Theory of Water Flow through Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 356

7.6.2.2 Computations of Unsaturated Coefficient
of Permeability Using Steady-State Method
The coefficient of permeability k w is computed based on
Darcy's law:

An indirect technique has also been used to infer the water
content at particular matric suctions by referring to an inde-
pendently measured SWCC. The SWCC and the coefficient of
permeability can be obtained simultaneously using the appa-
ratus (Ingersoll, 1981). The change in water content during
each increment of matric suction needs to be measured.
Having measured the coefficient of permeability k w cor-
responding to a particular matric suction (or water content),
the permeability test is then repeated for higher values of
matric suction. The matric suction of the soil specimen
is increased by increasing the applied air pressure or by
decreasing the applied water pressures. The average pore-
water pressure can be decreased by reducing the values of
h w 1 and h w 2 . At no time should the matric suction exceed the
air-entry value of the ceramic plates or the matric suction
limit that can be read on the tensiometers (i.e., approxi-
mately 90 kPa). The use of higher air-entry ceramic plates
allows testing at higher values of suction. High-air-entry
ceramic plates with the highest possible coefficient of per-
meability should be selected in the design of the apparatus
to prevent impeded flow (Klute, 1972).

Q
At

d t
h w 3 −

k w = (7.65)

h w 4

The pore-air pressure is assumed to be uniform throughout
the specimen:

u a = ρ m gh m (7.66)

where:

ρ m = density of the manometer fluid,

g = gravitational acceleration, and

h m = height of the manometer fluid.

The applied hydraulic head gradient causes the pore-water
pressures to differ at tensiometers T 1 and T 2 . The average
pore-water pressure is computed as follows:

h p 3 + ρ w g

u w ave = h p 4

(7.67)

7.6.2.3 Water Coefficients of Permeability or Hydraulic
Conductivity Function
A series of coefficient-of-permeability values is obtained by
the end of the test. A typical set of data for the coefficient of
permeability k w versus matric suction is shown in Fig. 7.28.
The measured water coefficients of permeability correspond
to the drying curve. It is noted that there is hysteresis in
the relationship of the water coefficient of permeability and
matric suction. Hysteresis in the permeability function can
be observed when the permeability test is performed for both
the drying and the wetting processes. However, the steady-
state method is normally performed only when going from
a saturated to an unsaturated condition.
Another apparatus which uses a steady-state flow sys-
tem is shown in Fig. 7.29 (Klute, 1965b). A cylindrical
soil specimen is placed between two high-air-entry ceramic
plates located within an air pressure chamber. The soil spec-
imen is subjected to an all-around controlled air pressure
u a . The pore-water pressure u w is measured by means of
tensiometers placed along the length of the specimen. A
constant-hydraulic-head gradient is applied across the spec-
imen, as described in Fig. 7.29. The permeability test is
performed using the procedure previously described. The
matric suction in the specimen is increased by increasing
the all-around air pressure.
The specimen diameter is typically on the order of
25-100mm and its length ranges from 10 to 500 mm. The
longer the length of the specimen, the longer is the time
required to reach steady-state conditions. Klute (1965b)
suggested a specimen height on the order of 10-50 mm.
The specimen should not be too short because space is
required between the two tensiometers inserted in the soil
specimen. A long specimen may also require more than

2

where:

ρ w = density of water and

(u w ) ave = average of pore-water pressure.

The calculated coefficient of permeability k w corresponds
to the average matric suction in the soil:

h p 3 + ρ w g

u a −

u w ave =

h p 4

ρ m gh m − (7.68)

2

where:

(u a − u w ) ave =

average matric suction.

The water content of the soil specimen can be measured
directly using either destructive or nondestructive tech-
niques. Using a destructive technique, water contents are
measured after each stage in the permeability test. The soil
specimen can therefore be used for only one stage of the
permeability test. Several “identical” specimens must be
prepared in order to obtain the coefficient of permeability
at different matric suctions or water contents.
Using a nondestructive technique, water contents at dif-
ferent matric suctions are measured using a single soil speci-
men. This can be done using a gamma attenuation technique
or by weighing the soil specimen (together with the appa-
ratus) in order to obtain the change in water content after
each stage of the test. The initial and final water contents
are computed from the initial and final masses of the soil
specimen. The mass of soil solids is obtained by oven drying
the specimen at the end of the test.