Geoscience Reference
In-Depth Information
4
sin
)
c
tan
F =
(10.12)
(
)
cos
cos
)
H
tan((
)
)
/
2
Usually slip surfaces are curved and Cullman's method overestimates the
stability. Formula (10.12) is more applicable for steep slopes, in particular for
undrained cohesive soils, for which, with
c = c
u
and
=
0, (10.12) gives
4
sin
)
c
F =
(10.13)
(
u
)
1
cos
)
H
For a vertical slope (10.13) yields with
F = 1
a maximum possible height of
H =
4
c
u
/
(10.14a)
Since the used approach is based on a plausible kinematic pattern, (10.14a) is an
upper limit (failure could occur at less height). A lower limit (equilibrium
solutions) can be obtained by considering the Mohr-Coulomb criterion, which
states for cohesive undrained soil (with
=
0
)
h
=
v
-
2
c
u
. At the toe of the
vertical slope, at maximum height
H
, the stresses are
H
, and
therefore the maximum height has a lower limit (stability is guaranteed; a deeper
cut may be possible). The following holds as a lower limit
h
=
0 and
v
=
H =
2
c
u
/
(10.14b)
Studies have shown that in reality the maximum height of a vertical slope of
cohesive soil is in between a lower limit of 3.64
c
u
/
and an upper limit of 3.83
c
u
/
.
Under submerged conditions (10.14) applies, with
replaced by
w
. Using
'heavy water' (bentonite slurry), in fact involving a large '
w
', vertical slopes can
be sustained to even larger depth. This method is applied to create slurry walls,
diaphragm walls, and soil mixing (see Chapter 11).
0.25
d
0
D
&
0.20
10
20
3
2
1.25
0
0.15
R
W
H
c
u
(
)
H
DH
)
c
u
0.05
)
0.00
20
40
60
80
(a) (b)
Figure 10.4 Circular slip failure of cohesive slopes (Taylor)
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