Civil Engineering Reference
In-Depth Information
b
Tension crack
k
H
W
z
Model I
z
w
V
H
Assumed water
pressure distribution
U
Slide plane
W
f
p
F
=
cA
+
[
W
(cos
p
-
k
H
sin
p
)-
U
-
V
sin
p
] tan
W
(sin
p
+
k
H
cos
p
)+
V
cos
p
p
)
1/2
]
where
Z
=
H
[1 - (cot
p
tan
A
=(
H
-
z
) cosec
p
H
2
[(1 - (
z
/
H
)
2
cot
1
2
1
2
1
2
W
=
p
- cot
f
]
U
=
w
z
w
A
V =
w
z
w
2
k
H
W
Assumed ground
water table
U
H
Model II
H
W
W
1
2
H
w
p
cA
+ [
W
(cos
p
-
k
H
sin
p
)-
U
] tan
F
=
W
(sin
p
+
k
H
cos
p
)
U
=
w
H
w
2
cosec
where
1
4
p
Figure 14.3
Theoretical models of plane slope failures for Case Study I.
The stability check carried out in Figure 14.2
suggested that both the overall cut and the indi-
vidual benches were potentially unstable, and
it was therefore clearly necessary to carry out
further analysis of both.
The two steeply dipping joint sets
J
1 and
J
2 were oriented approximately parallel to the
slope face, and there was a strong possibility
of a tension crack forming on these discontinu-
ities behind the crest of the cut. One possible
failure mode was that illustrated as Model I in
Figure 14.3; this theoretical model assumed that
a tension crack occurred in the dry state in the
most critical position (refer to Figure 6.6), and
that this crack filled to depth
z
w
with water
during a period of exceptionally heavy rain.
