Geoscience Reference
In-Depth Information
This formula applies to a situation involving no internal erosion of the sand layer
during deposition and for the situation where the water loss through the sand pores
can be neglected. The formula can be used to estimate the sedimentation rate at the
start of filling of the geotextile tube. Once the geotextile tube is largely filled, the
flow of water through the geotextile tube becomes significantly larger and erosion
will occur and the sedimentation rate will decrease causing the filling speed to fall
significantly.
To determine w 0 in formula 5.2, Stokes Law is used:
2
Δ
gD
g
mf
(5.3)
wX
X
0
18
v
where:
X
=
shape factor ([29] suggests 0.7) [
];
Δ
=
relative density of the fill material (
=
(
ρ s ρ w )
/ ρ w )) [
];
ρ s
=
density of the fill material [kg/m 3 ];
ρ w
=
density of the water [kg/m 3 ];
D mf
=
average grain diameter of the sand (formula 5.1) [m];
v
=
kinematic viscosity of water (
=
40.10 −6 /(20
+
T ) where T , the temperature,
is in
°
C) [m 2 /s].
When the output concentration of the mixture, the density and the fall velocity
of the grains are known, the sedimentation rate can be determined. Two solutions are
possible for the sedimentation rate:
￿
The sand-water mixture in the geotextile tube is approximately still above the
sand bed. In this case the sand concentration in the sand-water mixture is fairly
constant and only the thickness of the sand-water mixture reduces.
￿
There is turbulence in the sand-water mixture, leaving a single concentration over
the entire thickness which reduces as more sand from the mixture settles.
In the first instance, the sedimentation rate remains constant. In the second
instance, the sedimentation rate will vary depending on the sand concentration, c .
In the second instance it is also likely that the sand-water mixture could lead to
erosion, though this is not considered any further here.
For the first instance described above, the sedimentation rate is simple to cal-
culate. For various sand types and concentrations the sedimentation rate is given
in Figure 5.4. The sedimentation rate theoretically depends on both the grain
diameter and the concentration. In practice, because the concentration of sand in
the sand-water mixture is less than 0.4, the influence of the sand grain diameter
dominates.
For the second instance described above, a numerical simulation is required
since the sand concentration changes as does the sedimentation rate. As observed
already in Figure 5.4, the sedimentation rate at different sand concentrations below
0.4 remains relatively constant. Also, for the second instance, an estimate can be
made of the sedimentation rate using a combination of formula (5.2) and Figure 5.4
 
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