Civil Engineering Reference
In-Depth Information
use of Eq. (22.22)
3
E
ρ
1
u
ρ
d
=
4
1
−
ν
2
E
u
=
(22.23)
−
ν
)
2(1
ν
=
and, taking a typical value of
ρ
d
. Thus, for foundations
on a deep bed of elastic soil the settlements for undrained loading are of the order of
two-thirds those for drained loading of the same foundation; the difference is made up
by the additional settlements that occur due to consolidation after undrained loading.
If the depth of the soil is relatively small compared to the width of the foundation so
that the conditions in the soil are one-dimensional (see Sec. 22.10),
0.25 we have
ρ
u
=
0.67
0.
Non-linear soil stiffness was discussed in Chapter 13. The characteristic variation
of stiffness with strain is illustrated in Fig. 13.8. At very small strain the value of
Young's modulus is
E
0
. This can be determined from values of
G
0
measured in dynamic
laboratory or
in situ
tests and it varies with stress and state, as given by Eq. (13.8) and
shown in Fig. 13.9. Figure 18.6(b) shows the variations of tangent and secant modulus
with strain corresponding to the stress-strain curve in Fig. 18.6(a). The stiffnesses have
been normalized by dividing by
E
0
. At the critical state at
F
the strain is about 10%
and
E
tan
ρ
=
u
0.
As discussed in Sec. 13.4 the average strains in the ground near a typical foundation
at working load are about 0.1% but locally they cover a very wide range from less
than 0.01% to more than l%, as shown in Fig. 18.6(b). For design it is necessary to
choose a value of stiffness which corresponds to the mean strains in the ground, as
discussed by Atkinson (2000).
=
0. At the peak state at
P
the strain is about 1% and, again,
E
tan
=
22.10 Consolidation settlements for one-dimensional
loading
An assumption commonly made is that the thickness of a compressible soil layer is
small compared to the width of the loaded foundation: so that the horizontal strains
can be neglected. In this case the conditions of stress strain and consolidation in the
ground, shown in Fig. 22.13(a) are the same as those in the one-dimensional oedometer
test described in Secs. 7.6 and 8.5 and shown in Fig. 22.13(b).
Figure 22.13
One-dimensional consolidation in foundations.
