Geoscience Reference
In-Depth Information
Thenumericalpredictions,aswellasanumberofrelevantexperimentalstudies(e.g.Liu
and Dobry, 1997; Adalier et al., 2003), lean towards a linear
ρ
dyn
-
N
relationship. Thus,
the statistical analyses focused on the remaining problem parameters, i.e.:
- peak input acceleration, at thebase of theliquefiable sand layer,
a
max
(
=
0
.
15g
)
- excitation period
T
(
=
0
.
35s
)
- average contact pressure
q
(
=
100kPa
)
- relative density
D
r
(
=
)
- undrained shear strengthof the clay crust
C
u
(
=
50%
)
40kPa
)
- thickness of the liquefied (inthefree field) sand layer
Z
liq
(
=
/
(
=
.
- normalized thickness of the clay crust
H
B
0
80
16m
)
Namely, the effect of these parameters on settlements after ten uniform loading cycles
(ρ
dyn
,
10
)
is shown in Figure 11.17(a) to (g). The effect of each parameter is examined
separately, while all others are given the reference values provided in parentheses above.
Using the same format, these figures are also used to show the effect of the above para-
meters on the static loading ratio
Q
Q
deg
ult
FS
deg
. This parallel evaluation is driven
bytheperceptionthattheoveralleffectsofliquefactionon
/
=
1
/
FS
deg
aresimilar
in qualitative terms. In that case, these two quantities could be inter-related, leading to
a simpler expression for the computation of settlements. In addition, the target value of
FS
deg
couldberelatedtotheproject(andowner)dependentvalueofacceptabledisplace-
ments
ρ
dyn
and1
/
ρ
all
.
Figure 11.17(a) to (g) show that the effect of four problem parameters (
q
,
D
r
,
C
u
and
H
/
B
) is indeed qualitatively the same for
ρ
dyn
,
10
and 1
/
FS
deg
. The three remaining
parameters(
a
max
,
T
and
Z
liq
)affectstrongly
ρ
dyn
,
10
,buthaveaminoreffecton1
/
FS
deg
that can be readily overlooked. In view of the above observations,
ρ
dyn
was finally
relatedto1
FS
degr
,
a
max
,
T
,
N
and
Z
liq
bymeansofthefollowingapproximaterelation
(Figure 11.18):
/
1
FS
deg
2
.
50
a
max
T
2
Z
liq
0
.
50
ρ
dyn
=
0
.
016
·
·
N
·
(11.12)
The accuracy of Eq.11.12 is evaluated against the results of the numerical analyses in
Figure 11.19. Observe that the agreement between approximate and numerical predic-
tions isfairlyconsistent, with an average expected error lessthan
±
30%.
A similar verification against experimental and field evidence faces objective difficul-
ties due to the general scarcity of fully documented published data. Still, it was pos-
sible to collect seismic settlement measurements from five centrifuge testing programs
(Arulmoli et al., 1992; Carnevale and Elgamal, 1993; Farrell and Kutter, 1993; Krstelj
and Prevost, 1993; Liu and Dobry, 1997; Coehlo et al., 2004), as well as from one case
study: the settlement of buildings in the city of Dagupan, Philippines, during the Luzon
1990
(
M
=
7
.
8
)
earthquake(Ishiharaetal.,1993;Tokimatsuetal.,1994;Acacio,1997).
