Civil Engineering Reference
In-Depth Information
A simultaneous earthquake subjected the slope to
ground motion that was simulated with a hori-
zontal seismic coefficient
k
H
of 0.08, generating
a force of
k
H
W
, where
W
was the weight of the
sliding block. The factor of safety of this slope
with the inclusion of a pseudo-static horizontal
earthquake loading is given by the equations in
Figure 14.3 (refer to Section 6.5.4, pseudo-static
stability analysis).
To allow for the possible presence of sub-
stantial sub-surface water, an alternative theor-
etical model was proposed. This is illustrated as
Model II in Figure 14.3 and, again this model
includes the pseudo-static earthquake loading.
Having decided upon the most likely failure
mode and having proposed one or more the-
oretical models to represent this failure mode,
a range of possible slope parameter values was
substituted into the factor of safety equations to
determine the sensitivity of the slope to the dif-
ferent conditions to which it was likely to be
subjected. Table 14.2 summarizes the input data.
The factors of safety of the slopes were calculated
by substituting these values into the equations on
Figure 14.3 as follows:
Overall Cut Model II
4.28
H
w
2
)
tan
φ
17,279
104.6
c
+
(
20,907
−
FS
=
Individual benches Model I
2.81
z
w
2
)
tan
φ
17.6
c
+
(
2815
−
86.3
z
w
−
FS
=
4.02
z
w
2
2327
+
Individual benches Model II
4.28
H
w
2
)
tan
φ
3469
34.9
c
+
(
4197
−
FS
=
One of the most useful studies of the factor of
safety equations was to find the shear strength
which would have to be mobilized for failure
(i.e. FS
=
1.0). These analyses examined the over-
all cut and the individual benches for a range of
water pressures. Figure 14.4 gives the results of
the study and the numbered curves on this plot
represent the following conditions:
Curve 1
Overall Cut, Model I, dry,
z
W
=
0.
Overall Cut Model I
Curve 2
Overall
Cut,
Model
I,
saturated,
z
w
=
z
=
14 m.
2.81
z
w
2
)
tan
φ
80.2
c
+
(
18,143
−
393
z
w
−
Curve 3
Overall Cut, Model II, dry,
H
w
=
0.
FS
=
Curve 4
Overall
Cut,
Model
II,
saturated,
4.02
z
w
2
14,995
+
H
w
=
60 m.
Curve 5
Individual bench, Model I, dry,
z
w
=
0.
Curve 6
Individual bench, Model II, saturated,
z
w
=
Table 14.2
Input data for Case Study I plane stability
analysis
z
=
9.9 m.
Curve 7
Individual
bench,
Model
II,
dry,
Parameter
Parameter value
H
w
=
0.
Curve 8
Individual bench, Model II, saturated,
H
w
Cut height
H
c
=
60 m
50
◦
=
H
=
20 m.
Overall slope angle
ψ
f
=
70
◦
Bench face angle
ψ
b
=
Bench height
H
b
=
20 m
The reader may feel that a consideration of all
these possibilities is unnecessary, but it is only
coincidental that, because of the geometry of this
particular cut, the shear strength values found
happen to fall reasonably close together. In other
cases, one of the conditions may be very much
more critical than the others, and it would take
considerable experience to detect this condition
35
◦
Failure plane angle
ψ
p
=
Distance to tension crack
(slope)
b
s
=
15.4 m
Distance to tension crack
(bench)
b
b
=
2.8 m
25.5 kN
/
m
3
Rock density
γ
r
=
9.81 kN
/
m
3
Water density
γ
w
=
Seismic coefficient
k
H
=
0.08
