Civil Engineering Reference
In-Depth Information
2.3 Darcy's law of saturated low
In 1856, Darcy showed experimentally that a fluid's velocity of flow through a porous medium was directly
related to the hydraulic gradient causing the flow, i.e.
v
∝
i
where i
=
i = hydraulic gradient (the head loss per unit length), or
v Ci
=
where C
=
a constant involving the properties of both the fluid and the porous material.
2.4 Coefficient of permeability, k
In soils we are generally concerned with water flow: the constant C is determined from tests in which the
permeant is water. The particular value of the constant C obtained from these tests is known as the coef-
ficient of permeability and is given the symbol k.
It is important to realise that when a soil is said to have a certain coefficient of permeability, this value
only applies to water (at 20°C). If heavy oil is used as the permeant, the value of C would be considerably
less than k.
Temperature causes variation in k, but in most soils work this is insignificant.
Provided that the hydraulic gradient is less than 1.0, as is the case in most seepage problems, the flow
of water through a soil is linear and Darcy's law applies, i.e.
v
=
ki
or
Q Atki
=
or
From this latter expression a definition of k is apparent: the coefficient of permeability is the rate of flow
of water per unit area of soil when under a unit hydraulic gradient.
BS 1377 specifies that the dimensions for k should be m/s and these dimensions are used in this chapter.
Q
t
q Aki where q quantity of unit flow
=
=
=
2.5 Determination of permeability in the laboratory
2.5.1 The constant head permeameter
The test is described in BS 1377: Part 5 and the apparatus is shown in Fig.
2.3.
Water flows through the
soil under a head which is kept constant by means of the overflow arrangement. The head loss, h, between
two points along the length of the sample, distance l apart, is measured by means of a manometer (in
practice there are more than just two manometer tappings).
From Darcy s law
'
:
q Aki
=
Q
t
The unit quantity of flow q
,
=
h
l
The hydraulic gradient
,
i
=
and A area of sample
=
