Geoscience Reference
In-Depth Information
Soil surface
Divide
p
w
<0
WT
p
w
>0
Impermeable layer
Fig. 10.1 Sketch of the cross section of an unconfined riparian aquifer. WT refers to the water table, which is the
locus where the water pressure is atmospheric; above the WT the soil is partly saturated. The divide is
assumed to be the catchment boundary.
the Richards equation (8.56) (or also (8.89)) rewritten here for easy reference,
k
∂
k
∂
k
∂
∂
∂
h
∂
∂
h
∂
∂
h
=
∂θ
∂
+
+
(10.1)
x
∂
x
y
∂
y
z
∂
z
t
in which
h
=
(
z
+
p
w
/γ
w
) is the hydraulic head,
z
the vertical coordinate,
k
the hydraulic
conductivity and
the water content of the aquifer. The boundary conditions can be
prescribed in broad terms as follows. At the bedrock or impermeable bed underlying the
aquifer and at the catchment divide, the flux is usually parallel to the boundary, or if
n
is
the coordinate normal to the boundary,
θ
0. At the ground surface, the specific
flux
q
across the boundary can be given as the evaporation
E
, as the infiltration rate
f
,
or as a combination of both; for simplicity, however, in the analysis of base flow it is
often assumed to be zero, so that here also
∂
h
/∂
n
=
0. At the stream channel boundary,
the hydraulic head
h
is a constant that is equal to the height of the water surface in the
stream above the reference level of the elevation,
z
∂
h
/∂
n
=
0. Along the stream banks there
is often a seepage surface, where the pressure is atmospheric, so that
h
=
z
. The initial
conditions may vary, depending on the assumed initial moisture content distribution.
This problem is not easy to solve. Aquifer properties are generally not spatially
uniform and may even change with time; thus beside
=
(
x
,
y
,
z
,
t
) as the dependent
variable, two additional nonlinear functions come into play; these are
k
θ
=
θ
=
,
,
,
,θ
k
(
x
y
z
t
)
p
w
/γ
w
is the suction expressed
as equivalent water column. At present there are no methods available to determine
the spatial variability of these parameter functions. Moreover, in geological deposits
with an irregular geometry like that of the aquifer profile shown in Figure 10.1, the
boundary conditions prevail underground, and they are invisible; they are therefore nearly
impossible to validate or to formulate precisely. A general solution of this problem is
obviously unattainable. Nevertheless, some crucial features of the flow phenomena can
be brought out by the solution of special cases and simplified geometries.
One common simplification consists of the adoption of “effective” parameter
functions; the basic concept was introduced in Section 1.4.3. In brief, it is based on the
=
,
,
,
,θ
=−
and
H
H
(
x
y
z
t
), in which, as before,
H
