Civil Engineering Reference
In-Depth Information
Example 13.9:
Bishop and Morgenstern's charts (iii)
Slope
=
1 vertical to 4 horizontal, c
′
=
7.5 kPa,
φ
′
=
20°,
γ
=
17.5 kN/m
3
, H
=
17 m,
r
u
=
0.35. Find F.
Solution:
c
γ
′
=
7 5
17 5 17
.
=
0 025
.
.
×
Using D
=
1.0, r
ue
=
0.0 (r
ue
≯
r
u
).
Therefore use chart for D
=
1.25:
m
=
1 97
.
n
=
1 78
.
F
=
1 97
.
−
(
0 35 1 78
.
×
.
)
=
1 35
.
Example 13.10:
Bishop and Morgenstern's charts (iii)
Slope angle
=
24°, c
′
=
5 kPa,
γ
=
20 kN/m
3
,
φ
′
=
30°, r
u
=
0.3, H
=
13 m. Find F.
Solution:
Slope (24°)
=
1 vertical to 2.25 horizontal
c
γ
′
=
5
20 13
=
0 019
.
×
′
=
c
H
Chart
0 025
.
;
D
=
1 0
.
γ
m
=
1 76
.
n
=
1 68
.
F
=
1 76
.
−
(
0 3 1 68
.
×
.
)
=
1 26
.
′
=
c
H
Chart
0 00
.
γ
m
=
1 3
.
n
=
1 54
.
F
=
1 3
.
−
(
0 3 1 54
.
×
.
)
=
0 84
.
The actual F value can be found by interpolation:
1 26 0 84
0 019
0 025
.
.
F
=
0 84
.
+
( .
−
.
)
. . .
Note:
It is preferable to calculate the two F values and then interpolate rather than to
determine the m and n values by interpolation.
=
0 84
+
0 32
=
1 16
