Civil Engineering Reference
In-Depth Information
also
′
1
1
+
sin
sin
φ
φ
p
=
γ
z
′
−
2
′
1
1
+
sin
sin
φ
φ
⇒
q
=
γ
z
u
′
−
This is the formula for the ultimate bearing capacity, q
u
. It will be seen that it is not satisfactory for shallow
footings because when z
=
0 then, according to the formula, q
u
also
=
0.
Bell's development of the Rankine solution for c-
φ
soils gives the following equation:
2
3
′
′
′
1
1
+
sin
sin
φ
φ
1
1
+
sin
sin
φ
φ
1
1
+
sin
sin
φ
φ
+ ′
q
u
=
γ
z
2
c
+ ′
2
c
−
′
−
′
−
′
For, the undrained state,
φ
u
=
0°,
q
= +
γ
z
4
c
u
u
or q
=
4
c for a surface footing
.
u
u
9.3.2 Slip circle methods
With slip circle methods the foundation is assumed to fail by rotation about some slip surface, usually
taken as the arc of a circle. Almost all foundation failures exhibit rotational effects, and Fellenius (
1927
)
showed that the centre of rotation is slightly above the base of the foundation and to one side of it. He
found that in a saturated cohesive soil the ultimate bearing capacity for a surface footing is
q
=
5 52
.
c
u
u
To illustrate the method we will consider a foundation failing by rotation about one edge and founded
at a depth z below the surface of a saturated clay of unit weight
γ
and undrained strength c
u
(Fig.
9.2)
.
Disturbing moment about O:
2
B
q LB
u
q
× × =
2
LB
(1)
u
2
Resisting moments about O
Cohesion along cylindrical sliding surface
=
c LB
π
u
⇒
Moment
=
π
u
LB
2
c
(2)
Fig. 9.2
Foundation failure rotation about one edge.
