Environmental Engineering Reference
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100
10
Glass beads
Volcanic sand
Fine sand
Touchet silt loam
1
0
5
10
15
20
Matric suction ( u a u w ), kPa
(a)
(b)
Figure 7.9 Typical matric suction versus degree of saturation curves for soils with varying pore-
size distribution indices λ : (a) matric suction versus degree of saturation; (b) effective degree of
saturation versus matric suction (after Brooks and Corey, 1964).
greater than the air-entry value of the soil (Brooks and
Corey, 1964):
where:
k s
=
saturated soil coefficient of water permeability.
u a
2 + 3 λ
u w b
u w > u a
u w b
k w =
k s
u a
u w
for u a
Experimental data for sandstone expressed in terms of the
relative permeability are shown in Fig. 7.10. A hydrocarbon
liquid was used in the experiments instead of water in order
to produce a more stable soil structure and consistent fluid
properties. The results are essentially the same as for water
flow since the relative permeability is not a function of the
fluid properties.
The shape of the relative permeability plot shows an expo-
nential reduction in the relative coefficient of permeability
with respect to the degree of saturation of the soil. This
type of plot allows a visualization of the change in the coef-
ficient of permeability over about two orders of magnitude.
(7.19)
Several other relationships between the coefficient of per-
meability and matric suction have also been proposed and
are shown in Table 7.2 (Gardner, 1958a; Arbhabhirama and
Kridakorn, 1968).
The water coefficients of permeability k w corresponding to
various degrees of saturation can be expressed as the relative
water phase coefficient of permeability k rw in percent form:
k w ×
100
k rw =
(7.20)
k s
 
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