Civil Engineering Reference
In-Depth Information
Q
Q
P
n
P
n
-1
W
n
∆
x
Figure 9.11
Toppling block with external forces.
sliding of block
n
has the value
The limit equilibrium stability analysis then
proceeds as before using the modified versions of
the equations for
P
n
−
1,
t
and
P
n
−
1,
s
.
P
n
−
1,
s
=
P
n
+{−
W(
cos
ψ
p
tan
φ
p
−
sin
ψ
p
)
+
V
1
−
V
2
tan
φ
p
−
V
3
9.5 Stability analysis of flexural toppling
Figure 9.3(b) shows a typical flexural toppling
failure in which the slabs of rock flex and
maintain fact-to-face contact. The mechanism of
flexural toppling is different from the block top-
pling mechanism described in Section 9.4. There-
fore, it is not appropriate to use limit equilibrium
stability analysis for design of toppling slopes.
Techniques that have been used to study the sta-
bility of flexural toppling include base friction
models (Goodman, 1976), centrifuges (Adhikary
et al
., 1997) and numerical modeling (Pritchard
+
Q
[−
sin
(ψ
Q
−
ψ
p
)
tan
φ
p
+
cos
(ψ
Q
−
ψ
p
)
]}
tan
φ
p
tan
φ
d
)
−
1
×
(
1
−
(9.32)
where
1
y
w
;
V
1
=
2
γ
w
cos
ψ
p
·
1
V
2
=
2
γ
w
cos
ψ
p
(y
w
+
z
w
)x
1
2
γ
w
cos
ψ
p
z
w
V
3
=
(9.33)
