Civil Engineering Reference
In-Depth Information
5
(a)
(b)
∆
x
y
4
Stable block
p
<
W
sin
p
∆
x
/
y
> tan
p
3
Sliding only
p
>
p
∆
x
/
y
> tan
p
W
cos
p
2
W
Sliding and toppling
p
>
1
∆
x
/
y
< tan
p
Toppling only
p
<
p
0 0 0 0 0 0 0 0 0 0
;
∆
x
/
y
< tan
Base plane angle
p
(degrees)
Figure 1.10
Identification of sliding and toppling blocks: (a) geometry of block on inclined plane;
(b) conditions for sliding and toppling of block on an inclined plane.
angle (range 15-25
◦
) and the water pressure—
fully drained to fully saturated (Figure 4.20). This
plot shows that water pressures have more influ-
ence on stability than the friction angle. That is, a
fully drained, vertical slope is stable for a friction
angle as low as 15
◦
, while a fully saturated slope
is unstable at an angle of 60
◦
, even if the friction
angle is 25
◦
.
The value of sensitivity analysis is to assess
which parameters have the greatest influence on
stability. This information can then be used in
planning investigation programs to collect data
that will define this parameter(s) more precisely.
Alternatively, if there is uncertainty in the value
of an important design parameter, this can be
accounted for in design by using an appropriate
factor of safety.
parameter on slope stability. A probability distri-
bution of the factor of safety is calculated, from
which the probability of failure (PF) of the slope
is determined.
Probability analysis was first developed in the
1940s and is used in the structural and aeronaut-
ical engineering fields to examine the reliability
of complex systems. Among its early uses in geo-
technical engineering was in open pit mine slope
design where a certain risk of failure is accept-
able, and this type of analysis could be readily
incorporated into the economic planning of the
mine (Canada DEMR, 1978; Pentz, 1981; Savely,
1987). Examples of its use in civil engineering are
in the planning of slope stabilization programs
for transportation systems (Wyllie
et al
., 1979;
McGuffey
et al
., 1980), landslide hazards (Fell,
1994; Cruden, 1997) and in design of storage
facilities for hazardous waste (Roberds, 1984,
1986).
There is sometimes reluctance to use prob-
abilistic design when there is a limited amount
1.4.4 Probabilistic design methods
Probabilistic design is a systematic procedure for
examining the effect of the variability of each
