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t
m
=
(ln(
2
)
ln(
?
))/(
?
) with
2
=
1
u
0
(
?
)
/
0
(16.31b)
Thereafter, the pore pressure attenuates to zero. The parameters
u
0
,
0
, and
can
be determined by special laboratory tests and
?
by a special field test. In detail,
=
3
c
v
/d
2
with
c
v
the consolidation coefficient and
d
the layer thickness.
Here,
n
crit
the densification
60
,
?
=
(1
n
)
/
n
with
n
the porosity,
n
=
n
field
0
'
is obtained from tests (see Fig
16.19c) and
f
N
= 1/
T
c
is the cyclic frequency. The factor
r
=
0.65 relates the triaxial
stress configuration to the one-dimensional situation.
N
l
is the number of cycles when
liquefaction in the undrained triaxial test occurs. It depends on the loading intensity
characterised by the stress ration
'
and
the compressibility.
0
= f
N
r
'
0
/N
l
with
^
is the amplitude of shear loading). In Fig
16.19c, 4 such tests are shown. Here, sand samples from a location are prepared under
various densities; initial porosity in test (1) is 0.40, in (2) 0.38, in (3) 0.42, and in (4)
0.39.
^
/
'
0
(
A: undrained
A: undrained
A: undrained
A: undrained
u
J
u
J
u
J
u
J
u
J
u
J
@
@
@
B: drained
B: drained
B: drained
B: drained
C:presheared
C:presheared
C:presheared
C:presheared
presheared
presheared
presheared
J
J
J
J
u
0
J
u
0
J
u
0
J
u
0
J
u
0
0
u
0
0
u
0
0
u
0
0
/
/
/
/
/
/
/
/
t
or
NT
c
t
or
NT
c
t
or
NT
c
t
or
NT
c
t
or
NT
c
t
or
NT
c
t
m
t
m
t
m
(a) laboratory test observations (b) a simple 1D model
1.0
1.0
1.0
1.0
due to strain
localisation
in the test
due to strain
localisation
in the test
u/
'
0
u/
'
0
u/
'
0
u/
'
0
1
1
1
1
2
2
2
2
'
'
'
'
3
3
3
3
4
4
4
4
due to initial
effects
due to initial
effects
u
0
/
'
0
u
0
/
'
0
u
0
/
'
0
u
0
/
'
0
N/N
l
N/N
l
N/N
l
N/N
l
0.0
0.0
0.0
0.0
1.0
1.0
1.0
1.0
^
(c) cyclic undrained triaxial tests at specific value of
/
'
0
;
N number of cycles, N
l
number at liquefaction
Figure 16.19 Liquefaction phenomena
60
n
crit
the density at zero contraction/dilation, can be measured in the lab. In fact,
?
=
(1
'
the ratio of volume strain rate and
0
.
The assumption
' =
probably is a safe approximation.
n
)
0
'/
n
with
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