Geoscience Reference
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inter-slice forces on both sides act opposite and cancel out, giving
N' =
W
cos
-
ul
. Fellenius' stability factor becomes
h
i
cos
2
F
F
=
%
i
[(
c +
(
u
i
)tan
)/cos
i
] /
%
i
(
h
i
sin
i
)
(10.16c)
i
For a straight slip line in an infinite dry slope of non-cohesive soil (
c =
0)
(10.16c) becomes
F
F
=
tan
, equal to (10.11). Practice has shown that
Fellenius' method yields a relatively low stability factor (less by 5% to 20%).
Bishop's method assumes that the inter-slice shear forces on the vertical slice
interfaces balance (their contribution to vertical equilibrium cancels), and that the
same stability factor applies to every slice separately. Vertical equilibrium then
yields
W = T
sin
/
tan
)/
F
. From
these conditions
N'
can be determined in every slice. Bishop's stability factor
becomes
+
(
N'+ul
) cos
. Moreover,
T = T
crit
/F =
(
cl + N'
tan
F
B
=
%
i
[(
c +
(
h
i
u
i
)
tan
)/(cos
i
(1
+
tan
i
tan
/F
B
))]/
%
i
(
h
i
sin
i
)
(10.16d)
Since
F
B
appears implicitly, an iterative approach is required. For cohesive soils
(
=
0) and a straight slip surface both (10.16c) and (10.16d) become
F = c/
(
h
sin
), which is in accordance with (10.2b). Bishop's method is applicable
for heterogeneous soils. Strong negative values of
cos
, near the toe, may give
unrealistic contributions, it is suggested then to limit
/4. Many computer
programs based on Bishop's approach are available, which search for a minimum
F
while varying
R
and the centre point of the slip circle.
to
/2-
R
H
)
E
uplift
pore pressures
Figure 10.6 Slip surface with uplift
In some cases a circular slip surface does not fit, and one may apply a non-
circular slip method, e.g. the method of Janbu, Spencer, or Morgenstern and Price.
The latter rigorously solves for vertical, horizontal and moment equilibrium, both
locally per slice and globally. It requires input of an arbitrary function describing
the change of the angle of the interslice force in the slipping mass. Spencer
simplified this by assuming a constant angle throughout, and his method is also
widely used.
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