Page 125 - Biosystems Engineering

106 Cha pte r T h ree

soil capillary forces act together. As time goes on, the capillary effect
slowly diminishes as soil pores get filled with water, and gravity
forces start taking over. As time proceeds, the infiltration rate
decreases rapidly, exhibiting almost an exponential–decay–function
shape. The limiting infiltration rate at infinity, assuming unlimited
water supply, is shown as f . At this point, soil becomes saturated and
c
infiltration rate is driven only by gravity forces.
Infiltration rates measured in the laboratory have little value.
Therefore, in-situ tests are developed to measure infiltration. The
most common method is the use of double-ring infiltrometers. As its
name suggests, this method requires installation of two circular rings
into the soil, one inside the other. Water is filled in the inner circle and
in the area in between the two rings. The outer ring serves as a control
so that water in the inner circle only infiltrates vertically. The drop in
water level is measured with time. Best results are obtained when the
soil moisture is at field capacity.

Infiltration Models
Kostiakov Model Mathematically, this is the simplest model. Kostiakov
(1932) proposed the following equation:

F = at b (3.14)

where F is cumulative infiltration [L] at time t, and a and b are con-
stants. Parameters a and b need to be estimated from observed infil-
tration data by calibration. Kostiakov’s model should only be used
for small times because the model does not account for the limiting
infiltration rate ( f in Fig. 3.6).
c
Horton Model Horton’s model (1940) represents the infiltration pro-
cess better than Kostiakov’s model does. However, the model param-
eters still have to be estimated from experimental data. The form of
the equation is

f = f + ( f − f e ) − kt (3.15)
c
0
c
The parameters are as defined in Fig. 3.6, except for k, which is the
decay constant [1/T] and depends on soil and initial soil moisture
content. Cumulative infiltration can be obtained by simply integrat-
ing Eq. (3.15) from 0 to t.

Philip Model In contrast to the two previously listed empirical mod-
els of Kostiakov and Horton, Philip (1957) derived his equation from
theoretical analysis based on soil physics:

F = S t + Kt (3.16)