Geoscience Reference
In-Depth Information
Fall velocity of the geotextile
container
When the geotextile container impacts the bottom, a significant load is exerted on the
geotextile. This load must be quantified as best as possible because it is often the criti-
cal factor in determining the minimum required tensile strength of the geotextile.
An important parameter in determining the load upon impact on the bottom is
the fall velocity of the geotextile container, which can be determined analytically using
the following formula [1]:
⋅
e
⋅
2
h
h
h
h
h
h
′
′
2
h
′
1
h
h
h
1
−
h
e
e
e
e
e
⋅
−
⋅
(G.1)
e
e
e
vv
v
∞
2
⋅
h
h
h
h
h
h
′
′
2
⋅
h
′
1
e
e
e
e
e
e
⋅
−
where:
2
V
AC
d
ρρ
−
⋅
(G.2)
w
v
∞
=
⋅
ρ
w
h
′
=
(G.3)
h
′
vt
⋅
∞
2
⎛
⎝
⎞
⎠
1
⎛
⎝
⎞
⎠
ρ
+
+⋅
2
ρ
2
w
V
AC
⋅
2
⋅
(G.4)
′
=
t
⋅
(
)
ρ
⋅
(
g
−
⋅
d
w
(
(
w
where:
v
=
fall velocity [m/s];
v
∞
=
terminal fall velocity [m/s];
h
′
=
dimensionless water depth [
−
];
h
=
water depth [m];
V
=
volume of the geotextile container [m
3
];
A
=
maximum plan cross sectional area (in the horizontal plane) [m
2
];
d
=
drag coefficient (approximately
=
1) [
−
];
ρ
=
density of the geotextile container fill [kg/m
3
];
ρ
w
=
density of water [kg/m
3
];
t
′
=
characteristic time (
=
time necessary to reach 76% of the terminal velocity) [s];
g
=
acceleration due to gravity [m/s
2
].
