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The influence of the g-level for anchor tests in sand
L’influence du niveau de g pour les tests d’ancrage en sable
Bezuijen A.
Ghent University Ghent, Belgium/Deltares, Delft, Netherlands
Zwaan R., Lottum van H.
Deltares, Delft, Netherlands
ABSTRACT: Physical model tests in geotechnics are quite often performed in a centrifuge, because then the stresses are the same in
model and prototype, leading to comparable stress-strain behaviour. However, in theory for a pure friction material as sand, it should
be possible to get the same results in a reduced stress 1-g model as in an N-g model. This was checked in a series of anchor pulling
tests. The anchor was pulled through a sand bed and a gravel berm. Tests were run with the same set-up at 80-g and at 1-g. The
pulling force was measured as a function of time.
Results show that there is a clear distinction between the 1-g and 80-g tests. The pulling force was relatively higher in the 1-g tests.
This means that also for a pure friction material, stresses has to be the same in model and prototype.
RÉSUMÉ : Des essais sur modèles physiques en géotechnique sont souvent effectués en centrifugeuse, parce que les contraintes sont
les mêmes dans le modèle et le prototype, ce qui offre un comportement contrainte-déformation comparable. Cependant, en théorie,
pour un matériau purement frottant comme du sable, il devrait être possible d'obtenir les mêmes résultats dans un modèle 1-g aux
contraintes réduites, comme dans un modèle à N-g. Ceci a été vérifié dans une série de tests de traction d'ancre. L'ancre a été tirée à
travers un lit de sable et une berme. Le tests à 80-g et à 1-g ont été effectués d’un arrangement identique. La force de traction a été
mesurée en fonction du temps. Les résultats montrent qu'il y a une distinction claire entre les tests 1-g et les tests 80-g. La force de
traction est relativement plus élevée dans les essais 1-g. Cela signifie que pour un matériau purement frottant, il faut que les
contraintes soient identiques dans le modèle et le prototype.
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L’influence du niveau de g pour les tests d’ancrage en sable
A. Bezuijen
hent niversity hent, Belgiu / eltares, elft, etherlands
R. Zwaan, H. van Lottum
eltares, elft, etherlands
BSTR CT: Physical odel tests in geotechnics are quite often perfor ed in a centrifuge, because then the stresses are the sa e in
odel and prototype, leading to co parable stress-strain behaviour. o ever, in theory for a pure friction aterial as sand, it should
be possible to get the sa e results in a reduced stress 1-g odel as in an -g odel. This as checked in a series of anchor pulling
tests. The anchor as pulled through a sand bed and a gravel ber . Tests ere run ith the sa e set-up at 80-g and at 1-g. The
pulling force as easured as a function of ti e.
Results sho that there is a clear distinction bet een the 1-g and 80-g tests. The pulling force as relatively higher in the 1-g tests.
This eans that also for a pure friction aterial, stresses has to be the sa e in odel and prototype.
RÉS É : es essais sur odèles physiques en géotechnique sont souvent effectuésen centrifugeuse, parce que les contraintes sont
les ê es dans le odèle et le prototype, ce qui offre un co porte ent contrainte-défor ation co parable. Cependant, en théorie,
pour un atériau pure ent frottant co e du sable, il devrait être possible d'obtenir les ê es résultats dans un odèle 1-g aux
constraintes réduites, comme dans un modèle à N-g. Ceci a été vérifié dans une série de tests de traction d'ancre. L'ancre a été tirée à
travers un lit de sable et une ber e. Le tests à 80-g et à 1-g ont été effectués d’un arrange ent identique. La force de traction a été
esurée en fonction du te ps. Les résultats ontrent qu'il y a une distinction claire entre les tests 1-g et les tests 80-g. La force de
traction est relative ent plus élevée dans les essais 1-g. Cela signifie que pour un atériau pure ent frottant, il faut que les
contraintes soient identiques dans le odèle et le prototype.
KEYWORDS: centrifuge tests, scaling, anchor tests, friction material.
1 INTRODUCTION
Dragging anchors can be a real threat for pipe lines located at
the sea bottom. With the number of pipelines and cables
increasing as well as the number and size of the ships, it can be
expected that this threat will increase in the future.
Pipelines and cables that cross shipping lanes are usually
protected by gravel berms. The berm has to be stable against the
chain of the anchor and the anchor itself. Some damage to the
berms is allowed, but the pipeline and cable has to be protected,
even for the heaviest anchors that can be expected. These berms
are designed by experience and traditionally tested using large
scale (scale around 1:5) model tests. Some first attempts have
been made to simulate the process numerically using the so-
called ‘rigid body technique’, see the visualisation of a
numerical result in Figure 1. This is a promising path, see also
leQin (2010), but up to now not ready to be used in a design.
Figure 1.Visualisation of numerical simulation of an anchor passing a
berm using 'rigid body dynamics' (Bezuijen, 2011).
To avoid the relatively expensive large scale model tests, it is
also possible to use a centrifuge model. The advantage of a
centrifuge model is that a much smaller model is possible and
still the stresses are the same in model and prototype. For a 1-g
scale model the stresses in the model will always be smaller
than in the prototype, see Table 1.
However, in theory for a pure friction material as sand, it
should be possible to get the same results in a reduced stress 1-g
model as in an N-g model. This was checked in a series of
anchor pulling tests. The anchor was pulled through a sand bed
and a gravel berm. Tests were run with the same set-up at 80-g
and at 1-g. The pulling force was measured as a function of
time.
This paper presents the scaling rules, the set-up and results
of the 1-g and 80-g tests will be described in the paper.
2 SCALING
2.1 N-g scaling
In a centrifuge model the length is N times smaller than in the
prototype and the acceleration N times higher. The scaling
relations the relevant parameters are presented in Table 1. As
usual in centrifuge modelling the sand is not scaled from
prototype to the model, because the sand grains are much
smaller than the dimensions of the anchor, but the gravel
material is scaled and N-times smaller in the model compared to
prototype.
It is difficult to fulfil the scaling rule for the velocity. It is
necessary that the velocity is the same in model en prototype
when dynamic scaling is assumed, but the velocity has to be
even N times higher in the model compared to prototype when
consolidation is the dominant mechanism. Since ships dragging
anchors can still have a velocity of several metres per second, it
is rather difficult, even to achieve the ‘dynamic’ scaling rule. In
our tests an anchor velocity of 100 mm/min = 0.00167 m/s is
used (for higher velocities it would be difficult to control and
monitor the process during the test). This velocity will create a
drained behaviour of the sand in the model while a partly
drained behaviour in prototype is expected (see Van Lottum et
al, 2010) and a drained behaviour in the gravel for both model
