Civil Engineering Reference
In-Depth Information
Fig. 22.8(c) you should get everyone into the car and drive up the hill slowly. But if
you are at point B in overconsolidated clay in Fig. 22.8(b) there is no point in getting
into or out of the car: you are stuck and you cannot get up the hill.
22.8 Foundations in elastic soil
An assumption commonly made in practice is that soil is elastic and there are a number
of standard solutions for distributions of stresses and ground movements around foun-
dations subjected to a variety of loads. These solutions have generally been obtained by
integrating solutions for point loads and so they employ the principle of superposition
which is valid only for linear materials. We have seen earlier (Chapters 12 and 13)
that soils are usually neither elastic nor linear and so these solutions are not strictly
valid, although the errors in calculation of stresses are likely to be considerably less
than those in the calculation of ground movement.
The changes of the vertical stress
δσ
z
and the settlements
δρ
at a point in an elas-
tic soil due to a change
δ
Q
of a point load at the surface, shown in Fig. 22.9, are
given by
R
2
z
R
3
3
δ
Q
δσ
=
(22.14)
z
2
π
z
)
R
2
δρ
=
δ
Q
(1
+
ν
)
+
2(1
−
ν
(22.15)
2
π
ER
where
E
and
are Young's modulus and Poisson's ratio. Although these expressions
lead to infinite stresses and settlements immediately below the point load where
z
ν
=
R
0, they can be used to calculate stresses and settlements some way below small
foundations.
For circular or rectangular foundations on elastic soil the changes of vertical stress
=
δσ
z
and settlement
δρ
at a point below a foundation due to a change of bearing pressure
Figure 22.9
Stresses and settlements due to a point load.
