Geoscience Reference
In-Depth Information
The volumetric water content of a soil can be defined in a similar way as Equation
(8.1), namely
volume of water in
∀
θ
=
lim
∀→
0
(8.2)
∀
Clearly, when a soil is fully saturated, its water content, denoted by
θ
0
, is by definition
equal to the porosity, or
θ
0
=
n
0
.
8.2
HYDROSTATICS OF PORE-FILLING WATER
IN THE PRESENCE OF AIR
Water in the pores of near-surface soils and other geologic formations is usually in
intimate contact with atmospheric air. Although for most hydrologic purposes water and
air can be treated as immiscible fluids, it is still necessary to consider their interaction
in the description and formulation of the different water transport mechanisms. In this
section hydrostatic conditions are explored, i.e. when both fluids, water and air, are at
rest.
8.2.1
Pressure in relation to water content
As the water content of a soil is reduced, the pressure of the remaining soil water generally
becomes smaller than that in the atmospheric air, which displaces the water in the pores.
This process can be illustrated by the following thought experiment.
A thought experiment
Consider, as shown in Figure 8.3, a sample of soil SS to be tested; it is placed on a
porous plate PP in a container C, to which a flexible tube FT is connected. (In a real
experiment a Buchner filter with fritted disk with sufficiently small pores can be used
for this purpose.) The pores of the porous plate PP are much smaller than those of the
sample SS (see Figure 8.4). Set up the experiment in such a way that initially the entire
system, i.e. soil sample, container and tube, are filled with water, and that the vertical
distance
d
between the center of the sample and the outlet of the tube is zero. Assume
for this simple experiment that the soil sample is incompressible so that it maintains its
original volume throughout, and that the water has a constant density
ρ
w
. Now increase
d
stepwise by small increments and wait after each step until equilibrium is established,
that is, until water stops flowing out at the lower end of the tube. Record after each step
the value of
d
and the total volume
∀
d
of water drained during all previous steps. If
∀
is the volume of the sample SS, this total volume
∀
d
of drained water can be converted
to the volumetric water content of the soil sample simply by
). Note
that, relative to atmospheric pressure, the pressure of the water in the soil pores is given
by
p
w
=−
γ
w
d
, where
θ
=
(
n
0
−∀
d
/
∀
γ
w
=
ρ
w
g
is the specific weight of the water. In practice, when
the density of the water is constant, it is often convenient to express the pressure as
equivalent height of water column
ψ
w
; in these units the pore water pressure in this
experiment can simply be written as
ψ
w
=
p
w
/γ
w
. Thus the pressure is negative relative
