Geoscience Reference
In-Depth Information
q
A
q
0
n
e
B
q
u
C
D
g
w
H
0
(-
p
w
)
max
Fig. 10.12 Illustration of the concept of drainable porosity (or specific yield)
n
e
for the vertical soil column above
a water table, in which the maximal water suction is (
−
p
w
)
max
at the top of the column. The value of
n
e
can be defined by taking the area [
n
e
×
(
−
p
w
)
max
] as the difference between the area
[(
p
w
)
max
] and the area ABCD under the soil water characteristic curve. The water
drained from the soil at the top of the column is (
θ
0
− θ
u
)
×
(
−
θ
0
− θ
u
); thus
n
e
is the average amount drained per
unit volume of soil in the column and (
θ
0
−
n
e
) is the corresponding amount of water left in the soil.
Although this is a problem of unsteady flow, the time variable does not appear in the
governing Laplace equation. As already hinted in the second of (10.13), which describes
the seepage surface, the time variable enters the problem through the condition at the free
surface, which constitutes the moving upper boundary. Before deriving this free surface
condition, it is necessary to introduce the concept of the drainable porosity.
Drainable porosity
As the water table passes a point, say in the case of drainage when it is falling, the pores
do not empty immediately, but the water is retained by capillarity and other mechanisms
mentioned in Section 8.2.2; it is only when the water pressure decreases further, i.e. with
increasing suction, as illustrated in Figures 8.3-8.6, that water drains from the pores. In
the free surface approximation, the reality of this gradual transition is replaced by the
assumption of the
drainable porosity
,
n
e
. This drainable porosity, which is also called
the
effective porosity
or the
specific yield
, can be defined as the volume of water per unit
volume of porous material, that is released or imbibed, as the free surface passes a given
point. In general, the amount of water present in the pores at a point depends on the
local water pressure. From this it follows that the drainable porosity must depend on the
prevailing water pressure distribution above the water table and therefore on the nature of
the flow situation. Figure 10.12 further illustrates how the concept can be interpreted with
reference to the soil water characteristic. It can be seen that
n
e
depends on the value of the
maximum suction in the soil column above the water table; because (
p
w
)
max
changes
with time during unsteady flow, in principle
n
e
may also be time dependent to some
−
