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F =(strength)/(loading) = tan
/tan
?
with
tan
?
= |
| /
'
(10.8)
refers to the actual stress state in a potential slip plane. The slope is
stable for
F >
1, in a limit state at
F =
1, and unstable for
F <
1. Inserting (10.7)
yields
Here,
?
F =
(tan
/tan
)
) [1
(
w
/
)(
tan
)
tan(
)
+
) + 1
)
+
w
h
c
/(
cos
)
)]
(10.9)
=
k
;
/k
<
1 it enhances stability, i.e. perpendicular fissures may improve the stability,
but permeable strata parallel to the slope reduce stability. Formula (10.9) also
shows that for outflow perpendicular to the surface. i.e.
This shows that an anisotropic permeability affects the slope stability. When
=
90
o
, the slope is
)
+
90
o
, the slope is stable.
Finally, in the case of capillary pressure head
h
c
the stability increases, but this
effect decreases with depth. In the case of outflow, there is no capillary pressure
and (10.9) with
h
c
= 0 should be applied.
unstable, whereas for perpendicular inflow, i.e.
)
+
=
)
W
H
T
N
L
Figure 10.3 Slope sliding according to Cullmann
C
SLIDE ON SHORT SLOPES
(
MACRO
-
STABILITY
)
The simplest approach for sliding of a short slope, under angle
)
, is by
considering a straight slip surface at an angle
passing through the toe of the slope
(Fig 10.3), known as Cullmann's method. The weight of the sliding soil mass,
W =
, is counterbalanced by the normal and shear force in the slip
surface,
N = W
cos
LH
sin(
)
)/sin
)
. Adopting the Mohr-Coulomb failure criterion,
giving a maximum shear force of, |
T
crit
| = cL + N
tan
and
T =W
sin
, leads to the following
stability factor
F = |T
crit
|/|T| =
(
cL + W
cos
tan
)/
Wsin
=
2
sin
)
c
tan
=
(10.11)
(
)
sin(
)
)
sin
H
tan
The most unfavourable angle
follows from requiring
dF/d
=
0, giving
=
(
)
+
)/2. This renders (10.11) into
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