Environmental Engineering Reference
In-Depth Information
suction (or low water content) will have a lower water
coefficient of permeability than a point having low matric
suction.
Several functional relationships between the water coeffi-
cient of permeability and matric suction [i.e., k w u a
u w ]
have been described. The coefficients of permeability at
different points in a soil mass are obtained from the per-
meability function where the magnitude of the coefficient
of permeability depends on matric suction.
The coefficient of permeability at a point may also vary
with respect to direction, and this condition is referred to as
anisotropy. The largest coefficient of permeability is called
the major coefficient of permeability. The smallest coeffi-
cient of permeability is in a direction perpendicular to the
largest permeability and is called the minor coefficient of
permeability.
(a) Water flow above the phreatic line in an earthfill dam.
7.4.2 Heterogeneous, Isotropic Steady-State Seepage
Permeability conditions in unsaturated soils can be clas-
sified into three groups, as illustrated in Fig. 7.21. The
(b) Downward moisture movement (infiltration) and upward
moisture movement (evaporation) through the unsaturated zone.
Figure 7.20 Examples involving flow through unsaturated soils.
k x = k y
The main difference between saturated and unsaturated soil
problems is the difference in the water coefficient of perme-
ability which is assumed to be constant for saturated soils
while it is necessary that it be considered as a function of
suction, water content, or some other variable for unsatu-
rated soils. The pore-water pressure generally has a positive
gauge value in a saturated soil and a negative gauge value in
an unsaturated soil. The formulation of differential equations
of flow can be derived in a similar manner for both the satu-
rated and unsaturated soils even though there are significant
differences between the two cases. In other words, there is
a smooth transition when going from the unsaturated to the
saturated case (Fredlund, 1981b).
k y
k y
B
k x
y
k x
A
x
(a)
k x
k x
=
1
k y
k y
A
B
k y
k x
k y
B
7.4.1 Variation of Coefficient of Permeability
with Space for Unsaturated Soil
The coefficient of permeability is a constant with respect
to time at each point in a soil continuum for steady-state
seepage analyses. However, the coefficient of perme-
ability usually varies from one point to another in an
unsaturated soil. A spatial variation in permeability in
a saturated soil can be attributed to a heterogeneous
distribution of the soil solids. The variation in the volume
distribution of the pore-fluid (i.e., pore-water) gives
rise to a heterogeneous system in an unsaturated soil.
Consequently, there is a spatial variation in the coefficient
of permeability in an unsaturated soil system. Although
the soil solid distribution may be homogeneous, the
pore-fluid volume distribution can be heterogeneous due to
spatial variations in matric suction. A point of high matric
A
(b)
k x
k x
k y
k y
A
B
k y
k y
B
k x
k x
A
(c)
Figure 7.21 Principal coefficient-of-permeability variations in
unsaturated soil: (a) heterogeneous, isotropic conditions; (b) het-
erogeneous, anisotropic conditions; (c) continuous variation of per-
meability with space.
 
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