Geoscience Reference
In-Depth Information
(e)
is a function of the suction (
p
<
0) in the water in the soil;
(f)
the latter function exhibits hysteresis.
9.10
Multiple choice. Indicate which of the following statements are correct. The surface of a soil
is kept ponded by a thin layer of water. The cumulative infiltration volume (not the rate) into a
homogeneous, initially dry soil profile of infinite depth:
(a)
eventually (i.e. after a very long time;) becomes a linear function of time;
(b)
eventually becomes a constant and independent of time;
initially varies as
t
−
1
/
2
(c)
because mainly capillary forces are acting;
(d)
is initially equal to the hydraulic conductivity;
(e)
decreases as a smooth function with time.
9.11
Multiple choice. Indicate which of the following statements are correct. Infiltration capacity (which
is the rate of vertical infiltration when the water supply at the soil surface is not limiting):
(a)
may vary considerably with time;
(b)
may depend on the rainfall rate (e.g. drizzle);
(c)
is a function of the permeability of the soil;
(d)
becomes, theoretically, equal to a constant after a long time of infiltration when the soil
profile is very deep (i.e. without an impermeable layer at shallow depth) and uniform;
(e)
is largely independent of the vegetative cover of the surface or of the season of the year.
Assume that it is known that the similarity variable
φ
=
xt
−
1
/
3
allows the reduction of the following
partial differential equation:
2
x
∂θ
∂
9.12
∂
∂
∂θ
∂
4
t
=
θ
x
x
to an ordinary differential equation, whose solution is
θ
=
θ
(
φ
)
.
(a) Obtain that ordinary differen-
tial equation. (b) What are the restrictions on the problem geometry (time and space), as expressed
in the boundary conditions, to permit this type of similarity variable (two to three sentences only)?
9.13
Consider the differential equation (9.13) and the boundary conditions (9.14). If the solution of
this problem is
φ
=
(1
−
θ
)
n
for 0<
φ<
1, and
θ
=
0
for
φ
≥
1, in which
n
is a positive
constant, what is the diffusivity,
D
w
=
D
w
(
θ
)?
9.14
You are given the results of a horizontal infiltration experiment as shown in Figure 9.2. Initially,
the soil is totally dry or
θ
i
=
0 and its satiation water content is
θ
0
=
0
.
4
.
After
t
=
100 min, the
following water content distribution was obtained.
x
(cm)
0
5
10
15
17
19
20
20.5
21
θ
0.4
0.38
0.34
0.29
0.26
0.22
0.18
0.14
0
Calculate
D
w
=
D
w
(
θ
) (in cm
2
min
−
1
) for values of
θ
=
0.10, 0.25, 0.30, 0.35 by solving
Equation (9.25) graphically or numerically.
9.15
Same as previous problem for
θ
i
=
0.02,
θ
0
=
0.45. After
t
=
740 min, the water content distribution
was:
