439
Technical Committee 101 - Session II /
Comité technique 101 - Session II
Visco-plastic strain ε
vp
Logarithmic consolidation pressure log
p'
4 MODELLING WITH ISOTACHE CONCEPT
In this study, isotache concept (Šuklje, 1957) is modeled by
simple equations proposed by Leroueil et al. (1985), but applied
them only to visco-plastic strain
vp
. Watabe et al. (2008)
modeled strain rate dependency of preconsolidation pressure
'
p
as Equation (1):
vp
2 1
pL
pL
p
ln
ln
c c
(1)
Here,
'
pL
,
c
1
and
c
2
are constants. Equation (1) expresses that
the preconsolidation pressure
'
p
converges to a lower limit of
'
pL
.
Watabe et al. (2008) investigated the strain rate dependency
of preconsolidation pressure for Osaka Bay clays at various
depths from Holocene clay (Ma13) to Pleistocene clay (Ma12 to
Ma3) up to 300 m depth, and Watabe et al. (2012) examined the
applicability of Equation (1) to worldwide clays with various
characteristics. Reference compression curves, in which the
consolidation pressure
'
v
is normalized by the preconsolidation
pressure
'
p
, obtained from the constant rate of strain
consolidation tests are drawn in Figure 5. The clays examined
show various compressibility. For each clay, long-term
consolidation test was conducted in normal consolidation range,
then the relationship between preconsolidation pressure
'
p
and
strain rate
vp
was obtained (Figure 6a). Here, preconsolidation
pressure
'
p
is normalized by a reference value
'
p0
that
corresponds to a strain rate of 1.0×10
–7
s
–1
(equivalent to 24-h
incremental loading oedometer test). Strain rate dependency can
be approximated by a unique model curve with parameters
'
pL
/
'
p0
= 0.7 and
c
1
= 0.935 for Osaka Bay clays at all of the
depths (Watabe et al., 2008). Note here that, when the
approximate curve passes a certain point, the parameter
c
2
automatically determined by the other two parameters
'
pL
and
c
1
.
1E-12 1E-11 1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4
0.4
0.5
0.6
0.7
0.8
0.9
1
2
·
·
p'
c
/
p'
c0
,
p'
/
p'
= 10
7
s
1
Strain rate
(s
1
)
Osaka Bay
Ma13
Ma12
Ma11
Ma10
Ma9
Ma8
Ma7a
Ma7b
Ma4
Ma3
Ma13Re
In situ (Ma12 in 1st Phase)
Amagasaki
Rakusai
Ariake
Tokyo Bay
Louiseville
Onsoy
Pisa
Mexico City
c
'
c0
Figure 6a. Strain rate dependency for the worldwide clays.
1E-12 1E-11 1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4
0.4
0.5
0.6
0.7
0.8
0.9
1
2
·
p'
c
/
p'
c0
Strain rate
(s
1
)
Pisa
Figure 6b. Strain rate dependency for the Pisa clay.
Overconsolidation
Normal consolidation
The parameters determined for the Osaka Bay clays are
applicable to the worldwide clays examined in the previous
study (Watabe et al., 2012). Consequently, the isotache concept
can be commonly modeled by the unique approximation curve
for the worldwide clays. The unique approximation curve is
very useful; however, data for some clays, particularly for Pisa
clay, is apart from it. The relationship between preconsolidation
pressure
'
p
and strain rate
vp
for Pisa clay is compared to the
unique approximation curve in Figure 6b. Preconsolidation
pressure for Pisa clay does not decrease so much with decrease
of strain rate, indicating that the strain rate dependency of Pisa
clay is smaller than that of the other clays.
(a) In a case of high strain rate dependency.
Visco-plastic strain ε
vp
Logarithmic consolidation pressure log
p'
Overconsolidation
Overconsolidation
(b) In a case of low strain rate dependency.
Figure 7. Illustration of long-term consolidation settlement in over-
consolidation domain.
5 DISCUSSION
The key factor to model the isotache concept is the strain rate
dependency of preconsolidation pressure. From the previous
studies, it was found out that the strain rate dependency can be
expressed by the unique approximation curve. Pisa clay,
however, shows particularly smaller strain rate dependency than
the other clays. This different dependency strongly influences
the long-term consolidation behavior in over-consolidated
domain. In practice, consolidation settlement is predicted based
on the compression curve corresponding to a stain rate of
1.0×10
–7
s
–1
. Because the Osaka Bay clay has high strain rate
dependency, overconsolidation with a higher strain rate at the
beginning can be eventually changed to normal consolidation
with a smaller strain rate. Figure 7a illustrate the mechanism for
the significant delayed long-term consolidation when the Osaka
Bay clay was loaded in slightly overconsolidation. On the other
hand, because the Pisa clay has low strain rate dependency,
overconsolidation with a higher strain rate at the beginning can
be eventually maintained in overconsolidation with a smaller
strain rate. Figure 7b illustrate the mechanism for that the Pisa
clay remained in overconsolidation when it was loaded in
slightly overconsolidation.
