Civil Engineering Reference
In-Depth Information
In a model with the same soil and pore fluid as the prototype,
c
v
is the same and if the
scale is
n
we have
H
m
H
p
/
n
. Hence, from Eq. (27.5), the times for consolidation in
the model and prototype are related by
=
t
p
n
2
=
t
m
(27.6)
so that consolidation will proceed much more rapidly in the model than in the proto-
type. For a typical scale factor
n
10
−
4
t
p
so that 1 hour of model
time represents approximately 1 year of prototype consolidation time.
The relationship between the rate at which excess pore pressures dissipate as drainage
occurs and the rate of loading that generates additional excess pore pressures governs
whether a particular construction event is drained, undrained or partly drained, as
discussed in Sec. 6.9. Remember that for routine geotechnical calculations we have
to assume either that the soil is fully drained or that it is fully undrained, in which
case there will be subsequent consolidation. A model could, however, examine cases
of partial drainage in which the rates of loading and consolidation were coupled.
If the accelerations in the prototype and in the model are related by the scale factor
n
and are given by
=
100, we have
t
m
=
d
2
x
p
d
t
p
2
sin(
=
a
ω
ω
t
p
)
(27.7)
d
2
x
m
d
t
m
=
2
sin(
n
na
ω
ω
t
m
)
(27.8)
then the displacements are given by
x
p
=
a
sin(
ω
t
p
)
(27.9)
a
n
sin(
n
x
m
=
ω
t
m
)
(27.10)
and the times in the prototype and in the model are related by
t
p
=
nt
m
(27.11)
Any motion can be represented by a Fourier series which is a summation of sine
functions and so the time scaling rule given by Eq. (27.11) applies to any displacement
or loading. Notice that the scaling requirement for the rate of loading is that the times
should be related by
n
, which is not the same as the requirement for modelling consol-
idation where the times should be related by
n
2
. Therefore it is not generally possible
to model coupled loading and consolidation in the same model. This problem can be
avoided by using a pore fluid such as silicon oil with a viscosity
n
times greater than
that of water. In this case the coefficient of consolidation and the rate of consolidation
in the model are reduced by
n
times so that the scaling
t
p
=
nt
m
is then the same for
both the rate of loading and the rate of consolidation.
