state parameter
is illustrated in Fig. 1 with the
variation of parameter A. The current state-dependent dilatancy
angle and friction angle can be substituted into any modified Mohr-
Coulomb (MC) model such as the hyperbolic MC model (Abbo and
