Civil Engineering Reference
In-Depth Information
q = 10kPa
0.4m
P
q
5m
0.5m
P
a
“virtual plane”
0.4m
A
3m
(a) Wall geometry
(b) Pressure distributions
Fig. 8.11
Example
8.2.
′
φ
b h
≥
tan 45
°−
2
If the heel width satisfies the above inequality (it does in this example), Rankine's conditions apply
along this face and the earth pressures acting here are established in the design.
(a) Gross pressure method
Sliding:
Using Rankine's theory (with
φ
′
=
38°) K
a
=
0.238
1
2
1
2
Active thrust from soil P
,
=
K h
γ
2
= ×
0 238 18 5
.
× × =
2
53 6
.
kN
a
a
Active thrust due to surcharge P
,
=
K qh
=
0 238 10 5
.
× × =
11 9
.
kN
q
a
∑
=
65 5
H
.
kN
Vertical reaction R
,
=
weight of base weight of stem soil on
heel
(
incl surcharge
.
)
+
+
=
25 0 4 3 0
(
.
×
.
)
+
25 0 4 4 6
(
.
×
.
)
+
18 2 1 4 6
+
(
.
×
.
)
(
10 2 1
×
. )
30 0
.
46 0 173 9
.
.
21 0
.
=
+
+
+
=
270 9 kN
.
Total force causing sliding R
,
=
65 5
.
kN
h
Force resisting sliding R
=
tan
δ
=
270 9
.
×
tan
38
° =
211 7
.
kN
v
211 7
65 5
.
Factor of safety against sliding F
s
,
=
=
3 2
.
.
Overturning:
Taking moments about point A, the toe of the wall.
Disturbing moment, M
D
:
= ×
5
3
+ ×
5
2
M P
P
D
a
q
=
89 3
.
+
29 8
.
=
119 1
.
kNm
