1115
Technical Committee 106 /
Comité technique 106
also noticed suction reduction for axial strains until about 3%
and smaller changes as shearing progressed after that. The
authors performed CW tests on a compacted residual soil from
the Jurong sedimentary formation using a suction range that is
above the range chosen for the tests presented in this paper. As
pointed out, target initial suctions used in this experimental
program varied between 15 and 100 kPa. However, after
consolidation, the suction was allowed to vary and suctions at
failure ranged from 2 to 43 kPa.
- (kPa)
Figure 2. Typical stress-strain curves of the CW tests.
0
5
10
15
20
25
Axial strain (%)
0
10
20
30
40
50
u
a
-
u
w
(kPa)
50
150
300
500
-
u a
(kPa)
Figure 3. Typical suction changes during shearing of the CW tests.
Data from saturated and unsaturated tests were gathered in
the space [(
σ
1
-
σ
3
)/2], [(
σ
1
+
σ
3
)/2 -
u
a
] and (
u
a
-
u
w
). Thus,
points of maximum ordinates of the Mohr circles and the
associated suction at failure were plotted in Figure 4. It is
possible to notice that the points are approximately distributed
along a plane surface. Taking this into account, the
experimental points were fitted by a planar failure surface
according to the proposition of Fredlund et al. (1978), resulting
into a nice surface fitting with determination coefficient (
r²
) of
0.99. The obtained shear strength parameters were transferred to
the
(
σ
- u
a
) and (
u
a
- u
w
) space, resulting in
c’
of 8 kPa,
’
of
32
o
and
b
, the friction angle with respect to suction, equal to
27
o
. The planar shear strength envelope, expressed in Equation
3, shows an internal friction angle that is quite close to the value
derived from the saturated shear strength envelope. The friction
angle with respect to suction was lower than
’
and the cohesion
obtained from the three-dimensional fit was approximately the
same value obtained from the saturated envelope.
27
32
8
tan u u
tan u
w a
a
[kPa]
(3)
where
is the shear strength and (
σ
-
u
a
) is the net normal
stress.
Non-linearity in the relationship between shear strength and
soil suction has been recognized by many authors, however this
was not evident in this case probably due to the small range of
suction registered at failure.
Figure 4. Planar shear strength envelope in the space [(
σ
1
-
σ
3
)/2], [(
σ
1
+
σ
3
)/2 -
u
a
] and (
u
a
-
u
w
).
3.2. Small-strain shear modulus
From the tests performed with bender elements, the shear wave
velocities were calculated and plotted against the wave path
length (
L
) to wavelength (
λ
) ratios. The wavelength was
estimated from the relation between
V
s
and the frequency of the
input signal. According to Sanchez-Salinero et al. (1986) and
other authors, the
L
/
λ
is useful to select signals with reduced
near-field effects. An analysis of the results of the saturated and
unsaturated bender element tests indicated that the shear wave
velocity tended to remain constant when
L
/
λ
is larger than 3.
Therefore, the wave velocity in each stress condition was taken
as the average velocity for
L
/
λ
≥ 3.
The influence of isotropic confining stress and suction on the
small-strain shear modulus of the soil is shown in Figures 5 and
6. Both figures readily indicate that an increase in any of these
variables is able to rise
G
o
, which ranged from 78 to 468 MPa.
In Figure 5, it can be noticed that potential curves (Equation 4)
nicely fitted the experimental data of
G
o
versus
confining stress.
The parameters obtained from the fits can be seen in Table 1.
b
a
o
u .a G
3
(4)
where
G
o
is in MPa, (
σ
3
-
u
a
) represents either effective or
net isotropic stress in kPa, and
a
and
b
are empirical fitting
parameters.
In Table 1, some aspects of the influence of suction on the
small-strain shear modulus can be observed. The parameter
a
increased with increasing suction. Moreover, the constant
b
decreased when suction increased, which means that the net
confining stress has more influence on the soil under lower
suctions than on the soil under higher suctions.
The small-strain shear modulus variation with suction is
shown in Figure 6, where a hyperbolic function (Equation 5)
better suited the experimental data in comparison to the
potential fit. Table 2 shows the parameters of Equation 5 for
each confining stress.
)u u.(nm
u u
G G
w a
w a
sat o
o
(5)
where
G
o sat
is the small-strain shear modulus of the saturated
soil,
m
and
n
are empirical fitting parameters,
G
o
and
G
o sat
are
in MPa, (
u
a
-
u
w
) in kPa.
Figure 4. Planar shear strength envelope in the space [(
σ
1
-
σ
3
)/2], [(
σ
1
+
σ
3
)/2 -
u
a
] and (
u
a
-
u
w
).
3.2. Small-strain shear modulus
From the tests performed with bender elements, the shear wave velocities were calculated and plotted agai
length (
L
) to wavelength (
λ
) rati s. The wavel ngth was estimated from the relation bet een
V
s
and the
input signal. According to Sanchez-Salinero t al. (1986) and other authors, the
L
/
λ
is useful to select sig
near-field effects. An analysis of the results of the saturated and unsaturated bend r element tests indica
wave velocity tended to remain constant when
L
/
λ
is larger than 3. Therefore, th wave velocity in each str
taken as the average velocity for
L
/
λ
≥ 3.
The influence of isotropic confining stress and suction on the small-strain shear modulus of the soil is s
and 6. Both figures readily indicate that an in rease in an of these variables is able to rise
G
o
, which rang
MPa. In Figure 5, it can be noticed that potential curves (Equation 4) nicely fitted the experimental
confining stress. The parameters obtained from the fits can be see in Table 1.
b
a
o
u .a G
3
where
G
o
is in MPa, (
σ
3
-
u
a
) represents either effective or net isotropic stress in kPa, and
a
and
b
ar
parameters.
In Table 1, some aspects of the influence of suction on the small-strain shear modulus can be observed.
increased with increasing suction. Moreover, the constant
b
decreased when suction increased, which
confining stress has more influence on the soil under lower suctions than on the soil under higher suctions.
The small-strain shear modulus variation with suction is shown in Figure 6, where a hyperbolic func
better suited the experimental data in comparison to the potential fit. Table 2 shows the parameters of Eq
confining stress.
)u u.(nm
u u
G G
w a
w a
sat o
o
(5)
where
G
o sat
is the small-strain shear modulus of the saturated soil,
m
and
n
are empirical fitting parame
are in MPa, (
u
a
-
u
w
) in kPa.