Geoscience Reference
In-Depth Information
In theory, one finds that slopes are usually curved (logarithmic spirals). The
approximate approach of a circular slip surface is popular, because the kinematics
is rather simple. Stability is expressed by rotational equilibrium around the circle
centre (Fig 10.4a) and this yields the following stability factor for cohesive soils (
W
is the weight per metre longitudinal width in kN/m)
F = (shear resistance moment) / (driving moment) = c
u
LR/Wd
(10.15)
Here,
L
is the length of the circular slip surface. The most critical circle is found
by trial and error. Taylor worked it out for cohesive soils in a practical diagram
(Fig 10.4b). Comparison of the different methods, previously explained, shows a
large variation. For a slope under an angle of
=
35
o
with a deep subsoil, Taylor's
)
diagram gives a stability factor
F =
5.6
c
u
/
H
. It is an upper limit and it is essential
to use in addition an appropriate safety factor.
b
R
W
E
r
H
h
E
l
)
l
T
N
u
Figure 10.5 Method of slices
For layered soil and/or drained slopes the situation is more complicated, because
the shear resistance varies along the slip surface and the subsoil may contain
different layers. The assumed slipping soil mass is divided into vertical slices with
a fixed width
b
and an average height
h
(Fig 10.5). The weight of the slice
W =
bh
is counterbalanced by the normal and shear force in the slip surface,
N = W
cos
and
T =W
sin
. The Mohr-
Coulomb failure criterion yields a maximum shear force of
T
crit
= cl + N'
tan
. The width of the slip surface of the slice is
l = b/
cos
,
with
N' = N - ul
and with
u
the local pore pressure. Stability is satisfied by the
rotation equilibrium of the weight of all slices and the sum of the shear forces
%
i
G
i
R
sin
i
<
%
i
T
i,crit
R
(10.16a)
The corresponding stability factor is
F =
%
i
T
i,crit
/
%
i
W
i
sin
i
=
%
i
(
cl
i
+ N'
i
tan
) /
%
i
W
i
sin
i
(10.16b)
The problem is to determine
N'
, since the inter-slice forces
E
are unknown.
Fellenius' method, applied for the first time in 1915, assumes that the resultant of
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