Geoscience Reference
In-Depth Information
Table 11.1. Summary of centrifuge testing conditions and recorded foundation settlements used in
the comparison of Figure 11.21
BH
q
ϕ
o
α
max
T
liq
u
Name
(m) (m) (m) (kPa) (kPa) (deg) (g) (s)
N
ρ
(m)
Krstelj and Prevost (1993)
3
0
5.5 95
0
37 0.27 0.50 10 0.270
3
0
5.5 95
0
37 0.35 0.50 10 0.470
3
0
5.5 95
0
37 0.20 0.50 10 0.220
3
0
5.5 95
0
37 0.20 0.50 10 0.210
Farrell and Kutter (1993)
3
0
5.5 95
0
35 0.36 0.50 10 0.180
Carnevale and Elgamal (1993) 3
0
5.5 95
0
35 0.21 0.50 10 0.130
Coehlo et al. (2004)
4
0 18.0 75
0
37 0.19 1.00 10 0.500
Liu and Dobry(1997)
4
0 12.5 60
0
36 0.20 0.67 10 0.558
that analytically computed static elastic settlements for the actual footing and for
anequivalent stripof the samewidth
B
became equal.
(c) In the majority of centrifuge tests, the foundation rested directly upon the surface
of the liquefied sand, i.e. without interference of any soil crust. This situation is of
littlepractical interest, as it usually leads to foundation failure, and consequently it
has not been part of the numerical analyses program. Hence, the use of Eq.11.12
to predict the corresponding settlements isat thelimits of its application range.
The comparison between predicted and observed liquefaction settlements is shown in
Figure 11.20 for the centrifuge tests and in Figure 11.21 for the Dagupan case study.
Despite the above limitations, both comparisons reveal a consistent agreement, although
theaverageerrorhasnowincreasedascomparedtothatforthepredictionofthenumeri-
cal results.
In concluding with the prediction of seismic settlements, it is worth to note that the gen-
eralformofEq.11.12istypicalofsystemswithelasto-plastic(stick-slip)responseduring
seismic loading, which are commonly modeled on the basis of Newmark's sliding block
approach.Forinstance,itiseasytoshowthatthedownslopedisplacementofsuchablock
when subjected to
N
uniform cycles of sinusoidal motion is expressed as
a
max
a
cr
λ
a
max
T
2
d
=
0
.
159
·[
]·
N
·
(11.13)
where
a
cr
(<
a
max
)
is the horizontal acceleration required to trigger downwards slip and
exponent
λ
=
2
−
4.
In addition, dealing with another “sliding block” problem, i.e. that of liquefaction-
induced lateral spreading, Hamada (1999) proposed the following empirical relationship
for thecomputation of maximum lateral ground displacement:
θ
N
0
.
88
SPT
a
max
T
2
Z
liq
]
0
.
50
=
.
·[
·
·
d
0
0125
N
(11.14)
