Civil Engineering Reference
In-Depth Information
Since the effect of the water pressure tends to cancel on both sides of the wall, use
Eq. (10.7) and estimate
P
E
based on the buoyant unit weight
b
64 lb
ft
3
, or
2
k
A
1
2
(
a
max
g
)
(
H
2
b
)
1
2
(0.295)
1
2
(0.20)(50)
2
(64)
8690 lb
ft
____
P
E
1
And
P
E
acts at a distance of
2
3
(
H
D
) above the bottom of the sheet pile wall.
Moment due to
P
E
8690[
1
3
(50)
4]
1.10
10
5
Total destabilizing moment
7.80
10
5
1.10
10
5
8.90
10
5
Moment due to passive force
1.71
10
6
resisting moment
destabilizing moment
1.71
10
6
__________________
_________
FS
8.90
10
5
1.92
A
p
P
A
P
E
P
p
FS
27,500
8690
43,400
___
______
1.92
13,600 lb
ft
For a 10-ft spacing, therefore
A
p
10 (13,600)
136,000 lb
136 kips
Earthquake Analysis, Liquefaction of Passive Wedge.
For the second earthquake
analysis, assume that the sand located behind the retaining wall has a factor of safety
against liquefaction greater than 2.0. Also assume that the upper 10 ft of sand located in
front of the retaining wall will liquefy during the design earthquake, while the sand located
below a depth of 10 ft has a factor of safety greater than 2.0. Calculate the factor of safety
for toe kick-out and the tieback anchor force.
For the passive wedge:
●
0 to 10 ft: Passive resistance
0
●
At 10-ft depth:
Passive resistance
k
p
b
d
3.39(64)(10)
2170 lb
ft
2
Passive resistance
k
p
b
d
3.39(64)(20)
4340 lb
ft
2
●
At 20-ft depth:
Passive force
(2170
4340)
_____________
2
(10)
32,600 lb
ft
Moment due to passive force
2170(10)(45
4)
4340
2170
___________
2
(10)[40
2
3
(10)
4]
890,000
463,000
1.35
10
6
Including a pseudostatic force in the analysis gives these results:
2
k
A
1
2
(
a
max
g
)
(
H
2
b
)
1
2
(0.295)
1
2
(0.20)(50)
2
(64)
8690 lb
ft
____
P
E
1
And
P
E
acts at a distance of
2
3
(
H
D
) above the bottom of the sheet pile wall.
Moment due to
P
E
8690[
1
3
(50)
4]
1.10
10
5
Total destabilizing moment
7.80
10
5
1.10
10
5
8.90
10
5
