Civil Engineering Reference
In-Depth Information
Cohesion along CD c zL
=
u
⇒
Moment
=
c zLB
(3)
u
Weight of soil above foundation level
=
γ
zLB
2
γ
zLB
⇒
Moment
=
(4)
2
For limit equilibrium (1)
=
(2)
+
(3)
+
(4)
i.e.
q LB
2
γ
zLB
2
u
=
π
c LB
2
+
c zLB
+
u
u
2
2
2
c z
B
u
⇒
q
=
2
π
c
+
+
γ
z
u
u
1
z
B
1
2
z
γ
=
2
π
c
1
+
+
u
π
π
c
u
z
B
γ
z
=
6 28
.
c
1 0 32
+
.
+
0 16
.
u
c
u
Cohesion of end sectors
The above formula only applies to a strip footing, and if the foundation is of finite dimensions then the
effect of the ends must be included.
To obtain this it is assumed that when the cohesion along the perimeter of the sector has reached its
maximum value, c
u
, the value of cohesion at some point on the sector at distance r from O is c
r
=
c
u
r/B,
as shown in Fig.
9.3.
Rotational resistance of an elemental ring dr thick
c r
B
,
u
=
×
π
r dr
c r
B
c
B
r dr
u
u
Moment about O
=
×
π
r dr
× =
r
π
3
B
c
B
r dr
∫
u
3
Total moment of bot
h ends
=
2
π
0
c
B
B
4
π
c B
3
u
u
=
2
π
× =
(5)
4
2
This analysis ignores the cohesion of the soil above the base of the foundation at the two ends, but unless
the foundation is very deep this will have little effect on the value of q
u
. The term (5) should be added
into the original equation.
Fig. 9.3
Cohesion of end sectors.
