The cyclic behaviour of sand, from the Prevost model to offshore geotechnics

The main objective of this thesis is the studying of the cyclic behaviour of dense sand. Its
centre of gravity is the implementation of a convenient constitutive law in the finite element
code LAGAMINE.
The first step consists in summarising the salient features of the cyclic behaviour of sand
observed in laboratory tests. Undrained monotonic and cyclic experiments are addressed.
The phase transformation line is a key parameter in the description of its behaviour. The
plasticity effects in both loading and unloading, the progressive pore pressure accumulation
coupled with the degradation of the stiffness of the soil are of uttermost importance in the
cyclic behaviour.
The Prevost model is adopted for its conceptual simplicity and its physically related parameters.
The basic equations of the model are described and its variants are illustrated.
Calibration of the required parameters is carried out by means of simplified routines implemented
in Matlab. A unique set of parameters is determined for each soil at a given relative
density. Monotonic experiments are well reproduced. The model also replicates satisfactorily
the trend of cyclic experiments.
An implicit scheme is embraced in order to implement the model in the finite element
code LAGAMINE. The implicit Prager translation rule is adopted for that purpose. It is ensured
the discrete formulation reproduces exactly the analytical model. Accuracy, efficiency and
robustness of the model are addressed throughout triaxial and multi-axial numerical examples.
A hydro-mechanical interface finite element is developed. It consists in a three-node 1D
isoparametric element. It is able to reproduce fluid flows across and along the interface. The
unsticking of both walls of the interface is coupled with a suction effect due to the filling of
the vacuum created. The behaviour of the element is illustrated by simple 1D examples of
transient consolidation of a soil column.
A final application consists in the modelling of a suction caisson, part of a tripod structure
for wind turbines. An axisymmetric representation of this foundation is carried out. It
is assumed embedded into dense Lund sand described by the Prevost model. Monotonic
and cyclic simulations are performed in both drained and partially drained conditions. The
salient features of the resistance of such foundations are highlighted. Their partially drained
behaviour strongly increases their transient resistance. A storm including an extreme event
is employed to simulate a cyclic loading. A pseudo-random short signal and its sinusoidal
equivalent representation finally lead to an identical vertical settlement. This is confirmed by
a long duration storm. Finally, a cyclic diagram summarising the final settlement attained
for combinations of average and cyclic vertical loads is elaborated.
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