Civil Engineering Reference
In-Depth Information
2.6.2 The pumping in test
Where bedrock level is very deep or where the permeabilities of different strata are required, the pumping
in test can be used. A casing, perforated for a metre or so at its end, is driven into the ground. At intervals
during the driving, the rate of flow required to maintain a constant head in the casing is determined and
a measure of the soil's permeability is obtained.
2.7 Approximation of coefficient of permeability
It is obvious that a soil's coefficient of permeability depends upon its porosity, which is itself related to the
particle size distribution curve of the soil (a gravel is much more permeable than a clay). It would therefore
seem possible to approximate the permeability of a soil given its particle size distribution, and typical ranges
of k for different soil types are given below. In addition, k can be approximated for a clean sand thus:
k
≅
0 01
1
2
.
D m s
/
where D
10
=
effective size in mm.
Wise (
1992)
offered approximations for other soils based on pore size distribution but it should be
remembered that no formula is as good as an actual permeability test.
Typical ranges of coefficient of permeability
>
10
−
1
m/s
Gravel
Sands
10
−
1
to 10
−
5
m/s
10
−
5
to 10
−
7
m/s
Fine sands, coarse silts
Silts
10
−
7
to 10
−
9
m/s
<
10
−
9
m/s
Clays
Example 2.4:
Approximation of k
Compute an approximate value for the coefficient of permeability for the soil in
Example 1.2.
Solution:
2
2
4
k
=
0 01
.
D
=
0 01 0 17
.
×
.
=
2 9 10
.
×
−
m s
/
10
2.8 General differential equation of low
Figure
2.6
shows an elemental cube, of dimensions dx, dy and dz, in an orthotropic soil with an excess
hydrostatic head h acting at its centre (an
orthotropic
soil is a soil whose material properties are different
in all directions).
Let the coefficients of permeability in the coordinate directions x, y and z be k
x
, k
y
and k
z
, respectively.
Consider the component of flow in the x direction.
The component of the hydraulic gradient, i
x
, at the centre of the element will be
x
=−
∂
∂
h
x
i
(Note that it is of negative sign as there is a head loss in the direction of flow).
