1453
Technical Committee 203 /
Comité technique 203
Fitting of the monotonic curves can be considerably
improved considering a modified plastic potential (in Figure 3).
The potential is split into a near field (small
) in which the
potential is the original one and a far-field (large
) in which the
potential is modified. Only two new parameters are necessary.
P" =
⋅
⋅ (1 +
⋅ tan
||
∙ (η
− 1))
(14)
Figure 3. Comparison between experimental drained triaxial tests
(Arulmoli, et al., 1992) and numerical modelling for Nevada Sand
(Dr=40%) volumetric vs. vertical deformation. Tests are available for 3
different initial mean effective pressures (40-80-160 kPa).
Insufficiency of this adaptation is obvious in Figure 4. A
cyclic behaviour is modelled, based on parameters obtained
above. Stress path in p’-q plane is quite different but moreover,
the q-
ϵ
y
curve doesn’t match and isn’t represented here. An
accurate modelling of cycles in both q-p’ and q-
ϵ
y
planes
definitely requires a more complex expression of the plastic
potential such as in (Elgamal, et al., 2003). The immediate
consequence is an increase in the number of state parameters
necessary to describe the model, though the number of
laboratory tests increases.
Figure 4. Comparison between experimental drained triaxial tests
(Arulmoli, et al., 1992) and numerical modelling (with modified plastic
potential) for Nevada Sand (Dr=40%) deviatoric vs. mean effective
stress.
Despite its drawbacks, the Prevost’s model can qualitatively
capture the main features of the cyclic behaviour of a soil: pore
pressure build up (Zerfa, et al., 2003) and plastic deformation
accumulation. Hence it’s better than classical isotropic
hardening models to represent cyclic behaviour of soils.
3 PRACTICAL EXAMPLE: SUCTION CAISSON
The advantages of the model are shown through an application,
based on (Vertseele, 2012). The case study is a suction caisson
part of a tripod foundation for wind turbine firstly loaded by the
dead weight and then submitted to a cyclic loading. The latter
consists of two phases of loading with different amplitudes
(period=10s). The second amplitude is twice the first one.
Results obtained from the Prevost’s model (PR) are compared
to the classical Drucker-Prager model (DP). The PR model is
used in its basic form since the proposed modification of the
plastic potential doesn’t improve the fitting of the cyclic
behaviour. Furthermore, the p’-dependency of the stiffness is
not taken into account (
= 0)
because the DP model
implemented in the code is not able to represent it.
3.1
Geometry
In order to simplify comparison, the mesh is supposed
axisymmetric and the horizontal load is neglected. The loading
is only a compression/decompression vertical force. The caisson
has a diameter of 8m and a skirt depth of 4m. The total mesh
size is 24mx22m to avoid problems with boundaries. There are
1892 finite coupled elements (from FE code LAGAMINE).
Parameters are those obtained for a Nevada Sand isotropically
consolidated at a relative density of 60% (Table 1).
Table 1. Parameters characterizing the models. Elastic parameters (E,
ν
)
and permeability are common to both models.
and
are
respectively the initial and final friction angle of the DP model whilst
is the dilatancy angle.
Com.
Elastic
E (kPa)
2,7.105
ν
(/)
0.25
k (m/s)
1.10
-5
PR model
Surface
1
2
3
4
5
6
7
8
9
H’ (kPa) 5.10
4
4.10
4
3.10
4
2.10
4
1.10
4
7.10
3
2400 1000 300
(/) 0.065 0.135 0.220 0.250 0.325 0.400 0.400 0.400 0.385
(/) 0.165 0.265 0.380 0.450 0.575 0.700 0.900 1.050 1.165
̅
0.7
DP
(°)
10
(°)
42
(°)
4.5
3.2
Results
Figure 5. Comparison between vertical displacement at 0.5m depth
under the top of the suction caisson for PR and DP models.
The first comparison in Figure 5 depicts the accumulation of
vertical displacement of the soil under the top of the caisson.
The weight of the wind turbine causes the first initial
displacement. Afterwards, the behaviour under cyclic loading is
quite different. For the DP model, the displacement oscillates
between nearly fixed boundaries and the soil lies within the
elastic zone most of the time. Actually the median displacement
is not exactly constant but changes very slightly at the
beginning of both loading phases.