Environmental Engineering Reference
In-Depth Information
One χ value is theoretically obtained for a particular soil
when the failure envelope is planar. A planar failure enve-
lope uses one value of φ and one value of φ b . If the failure
envelope is nonlinear with respect to φ b , there will be two
or more values for χ .A χ value equal to 1.0 corresponds
to the condition where φ b
φ b and
11.2.11 Relationship between tan
χ
The shear strength equation proposed by Bishop et al. (1960)
and that proposed by Fredlund et al. (1978) appears to be
similar in form. The χ parameter emerged in the shear
strength equation from an extension of the effective stress
equation. Equating the linear form of the Fredlund et al.
(1978) shear strength equation and the Bishop et al. (1960)
equation yields the following relationship:
u a
φ .A χ value less than 1.0
corresponds to the condition when φ b . There will be
various χ values corresponding to different matric suction
values for envelopes which are curved with respect to matric
suction.
Attempts have been made to correlate the χ parameter
with the degree of saturation of the soil (Bishop et al., 1960).
Curvature in the shear strength envelope results in nonlin-
earity of the χ parameter. The φ b and χ relationship applies
to initially “identical” soils. These may be soils compacted
at the same water content to the same dry density. The use
of σ
=
u w f
χ u a
u w f
tan φ b
tan φ
=
(11.29)
Equation 11.29 can be solved for the parameter χ :
tan φ b
tan φ
χ
=
(11.30)
u w as independent stress state variables
provides greater flexibility in terms of characterizing non-
linear shear strength behavior corresponding to a variety of
stress paths.
u a and u a
A graphical comparison between the φ b representation of
strength and the χ representation of strength is shown in
Fig. 11.19. The increase in shear strength due to matric
suction is represented as an upward translation from the
saturated failure envelope when using the Fredlund et al.,
(1978) designation. The magnitude of the upward translation
is equal to u a
u w tan φ b f (i.e., point A in Fig. 11.19).
In this case, the failure envelope for the unsaturated soil is
viewed as an upward translation of the failure envelope for
a saturated soil.
The Bishop et al. (1960) equation with the χ parameter
suggests that the same failure envelope applies for saturated
and unsaturated conditions. Matric suction is assumed to
produce an increase in the net normal stress. The increase
in net normal stress is a fraction of the matric suction at
11.3 MEASUREMENT OF SHEAR STRENGTH
The shear strength of unsaturated soils has been studied
in the laboratory using both triaxial and direct shear test-
ing equipment. It is necessary to make modifications to
conventional shear strength testing equipment in order to
independently control pressures in the air and water phases.
Modifications to shear strength testing apparatuses to accom-
modate unsaturated soils were commenced in the 1950s.
Following is a brief summary of some of the test results
obtained.
failure [i.e., χ u a
u w f ]. The shear strength at point A
using the φ b method is equivalent to the shear strength at
point A when using the χ parameter method.
11.3.1 Background of Shear Strength Measurements
A series of direct shear tests on unsaturated fine sands and
coarse silts were conducted by Donald (1956). The tests
were performed on a modified direct shear box as shown
in Fig. 11.20a. The pore-air and pore-water pressures were
controlled during shear. The top of the direct shear box
was open to the atmosphere, thereby controlling the pore-
air pressure u a (i.e., zero gauge pressure). The pore-water
pressure u w was controlled at a negative value by apply-
ing a constant negative water head below the lower porous
stone. The specimen was in contact with water below the
base of the shear box through use of a colloidon mem-
brane. The water in the base of the shear box was then
connected to a constant-head-overflow tube to produce the
desired negative water pressure (Fig. 11.20b). The negative
pore-water pressures applied to the soils were generally less
than 50 kPa.
The soil specimens of uniform initial density were con-
solidated under a total stress of approximately 48 kPa. The
desired negative pore-water pressure was applied for sev-
eral hours while the specimens came to equilibrium. The
Figure 11.19 Comparison between φ b
and χ methods of desig-
nating shear strength.
 
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