Civil Engineering Reference
In-Depth Information
where the increase of stress due to the foundation is more than about 10% of the
original
in situ
stress.
22.9 Parameters for elastic analyses
The parameters in these elastic calculations are Young's modulus and Poisson's ratio.
In selecting values for design of foundations it is necessary, as always, to distinguish
between drained and undrained loading. It is also necessary to recognise that soil
stiffness is highly nonlinear and values appropriate to the strains in the soil in the
ground should be selected.
Analyses can be done in one step using secant moduli or in several steps using tangent
moduli, as described in Sec. 18.7 where the secant modulus is
=
q
ε
a
E
sec
(22.18)
and the tangent modulus is
d
q
d
E
tan
=
(22.19)
ε
a
where
represents the change of stress and strain from the start of the loading. For
simple analyses the secant modulus method would normally be used and the step
taken as the whole foundation loading. For drained loading you should choose the
parameters
E
and
ν
corresponding to effective stresses and for undrained loading you
should choose
E
u
and
0.5 corresponding to undrained, constant volume loading.
The basic relationship between the elastic shear modulus
G
and the elastic Young's
modulus
E
(see Sec. 3.8) is
ν
=
u
E
G
=
(22.20)
2(1
+
ν
)
For an elastic material for which shear and volumetric effects are decoupled we have
G
=
G
u
and hence
E
E
u
+
ν
)
=
(22.21)
+
ν
2(1
2(1
u
)
or, with
ν
u
=
0.5.
3
E
2(1
E
u
=
(22.22)
+
ν
)
The settlements of a foundation for drained loading
ρ
d
or for undrained loading
ρ
u
are given by Eq. (22.17) or with the appropriate values for
E
and
ν
. Hence, making
