Infiltration of Water into Soil

9.2 Infiltration of Water into Soil

If water were to pond on a soil surface and the rate at which it infiltrated the soil was measured, results similar to those shown in Fig. 9.1 would

be obtained. Results of experiments are shown, two with vertical infiltration and one with horizontal. Of the two vertical experiments, one was with wet soil and the other dry. For the horizontal column the gravita- tional gradient is zero, so the matric potential gradient is the only driving

force for water flow. The results of the experiments are in agreement with the predictions that would be made using Eq. (9.1). Initial infiltration is dominated by matric forces, so vertical and horizontal infiltration occur at

similar rates. The matric potential gradient is smaller for the wet soil than for the dry, so infiltration rate at early times is greater for dry soil than for wet. The water potential gradient for the dry soil is

times greater than that for the wet, yet there is hardly a difference in the infiltration rates. This is because the hydraulic conductivity for the dry soil is much smaller than for the wet.

and eventually the gravitational gradient becomes the dominant driving force for flow. Equation (9.1) indicates that the gravitationally-induced flow

The influence of matric potential gradients decreases with

Time (min)

F IG U RE 9.1. Vertical infiltration rate for water into initially dry and wet soil, and horizontal infiltration into dry soil.

Water Flow in Soil

for a saturated soil is The saturated conductivity for the soil in Fig. 9.1 was set at 0.001 kg s

so the final infiltration rate should

be 0.0098 kg (0.0098 It can be seen that both curves are approaching this value. The final infiltration rate for the horizontal

column is zero. The important result of the foregoing analysis is that the final infiltra- tion rate can be predicted if the saturated conductivity of soil is known.

A simple analysis by Green and Ampt (191 1) can be used to estimate the

infiltration rate. If we were to measure the water content in the soil as the infiltration shown in Fig. 9.1 occurred, we would obtain the result shown in Fig. 9.2. At each time the soil column consists of essentially wet soil overlying dry soil. A sharp wetting front separates the wet and dry soil. You can see that sharp boundary between the wet and dry soil when you watch water infiltrate dry soil.

The calculation is made by specifying the location of the wetting front at a point

ignoring the gravitational influence, and approximating the derivative as

where is the average hydraulic conductivity of the wet soil (called the transmission zone) and

are the water potentials at the wetting front and the infiltration boundary.

and

The rate of water storage in the soil is equal to the average change in water content of the transmission zone multiplied by the rate of advance

Water Content

F IGURE 9.2. Water content profiles in soil during infiltration.

Redistribution of Water in Soil

of the wetting front. For mass balance, the rate of infiltration must equal the rate of storage so:

where is the density of water, and A0

+ )/2 - is the vol- ume 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

be integrated over time to give an equation for cumulative infiltration:

The most challenging aspect of using Eq. (9.8) is estimating

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

can be estimated from Table 9.1.