Redistribution of Water in Soil
133
of the wetting front. For mass balance, the rate of infiltration must equal
the rate of storage so:
where p, is the density of water, and A0 = (Oi + 0 ) / 2 - 0,; 0 is the volume fraction of water, and the subscripts i , f , and o are for the infiltration
boundary, the wetting front, and the initial water content, respectively. To
obtain the position of the wetting front as a function of time separate the
variables and integrate:
All but t can be expected to be relatively constant during infiltration, so
the wetting front will advance linearly with square root of time.
Equation (9.6) can be substutued into Eq. (9.4) to obtain the infiltration
rate:
showing that the infiltration rate is linearly related to the reciprocal of
the square root of time. If the data in Fig. 9.1 were replotted with the
reciprocal of square root of time as the horizontal axis, the data for the
horizontal soil would plot as a straight line. In Ch. 8 we showed that
the rate of heat flow into a one-dimensional slab also goes as the inverse
square root of time (Eq. (8.22)). It is interesting that the time dependence
is the same for heat and water flow, even though the Darcy equation for
water is highly nonlinear.
The Green-Ampt approach is strictly only for horizontal infiltration.
However, vertical infiltration can be approximated by adding a gravity
term to Eq. (9.7). This canthen be integrated over time to give an equation
for cumulative infiltration:
Zw = J ~ P w A ~
Kave(@mi - Ilr,f)t + gKavet(9.8)
The most challenging aspect of using Eq. (9.8) is estimating ymf, the
matric potential at the wetting front. If we assume that the wetting
front is symmetric, then the following approximate expression holds:
where b and @e can be estimated from Table 9.1.
9.3 Redistribution of Water in Soil
When infiltration ceases, water continues to move down into the soil under
the influence of matric and gravitational forces. Infiltration was stopped
with the final profile shown in Fig. 9.2. The redistribution profiles at four
133
of the wetting front. For mass balance, the rate of infiltration must equal
the rate of storage so:
where p, is the density of water, and A0 = (Oi + 0 ) / 2 - 0,; 0 is the volume fraction of water, and the subscripts i , f , and o are for the infiltration
boundary, the wetting front, and the initial water content, respectively. To
obtain the position of the wetting front as a function of time separate the
variables and integrate:
All but t can be expected to be relatively constant during infiltration, so
the wetting front will advance linearly with square root of time.
Equation (9.6) can be substutued into Eq. (9.4) to obtain the infiltration
rate:
showing that the infiltration rate is linearly related to the reciprocal of
the square root of time. If the data in Fig. 9.1 were replotted with the
reciprocal of square root of time as the horizontal axis, the data for the
horizontal soil would plot as a straight line. In Ch. 8 we showed that
the rate of heat flow into a one-dimensional slab also goes as the inverse
square root of time (Eq. (8.22)). It is interesting that the time dependence
is the same for heat and water flow, even though the Darcy equation for
water is highly nonlinear.
The Green-Ampt approach is strictly only for horizontal infiltration.
However, vertical infiltration can be approximated by adding a gravity
term to Eq. (9.7). This canthen be integrated over time to give an equation
for cumulative infiltration:
Zw = J ~ P w A ~
Kave(@mi - Ilr,f)t + gKavet(9.8)
The most challenging aspect of using Eq. (9.8) is estimating ymf, the
matric potential at the wetting front. If we assume that the wetting
front is symmetric, then the following approximate expression holds:
where b and @e can be estimated from Table 9.1.
9.3 Redistribution of Water in Soil
When infiltration ceases, water continues to move down into the soil under
the influence of matric and gravitational forces. Infiltration was stopped
with the final profile shown in Fig. 9.2. The redistribution profiles at four