Geoscience Reference
In-Depth Information
satiation. Calculate the following. (a) The cumulative infiltration volume (per unit area of ground
surface) as a function of time. (Specify the units of your result.) (b) The rate of infiltration as a
function of time. (c) The depth of the wetting front after one minute. The wetting front is the depth
below the surface, where the soil is just beginning to be wetted.
9.2
Calculate the same items, (a), (b) and (c), as in the previous problem; however, here the approximate
solution of the Richards equation is as follows: z = 2 . 90 (1 S 4 ) t 1 / 2
+ 0 . 05(1 S 9 ) t . The variable
S = θ/θ 0 is the degree of saturation, z is the depth into the soil in cm, t is the time in min and θ 0
is the water content at satiation.
9.3
Derive Equation (9.71) from (9.68), by scaling the variables.
9.4
Derive an expression for the cumulative infiltration volume F c from Horton's exponential equation
(9.76).
9.5
Derive an expression for the cumulative infiltration volume from Horton's exponential equation
(9.76). Try to give physical meaning to the parameters, b and c , by expressing them as functions
of the sorptivity A 0 and of the hydraulic conductivity at saturation k 0 . To accomplish this, compare
F c from the Horton equation with (9.69), such that both expressions produce the same infiltrated
volume for very large values of t . Recall that β 0 = 2 / 3 in Equation (9.69) and that a = k 0 in
Equation (9.76).
Assume that the infiltration capacity rate in a given soil can be described by f c = 0 . 5 A 0 t 1 / 2
9.6
+
k 0 / 3 , in which A 0 is the sorptivity and k 0 is the hydraulic conductivity at satiation. Derive an
expression for the cumulative infiltration capacity F c .
A steady light rain P = 0.45 cm h 1 is infiltrating into a deep homogeneous soil, whose hydraulic
conductivity (in cm d 1 ) is given by Equation (8.37) (see also Figure 8.29), with a = 170 × 10 6 ,
b = 2.5 × 10 6 , c = 4, and H in cm. Two tensiometers measure the pressure at 0.5 m and at 1.0 m
below the ground surface. If the manometers of these two tensiometers are located at 0.5 m above
the ground, what is the pressure reading in each of these manometers? Express the result in cm of
equivalent water column.
9.7
9.8
Consider the soil whose infiltration characteristics are given in Problem 9.6. (a) Calculate the
time to ponding in terms of A 0 and k 0 , for a rainfall intensity 1.3 times as large as the hydraulic
conductivity, that is P
calculate the compression reference
time t cr1 in terms of A 0 and k 0 by means of (9.91). (c) Write down an expression for the actual
cumulative infiltration F ( t ) making use of Equation (9.92). (d) Estimate the time to ponding for this
case if the hydraulic conductivity is k 0 = 0 . 08 cm min 1
=
1
.
3 k 0 . (b) Using this value of t p ,
and the sorptivity is A 0 = 1 cm min 1 / 2
.
9.9
Multiple choice. Indicate which of the following statements are correct. The hydraulic conductivity
of a partly saturated soil:
(a)
becomes smaller when the soil becomes drier;
(b)
is minimum near the wetting front during infiltration of ponded water (in contrast to near
the surface);
(c)
may increase with time during infiltration, as air, entrapped initially, goes into solution;
(d)
is a function of the water content gradient;
Search WWH ::




Custom Search