Environmental Engineering Reference
In-Depth Information
Table 11.8 Strain Rate and Strain at Failure for Triaxial on Unsaturated Soils
Approximate
Strain Rate,
Strain at Failure,
Soil Type
Triaxial Test
(% /s)
˙
f
(%)
References
10
−
5
=
11
.
6%
3
.
5
×
Boulder clay;
w
CW
15
Bishop et al. (1960)
=
and % clay
18%
10
−
5
Braehead Silt
CW
4.7
×
11
Bishop and Donald (1961)
10
−
6
CD
8.3
×
12
10
−
7
Talybont boulder clay;
w
=
Undrained with
pore pressure
measurements
4.7
×
σ
3
=
83 kPa : 8.5
Donald (1963)
9.75% and % clay
=
6%
σ
3
=
207 kPa : 11
10
−
4
Dhanauri clay;
w
=
22.2%
CW
6.7
×
20
Satija and Gulhati (1979)
10
−
4
and % clay
=
25 %
CD
1.3
×
20
10
−
5
Undisturbed decomposed
CD
1.7
×
Stage I: 3-5
Ho and Fredlund (1982a)
10
−
5
granite and rhyolite
Multistage
6.7
×
Stage II: 1-3
Stage III: 1-3
10
−
3
Clayer sand;
w
=
14-17%
Undrained and
unconfined
1.7
×
15-20
Chantawarangul (1983)
and % clay
=
30%
The time required to fail the soil specimen,
t
f
, can be
expressed in terms of a desired degree of dissipation of
excess pore-water pressure (Bishop and Gibson, 1963):
L
2
ηc
v
w
1
t
f
=
−
U
f
(11.34)
where:
L
=
half of the actual length of the soil specimen, which
is the same for single or double drainage,
η
=
0.75 / (1
+
3/
λ
) for single drainage,
η
=
3/(1
+
3/
λ
) for double drainage,
k
w
/
ρ
w
gm
2
, the average coefficient of consolida-
tion with respect to the water phase,
c
v
=
ρ
w
=
density of water,
g
=
gravitational acceleration,
slope of the plot of water volume change,
V
w
/
V
versus suction, and
m
2
=
U
f
=
average degree of dissipation of the excess pore-
water pressure at failure.
The effect of impeded flow on the time to failure
t
f
is
taken into account through the impedance factor
λ
in the
η
parameter in Eq. 11.34. The properties of an unsaturated
soil specimen are taken into account through the
L
and
c
v
terms. Approximate properties for the unsaturated soil (i.e.,
k
w
and
m
2
) can be used to estimate the average coefficient of
consolidation
c
v
. Any desired value for the average degree
of dissipation
U
f
can be used, but a value of 95% is rec-
ommended (Gibson and Henkel, 1954; Bishop and Henkel,
1962). An average degree of dissipation of 95% means that
95% of the excess pore-water pressure developed during
shear will be dissipated at the time of failure.
Figure 11.88
Impedance factors
λ
for various ratios
k
w
/k
d
and
L
d
/d
for single drainage.
The time to failure
t
f
(i.e., Eq. 11.34) can be plotted with
respect to the impedance factor
λ
for various values of the
coefficient of consolidation
c
v
, as shown in Fig. 11.89. For
single drainage testing the length of the drainage path is
equal to the height of the soil specimen (i.e., 140 mm). The
graph indicates that more time is required to reach failure
as the coefficient of consolidation decreases (i.e., a decrease
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