Civil Engineering Reference
In-Depth Information
tan
1
a
max
____
tan
1
k
h
g
tan
1
0.20
11.3° Eq. (10.10)
w
0°
33°
0°
18.4°
Inserting the above values into the
k
AE
equation in Fig. 10.3 gives
k
AE
0.641
P
AE
P
A
P
E
1
2
k
AE
H
2
t
Eq. (10.9)
Since the effect of the water pressure tends to cancel out on both sides of the wall, use Eq.
(10.9) and estimate
P
E
based on the buoyant unit weight (
b
64 lb/ft
3
).
P
AE
1
2
(0.641) (50
2
) (64)
51,300 lb/ft
Since
0°,
P
H
P
AE
51,300 lb/ft
and
P
v
0
And
P
AE
acts at a distance of
1
3
(
H
D
) above the bottom of the sheet pile wall.
Moment due to
P
AE
51,300 [
2
3
(50)
4]
1.50
10
6
resisting moment
destabilizing moment
1.71
10
6
__________________
__________
FS
1.50
10
6
1.14
A
p
P
AE
P
p
FS
51,300
43,400
___
______
1.14
13,200 lb/ft
For a 10-ft spacing, therefore,
A
p
10 (13,200)
132,000 lb
132 kips
Earthquake analysis, liquefaction of passive wedge:
10
6
Moment due to passive force
1.35
resisting moment
__________________
FS
destabilizing moment
1.35
10
6
__________
1.50
10
6
0.90
Note that the substantial differences in the factor of safety for toe kick-out for the earth-
quake analysis in Probs. 10.10 and 10.11 are due in large part to the assumed location of
P
E
and
P
AE
[that is,
P
E
is assumed to act at a distance of
2
⁄
3
(
H
D
) while
P
AE
is assumed to act
at a distance of
1
⁄
3
(
H
D
) above the bottom of the sheet pile wall].
