Environmental Engineering Reference
In-Depth Information
of water is assumed to be 1000 kg/m
3
and the dynamic
viscosity
v
is selected for a temperature of 20
◦
C. (Note that
1 cP is equal to 10
−
3
Pa
s.)
Intrinsic permeability is often used to convert flow
properties from one discipline to another discipline (e.g.,
between petroleum, agriculture disciplines, and geotechnical
engineering). The concept of intrinsic permeability also has
an important role to play in unsaturated soil mechanics
because the soil has two fluid phases (i.e., water and air). For
example, measurements of saturated water hydraulic con-
ductivity can be used to calculate a value for air hydraulic
conductivity for a dry soil at the same void ratio. Saturated
water hydraulic conductivity measurements can also be
used along with a SWCC to estimate an air permeability
function for an unsaturated soil. The properties of fluids in
a porous medium can provide an estimate of the relative
magnitude differences between the ease of flow of the
two fluids (e.g., air and water).
The intrinsic permeability of a soil,
K
, represents the char-
acteristics of the porous medium and is independent of the
fluid properties. The porous medium, in turn, is a function
of the volume-mass properties of the soil. In geotechnical
engineering, the coefficient of permeability
k
w
is used to
embraces the overall effect of variables related to the porous
medium and the pore fluid. The coefficient of permeability
k
w
is the variable form most commonly used in geotechnical
engineering and is used throughout this topic.
·
sor1mPa
·
Figure 7.7
Development of unsaturated soil by retraction of air-
water interface under increasing matric suctions (i.e., stages 1-5)
(after Childs, 1969).
flows through the pore space filled with water; therefore,
the percentage of the voids filled with water is an important
factor. As a soil begins to desaturate, air first replaces some
of the water in the large pores. The onset of desaturation
causes water to flow through the smaller pores. The path-
way through the smaller pores leads to increased tortuosity
and consequently much slower flow. An increase in matric
suction in the soil leads to a further decrease in the pore
volume occupied by water. The air-water interface is drawn
closer and closer to the soil particles (Fig. 7.7). As a result,
the coefficient of permeability with respect to the water
phase decreases rapidly as the space available for water flow
is reduced.
7.3.3 Relationship between Permeability and
Volume-Mass Properties
The coefficient of permeability
k
w
is a function of any two of
three possible volume-mass properties (Lloret and Alonso,
1980; Fredlund, 1981b):
7.3.4 Effect of Variations in Degree of Saturation
on Coefficient of Permeability
The coefficient of permeability of an unsaturated soil can
vary considerably during a transient process as a result of
changes in the volume-mass properties. The change in void
ratio in an unsaturated soil may be small in soils of low
compressibility and its effect on the coefficient of perme-
ability may be secondary. However, changes in degree of
saturation generally produce large changes in the coefficient
of permeability. As a result, the coefficient of permeability
is often described as a singular function of the degree of
saturation,
S
. The degree of saturation is related to matric
suction and the relationship is referred to as the SWCC
(Fig. 7.8a).
Numerous semiempirical equations for the coefficient of
permeability have been derived using the matric suction ver-
sus degree of saturation curve. The soil pore-size distribution
forms the basis for predicting the coefficient of permeabil-
ity. The pore-size distribution concept originated in the soil
sciences and has been introduced into geotechnical engi-
neering. The pore-size distribution has also been used in
other disciplines to provide an estimate of the rate at which
the coefficient of permeability decreases with the degree of
saturation of a soil.
k
w
=
k
w
(S,e)
(7.11)
or
k
w
=
k
w
(e,
w
)
(7.12)
or
k
w
=
k
w
(
w
,S)
(7.13)
where:
S
=
degree of saturation,
e
=
void ratio, and
w
=
gravimetric water content.
The coefficient of permeability in a
saturated
soil is a
function of the void ratio (Lambe and Whitman, 1979).
However, the coefficient of permeability is generally
assumed to be a constant when analyzing most steady-state
and transient flow problems in saturated soils.
The coefficient of permeability in an
unsaturated
soil is
significantly affected by combined changes in void ratio and
degree of saturation (or water content) of the soil. Water
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