Geology Reference
In-Depth Information
where
is total stress (generally due to weight)
normal to the failure plane;
u
is water pressure reducing
τ
is shear strength;
σ
σ
to an
effective stress,
is angle of friction; and
c
is cohesion.
Frictional resistance changes with stress conditions, which vary
throughout the slope, and to deal with this, a method of slices is used
typically to calculate stability.
Figure 6.24
shows a slope with the poten-
tial failing mass split into four vertical slices. In this diagram, the weights
of slices 1 and 3 have been resolved into destabilising shear force,
S, parallel to the tangent to the section of slip surface below each slice
and a normal force acting normal to the shear surface (N). It is evident
that the ratio of S to N varies considerably from one slice to the next.
Slices 1 and 2 are being prevented from failing by Slices 3 and 4. The FoS
for the slope as a whole is the ratio of the summation of shear resistances
beneath each slice to the summation of the shear components. There are
many different versions of the method of slices. For some, circular slip
planes are assumed, in others, irregular slip surfaces can be analysed
(e.g. Morgernstern & Price, 1965). Slice boundaries are generally taken
to be vertical and assumptions need to be made regarding the forces at the
vertical interfaces between each slice. The method of Sarma (1975)
allows non-vertical slices, which gives some
σ′
;
ϕ
flexibility in dealing with
more complex geology. Software packages (limit equilibrium) give a
range of options regarding the method of analysis and give almost instant
answers so the results from the various analytical models can be com-
pared. Sometimes this is done in a probabilistic manner, varying the
various strength parameters through their anticipated ranges and distri-
butions (Priest &Brown, 1983). Generally, these analyses are carried out
to try to establish that the FoS exceeds some chosen value
typically
between 1.2 for a slope with low consequence of failure and 1.4 for a
higher risk slope and, empirically, most slopes analysed with such FoS
-
Figure 6.24
The
method of slices for
slope stability
analysis.
Normal component
(N) of weight of
slice (W)
1
W
1
2
Shear
component
of weight of
slice (S)
3
W
3
N
4
Shear strength for each slice
= N tanφ + C
Where C = 'cohesion' along
slice base length
