Environmental Engineering Reference
In-Depth Information
where:
but the methods are not as advanced and standardized as
laboratory methods. Laboratory tests are more economical
to perform.
k w / ρ w gm 2 , coefficient of consolidation for the
unsaturated soil, and
c v
=
1 /m 2 , the gravity term.
c g
=
7.6.1 Laboratory Test Methods
Various laboratory methods can be used for measuring the
coefficient of permeability with respect to the water phase,
k w , in unsaturated soils (Klute, 1972). All methods assume
the validity of Darcy's law, which states that the coefficient
of permeability is the ratio of the flow rate to the hydraulic
head gradient. The flow rate and the hydraulic head gradi-
ent are the variables usually measured during a permeability
test. The flow rate and the hydraulic head gradient can either
be kept constant with time (i.e., time independent) or varied
with time during the test. Correspondingly, the various test-
ing procedures can be categorized into two primary groups:
steady-state methods where the quantity of flow is time inde-
pendent and unsteady-state methods where the quantity of
flow is time dependent.
The steady-state method is described first, followed by
a description of the unsteady-state, instantaneous profile
method. Some recent applications of the instantaneous
profile method for measuring the unsaturated permeability
function are also presented. The method is referred to as the
“wetting front advancing method” and was developed by Li
et al.(2009). In this method, a large-scale soil column is used
to simulate the flow of water into an unsaturated soil column.
The rate of water rise in the column along with other data is
monitored and used to calculate the permeability function.
Results when using this test procedure are later reported
for several coarse-grained soils. The measurement of the
saturated coefficient of permeability has been described in
numerous soil mechanics topics and is not repeated herein.
The general governing equation for an anisotropic soil can
be simplified to an anisotropic case which coincides with
the Cartesian coordinates by setting the α angle to zero.
Isotropic soil conditions are obtained by setting k wx =
k wy .
The general governing equation can therefore be used to
solve transient or unsteady-state water seepage problems
through saturated-unsaturated flow systems. The water coef-
ficient of permeability becomes equal to the saturated coef-
ficient of permeability k s for the saturated portion. The
saturated coefficient of permeability may vary with respect
to direction (i.e., anisotropy) or with respect to location (i.e.,
heterogeneity). In this case, both anisotropy and heterogene-
ity with respect to permeability can be taken into account.
The coefficient of water volume change, m 2 , approaches the
value of the coefficient of volume change, m v ,asthesoil
becomes saturated.
7.6 DIRECT MEASUREMENT OF WATER
FLOW PROPERTIES
The application of flow laws to engineering problems requires
the determination of the hydraulic properties of a soil. The
water phase coefficient of permeability for an unsaturated
soil can be determined either using direct laboratory mea-
surements or through indirect estimation techniques based on
the SWCC. Direct measurements of the water coefficient of
permeability can be performed either in the laboratory or in
the field. The direct measurements are referred to as perme-
ability tests and the apparatus used to perform the test in the
laboratory is called a permeameter.
Indirect estimation techniques make use of the volume-
mass properties, the SWCC, and the saturated coefficient of
permeability. The coefficient of permeability is computed
for a range of soil suctions and the results are referred to as
a permeability function for the soil.
There is no theoretical procedure whereby the coefficient
of permeability for a soil can be computed with the same
confidence that is obtained from a direct measurement (Hil-
lel, 1982). The hydraulic head gradient and the flow rate are
determined from pore-water pressure head and quantity of
flow measurements when directly measuring the coefficient
of permeability. Measurements of the coefficient of perme-
ability for an unsaturated soil must be measured at a variety
of soil suction values.
There are a number of other procedures that have been
proposed for measuring the coefficient of permeability of an
unsaturated soil. Sometimes the pore-water pressure or the
water content is measured while other variables are inferred
from the SWCC. Measurements can be performed in situ,
7.6.2 Steady-State Methods to Measure Permeability
The steady-state method for the measurement of the water
coefficient of permeability is performed by maintaining a
constant hydraulic head gradient across an unsaturated soil
specimen. The matric suction and water content of the soil
are also maintained constant. The constant hydraulic head
gradient produces a steady-state water flow across the spec-
imen. Steady-state conditions are achieved when the flow
rate entering the soil is equal to the flow rate leaving the
soil. The coefficient of permeability k w corresponding to
the applied matric suction is computed. The experiment can
be repeated for different magnitudes of matric suction (or
water content). The steady-state method can be used for both
compacted and undisturbed specimens.
7.6.2.1 Apparatus for Steady-State Method
An assemblage of the equipment used for the steady-state
method is shown in Fig. 7.27 (Klute, 1965a). A cylindri-
cal soil specimen is placed in a permeameter between two
high-air-entry ceramic plates. The pressure applied at the
 
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