Drainage of Agricultural Lands - Practices of Irrigation and On-farm Water Management - page 344

K i d i

d i

K H = (9.8)

9.3.3.2 Resultant Vertical Hydraulic Conductivity

Consider a soil column having n layers, and with different thickness and hydraulic
conductivity for each layer (Fig. 9.10 ) . Now, we are interested to know the resultant
(or equivalent) hydraulic conductivity for the soil column.

Fig. 9.10 Schematic of
vertical soil layer with
differential hydraulic
conductivity

q mm/d

1 d 1

K 1 (say, 10 mm/d)

2

d 2

K 2 (2 mm/d)

3

d 3

K 3 (4 mm/d)

n

d n

K n (3 mm/d)

For explanation purpose, assume that layer-2 is relatively impervious than the
other layers (sample values are given within the parenthesis). Assume that constant
input, q (rainfall or irrigation rate), is higher than the lowest conductivity value
( K min ) of the layers (here K 2 ). Although the layer-3 is relatively more pervious than
the layer-2, the resultant flux or hydraulic conductivity will be limited by this layer.
That is, if q K min , the unit flux or flux density will be controlled by the K min .This

is because, the K , Darcy's proportionality constant, or the hydraulic conductivity
of the media, is the flux density (or in short “flux”) under unit hydraulic gradient
(m 3 /m 2 /d), not the flow velocity (m/d). In some text books, it is erroneously treated
and expressed as flow velocity.
If the supply flux ( q ) is smaller than the K min , the resultant vertical conductivity
( K V ) will be limited by the q . Thus,

≥

K V = K min ,if q K min

= q ,if q < K min

≥

(9.9)

In reference to Fig. 9.10 , at the top of layer-2 (i.e., at the bottom of layer-1),
positive pressure will exist, since the incoming flux is higher than the outgoing flux.
In contrast, at the top of layer-3 (i.e., at the bottom of layer-2), negative pressure
will exist, as the outgoing flux capacity is higher than the incoming flux.