Shear Strength of Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 583

(a)

Figure 11.87 Properties and variables required to model pore
pressure equalization for unsaturated soil specimen placed on high-
air-entry disk.

be incompressible, and its properties appear in the form of
an impedance factor λ :

k d d
k w L d

λ = (11.33)

where:
λ

(b)

= impedance factor,

k d = water coefficient of permeability of the high-air-entry

disk,

k w = coefficient of permeability of the unsaturated soil

with respect to the water phase,

d = length of drainage path in the soil, and

thickness of the high-air-entry disk.
Let us consider the case of single drainage where pore-
water drains only to the bottom (or top) of the soil specimen.
The length of the drainage path, d , is equal to the height
of the soil specimen, 2 L (i.e., d

L d =

(c)

Figure 11.86 Undrained test on compacted clay shale specimen
tested at strain rate of 4 . 6 × 10 − 5 % /s : (a) shear stress versus strain
curve; (b) pore-water pressure versus strain at two points of mea-
surement; (c) total volume change versus strain (after Bishop et al.,
1960).

2 L ; see Fig. 11.87). If
the pore-water is allowed to drain from the top and bottom
of the specimen (i.e., double drainage), the length of the
drainage path becomes half of the specimen height (i.e.,
d

=

k w . When the air phase is occluded, the air coefficient of
permeability reduces to the diffusivity of air through water.
It is assumed that the dissipation of the excess pore-water
pressure requires more time than the dissipation of the
excess pore-air pressure. The time required to fail an
unsaturated soil specimen can be computed by considering
the dissipation of excess pore-water pressure.
The solution to the problem of excess pore-water pressure
dissipation with impeded flow is mathematically equivalent
to the heat conduction of a slab initially at a uniform
temperature being cooled at its surface in accordance with
Newton's law (Carslaw and Jaeger, 1959). The solution can
be written as a Fourier series (Gray, 1945). Figure 11.87
shows the dimensions and property variables of an un-
saturated soil specimen and high-air-entry disk required
in the solution to the impeded dissipation of excess
pore-water pressures. The high-air-entry disk is assumed to

L ). Water is usually permitted to drain through the high-
air-entry disk at the bottom of the specimen when testing
unsaturated soils.
Equation 11.33 is plotted in Fig. 11.88 in terms of dimen-
sionless ratios k w / k d and L d / d for single drainage dissi-
pation (i.e., d

=

2 L ). The dimensionless form allows the
assessment of the impedance factor λ for a wide range of
soils and high-air-entry disks. The impedance factor λ can
be obtained directly from Fig. 11.88 when the properties of
the specimen and the high-air-entry disk are known. The
coefficient of permeability with respect to the water phase,
k w , may vary depending upon the matric suction of the
specimen. The coefficient of permeability of the soil can

=

be expressed as a function of matric suction, k w u a − u w .

It would appear that the rate of strain should be decreased
as matric suction is increased.