Geoscience Reference
In-Depth Information
In Equation (9.1)
H
) is the water suction or negative pressure expressed as
equivalent water column, and
z
(contrary to its normal usage) denotes the depth, that is
the vertical coordinate pointing down.
Infiltration can take place in one of two possible ways. When the surface water supply
rate resulting from precipitation or other sources is intense enough, part of it remains
ponded or runs off, and part of it infiltrates at the maximal rate; this maximal rate of
infiltration is the
infiltration capacity
. When the intensity is low, all of the precipitated
water seeps into the pores; this is
rainfall infiltration
.
=
H
(
θ
9.1.1
Infiltration capacity
For the purpose of analysis, consider the simple case of a deep uniform soil profile. The
soil surface is assumed to be covered by a layer of water, which is sufficiently thin, so
that at the soil surface the water pressure is atmospheric and the soil saturated; also, the
initial water content is assumed to be constant throughout the profile. The corresponding
boundary conditions are then as follows
θ
=
θ
i
H
=
H
i
z
>
0
t
=
0
(9.2)
θ
=
θ
0
H
=
0
z
=
0
t
≥
0
The first of these two conditions represents the initial situation at
t
=
0 characterized
θ
i
and water pressure
H
i
, throughout the soil profile. The
second represents the condition at the soil surface
z
by a constant water content
=
0, maintained indefinitely after
the onset of the infiltration. As an illustration of the kind of solution that can be expected,
Figure 9.1 shows the water distribution during infiltration into a soil column, observed
in a laboratory experiment. Without going into the details of the solution of (9.1) subject
to (9.2), at this point it is useful to make some general observations regarding the short
and long time nature of the flow.
Short-time behavior
In Equation (9.1), the first term on the right represents the flow caused by the pressure
gradient owing to capillarity and the second term represents the flow caused by the
Earth's gravity field. As the water starts to enter the relatively dry soil, the pressure
differences in the water at the surface and in the soil are quite large and, as a result,
the second term on the right is practically negligible compared to the first one. Therefore
in its early phase, infiltration can be described by the following
k
∂
∂θ
∂
t
=−
∂
H
∂
(9.3)
∂
z
z
When cast in the form of a diffusion equation by means of (8.32), (9.3) subject to (9.2)
is referred to as a
sorption
problem. More detailed aspects of the short-time behavior of
infiltration capacity are treated in Section 9.2.
