Civil Engineering Reference
In-Depth Information
The foundation can be said to fail if all the elements along a critical slip surface such
as that in Fig. 19.3 reach the critical state line. The distance of B
from the critical state
line is a measure of the factor of safety of the foundation and Fig. 22.5 demonstrates
that the factor of safety of a foundation initially loaded undrained generally increases
with time but there will be continuing settlements due to consolidation.
The stress path for drained loading of a foundation is the broken line A
→
D
in Fig. 22.5(b) and (c). From the geometry of the diagram the stress path approaches
the critical state line slowly and you can continue adding load to a foundation on sand
although settlements will become large.
C
→
22.5 Bearing capacity of shallow foundations
The bearing capacity of a foundation can be calculated using the upper and lower
bound methods (Chapter 19) or the limit equilibrium method (Chapter 20). There are
standard solutions which are routinely used in practice.
(a) Undrained loading
The gross undrained bearing capacity of the simple shallow foundation shown in
Fig. 22.6(a) is
q
c
=
s
u
N
c
+
p
0
(22.6)
where
N
c
is a bearing capacity factor and
p
0
is the total stress at the level of the base
of the foundation. For a long foundation at ground level the equal upper and lower
bounds obtained in Sec. 19.10 given by Eqs. (19.43) and (19.46) are equivalent to
N
c
=
(2
+
π
)
(22.7)
The value of
N
c
depends on the shape and depth of the foundation and values given
by Skempton (1951) are shown in Fig. 22.6(b). The allowable gross bearing pressure
q
a
is obtained by applying a load factor to the net bearing pressure and is given by
q
a
=
L
f
s
u
N
c
+
p
0
(22.8)
Remember that the gross bearing pressure is the total stress at the base of the foundation
and it includes the applied load and the weight of the foundation so the allowable
applied load
V
a
is
V
a
+
W
=
L
f
s
u
N
c
B
+
γ
BD
(22.9)
If the soil is water so
s
u
w
Eq. (22.9) states that the weight of the
foundation and the applied load is equal to the weight of water displaced, which is
Archimedes' principle.
=
0 and
γ
=
γ
