888
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
and prototype conditions. Further it is assumed that dynamic
forces are limited during the anchor dragging.
Table 1. General scaling laws with scaling factor
N.
Parameter
scaling law
model/prototype
Ng-model 1g-model
Unit
Length
1/
N
1/
N
m
Mass
1/
N
3
1/
N
3
kg
Force
1/
N
2
1/
N
3
N
Stress
Time (dynamic)
Time (consolidation)
1
1/
N
1/
N
2
1/N
1/
√N
1/
N
2
kPa
s
s
Velocity (dynamic)
Velocity (consolidation)
1
N
1/
√N
N
ms
-1
ms
-1
2.2 1-g conditions
The scaling in 1-g conditions is also presented in Table 1. It
appears from the table that the stresses will be N times lower in
the model compared to prototype. This means that also the
strength of the soils has to be N times lower. For a soil with an
undrained shear strength, as clay, this is difficult to achieve.
However, for a pure friction material this is rather easy, because
the N-times lower stress results automatically in a lower
strength, assuming that the friction angle remains constant for
the various stress levels.
Using dynamic scaling, the same scaling law for the velocity
(Froude scaling) as in 1-g hydraulic modelling tests is found.
However, when consolidation is dominant, again the velocity in
the model has to be N times higher than in the model. As in the
centrifuge model, it is assumed that the anchor will behave
drained in both the sand and the gravel layer.
2.3 Conclusions scaling
The scaling laws cannot be fulfilled completely with respect to
the prototype. However, assuming that consolidation is more
important than dynamic forces, the error made because of
assuming undrained behaviour in the sand and drained
behaviour in the gravel is exactly the same in both models. This
makes a good comparison possible between the 1-g and N-g
1:80 g models.
3 TESTS PERFORMED
3.1 Test set up centrifuge tests
Tests were run at 80 g in a specially developed container of L x
W x H: 1.80 x 0.5 x 0.5 m, see Figure 2 and Figure 3. The
length was necessary since a berm can be damaged not only by
an anchor, but also by the anchor chain that removes stones on
the berm before the anchor reaches the berm. The container is
placed on a water reservoir, so that the water level can be
changed during the test (by adding water from the reservoir or
vice versa). This is of importance for such a long container,
since during spinning up and spinning down, water movements
in the container can destroy the soil model (sand and anchor
berm). Therefore the water level was increased after spinning up
and decreased before spinning down.
A pulley system was constructed on top of the container, see
Figure 4, to be able to drag the anchor over the full length of the
container using a hydraulic plunger with a stroke of 0.5 m. As
usual in the Geo-Centrifuge of Deltares tests were performed
under reduced air pressure conditions of 50-60 mbar. More
details on the set up can be found in Van Lottum et al. (2010).
The anchor used in the tests was an AC-14 anchor. The
model is shown in Figure 5. The model anchor and anchor chain
were made of stainless steel using a 3-D print technique and
cast with the so called lost wax method. The anchor and chain is
printed in wax, which is replaced by stainless steel. By this
technique an accurate scaled copy of the original was obtained.
Water reservoir
Assembly plate
Hydraulic actuator
Valves for water su
Anchor
Pulley
system
Cameras
pply
Figure 2. Anchor dragging test setup on assembly plate
32 cm
125 cm
Chain
Anchor
Dyneema Rope
Pulley system
Force transducer
Actuator rod
Hydraulic actuator
10 cm
18 cm
Figure 3. Sketch set-up
Figure 4. Pulley system in test set up.
30 mm
46 mm
52 mm
Figure 5. Model AC-14 anchor.
The soil model consists of a homogeneous sand layer of
Baskarp sand (d
50
= 135
m) with a relative density of 65 – 75%
and a peek friction angle of 40 degrees. On the sand a pipe line
of 13 mm diameter and a gravel berm was placed (d
50
=5.3 mm),
see Figure 6. The porosity of the gravel was around 40% and
the peek friction angle 48 degrees.
0
20
40
Y (mm)
0
50
100
150
200
250
300
X (mm)
Figure 6. Dimensions of model berm
