Civil Engineering Reference
In-Depth Information
displacements should be considered order-of-
magnitude estimates of actual field behavior,
CDMG
Examples of variability in design parameters
are as follows. The orientation of a discontinuity
may vary across the slope due to surface irregular-
ities or folding. This variation will be evident from
scatter in the pole locations on the stereonet, and
can be quantified in terms of means and standard
deviations of the dip and dip direction using the
procedure shown in Section 3.5. Also, the shear
strength may vary over the sliding surface because
of variations in surface roughness and infilling,
and can be quantified by testing a number of drill
core or lump samples in the laboratory. The water
pressure is likely to vary with time in response to
precipitation events such as heavy rain storms or
melting snow.
Figure 6.14 shows the results of a probabil-
istic stability analysis of the slope described in
Section 4.4 (see Figures 4.18 and 4.19). Sec-
tion 4.4 describes the calculation of the shear
strength properties of the bedding planes, assum-
ing that the factor of safety was 1.0 when the
tension crack filled with water and the slope
failed. The purpose of the probabilistic ana-
lysis described in this section is to show the
range in factor of safety that is likely to exist in
practice due to the variability in the slope para-
meters. Figure 6.14(b)-(c) show the probability
distributions of the following parameters:
(1997)
has
developed
the
following
guidelines on likely slope behavior:
•
0-100 mm displacement—unlikely to corres-
pond to serious landslide movement;
•
100-1000 mm—slope deformations may be
sufficient to cause serious ground cracking or
enough strength loss to result in continuing
post-seismic failure; and
•
>
1000 mm displacement—damaging landslide
movement and slopes should be considered
unstable.
When applying these displacement criteria
in rock slope design, consideration should be
given to the amount of displacement that will
have to occur before the residual shear strength
is reached. For example, if the sliding sur-
face is a single discontinuity surface containing
a weak infilling, a few centimeters of move-
ment may be sufficient for the strength to be
reduced to the residual value. In contrast, a
fractured rock mass may undergo several meters
of displacement with little reduction in shear
strength.
6.6 Example of probabilistic design
The design procedures discussed so far in this
chapter all use, for each design parameter, single
values that are assumed to be the average or
best estimate values. In reality, each parameter
has a range of values that may represent natural
variability, changes over time, and the degree of
uncertainty in measuring their values. Therefore,
the factor of safety can be realistically expressed
as a probability distribution, rather than a single
value. In design, this uncertainty can be accoun-
ted for by applying judgment in using a factor of
safety consistent with the variability/uncertainty
in the data. That is, a high factor of safety would
be used where the values of the parameters are not
well known. Alternatively, the uncertainty can
be quantified using probabilistic analysis, such as
Monte Carlo analysis, to calculate the probability
of failure (see Section 1.4.4).
•
Dip of the sliding plane
,
ψ
p
—Normal dis-
tribution with a mean value of 20
◦
and a
standard deviation of 2.4
◦
.
•
Cohesion
,
c
—Skewed triangular distribution
with most likely value of 80 kPa and max-
imum and minimum values of 40 and 130 kPa,
respectively (4-13.3 ton /m
2
).
•
Friction angle
,
φ
—Normal distribution with
a mean value of 20
◦
and a standard deviation
of 2.7
◦
.
•
Water pressure expressed as percent filling
of tension crack
—Triangular distribution ran-
ging from dry (0%) to full (100%), with the
most likely value being 50%.
The triangular distribution is used where the
most likely value and the upper and lower bounds
can only be estimated, whereas the normal
distribution is used where there is sufficient data
