Geoscience Reference
In-Depth Information
u
u
u
h =
h =
h =
is constant for
hydrostatic pressure
is constant for
hydrostatic pressure
is constant for
hydrostatic pressure
h
h
h
hydrostatic
hydrostatic
hydrostatic
z
z
z
z
z
z
h
p
h
p
h
p
h
p
= u
B
/
h
p
= u
B
/
h
p
= u
B
/
w
w
w
h = z
h = z
h = z
h
h
h
u
B
u
B
u
B
H
H
H
dz
dz
dz
L
L
L
not
hydrostatic
not
hydrostatic
not
hydrostatic
L
L
L
sand
sand
sand
d
d
d
H
H
H
A
A
A
hydrostatic
hydrostatic
hydrostatic
Q
Q
Q
Figure 4.2 Darcy permeability test and corresponding pressure and potential head
distribution.
For less permeable soils the cylinder test takes too long and the falling head test
is applied (Fig 4.3). The tube cross-section
a
is very small compared to the sample
cross-section
A
so that tiny changes in the volume are easily observed.
A
= Cross-section of soil sample
a
= Cross-section of tube
L
= Height of soil sample
V
= Change of volume between time
t
0
and time
t
h
0
= Height of water table at time
t
0
h
t
= Height of water table at time
t
V
h
0
h
t
A
Q
L
a
Figure 4.3 Falling head test
In the falling head test the water table
h
in the tube varies in time. Initially, at
t =
t
0
, the water table is
h(t
0
)
=
h
0
.
V
is the volume of water that leaves the tube during
t
, while the water table drops from
h
0
to
h
t
at
t = t
0
t
. So,
V = a
(
h
0
- h
t
)
= -
a
h
. The same amount of water flows through the soil sample. Thus
Q = - a
h/
t
,
which gives, with Darcy's law applied to the sample,
Q = - a
h/
t = kAh
t
/L
(assuming that
h << h
0
). This leads to
h/h
t
=
(
KA/aL
)
t
. Integration gives
h
t
=
h
0
exp[
(
kA/aL
)(
t
t
0
)]. Thus, the permeability is found by measuring
h
0
,
h
t
and
t
,
according to
k = aL
ln(
h
0
/h
t
)
/ A
t
(4.14)
In the field, the permeability can be determined by measuring the local
groundwater head using observation pipes. A geological profile can help to
recognise a specific groundwater regime or reservoir, which is essential for a
proper interpretation of groundwater head observations. A particular field test
concerns the permeability of the soil surface, i.e. to determine the drainage capacity
under conditions of heavy rain or free surface flow. An open-end pipe is placed
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