Civil Engineering Reference
In-Depth Information
Figure 13.8
Characteristic ranges of stiffness in the field and in laboratory tests.
soil stiffness is highly non-linear, but we might expect that the stiffness at a particular
strain will also depend on the current state and on the history.
(a) Stiffness at very small strain
In dynamic tests used to measure
G
0
, samples are vibrated at a constant state at strains
less than about 0.001%. The damping is a negligible and at these very small strains
soil is assumed to be linear and elastic. (If a typical value for
G
0
is 100 MPa then a
strain
q
of only 3 kPa.)
The general relationship between
G
0
and the current state is of the form
δε
s
=
0.001% corresponds to an increment of stress
δ
A
p
p
r
n
G
0
p
r
=
Y
p
(13.8)
where
p
r
is a reference pressure included to make Eq. (13.8) dimensionless
Y
p
is the
current yield stress ratio defined in Sec. 8.3 and
A
,
m
and
n
depend on the nature of
the soil (Viggiani and Atkinson, 1995). Notice that in Eq. (13.8) the value of
G
0
is
related to
p
and
Y
p
without the specific volume or voids ratio. This is possible because
v
,
p
and
Y
p
are not independent as discussed in Sec. 8.3 and so
v
is included in the
parameters
p
and
Y
p
. Alternatively,
G
0
could be related to
v
and
Y
p
. The value of
the exponent
n
is generally in the range 0.5 to 1.0 and typical values for
m
are in the
range 0.2 to 0.3. Equation (13.8) can be rewritten as
ln
G
0
p
r
n
ln
p
p
r
=
ln
A
+
m
ln
Y
p
+
(13.9)
Plotting data from a set of tests carried out at different values of
p
and
Y
p
, as shown
in Fig. 13.9, provides a convenient method for evaluating the parameters
A
,
m
and
n
.
