Environmental Engineering Reference
In-Depth Information
Tension crack
7
6
Possible excess
pore pressure
in lower slope
5
4
w 4
3
F 4
N 4
2
1
θ
u 4
(a)
=
w h L
u 4
h
L
u 4
(b)
o
1
Arc with
total
length L
FIGURE 9.77
The ordinary method of slices. (a) Draw the slope and
flow net to scale Select failure surface and divide into
equal slices of similar conditions. (b) Pore pressures
for slice U 4 . (c) Determine forces and safety factor:
7
6
5
4
N 6
6
4
w 6
5
3
F 6
N 5
4
θ u i L i and F W i sin
θ
N i
W i cos
2
w 5
3
F 5
N 4
1
w 4
FS = resisting force
driving force
= CL +( N - U ) tan
L i
φ
c ¯
N i tan
w 3
F 4
FS
W i sin
θ i
L
F
(c)
Repeat for other r values to find FS min .
cases (Janbu, 1973; Morganstern and Sangrey, 1978). Suitable for hand calculations it is
particularly useful in slopes undergoing progressive failure on a long, noncylindrical fail-
ure surface where the location is known. It was used to analyze the failure illustrated in
Figure 9.33. The equations are as follows:
FS
f o (
{[ c ' b
( W - ub ) tan
φ
'] [1/cos
θ
M i (
θ
)]}/
W tan
θ
V )
(9.17)
where
M i (
θ
)
cos
θ I (1
tan
θ i tan
φ
'/FS)
(9.18)
f o
1
0.50 [ d / L -1.4( d / L 2 ]
for c
0,
φ
0
(9.19)
f o
1
0.31 [ d / L -1.4( d / L 2 ]
for c
0
f o
1
0.66 [ d / L -1.4( d / L 2 ]
for
φ
0
Data are input for each slice. Substitution of Equation 9.18 into Equation 9.17 results in FS
on both sides of the equation. For solution a value for FS 1 is assumed and FS 2 calculated,
 
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