Geoscience Reference
In-Depth Information
2.4.2. Estimate loads from the superstructure
The effects of liquefaction on the inertia loads from the superstructure and pile cap have
beenevaluatedbyparametricstudiesusingnonlineardynamicfiniteelementanalysesthat
werecalibratedagainsttheresultsofdynamiccentrifugemodeltests(Changetal.,2005,
2006;Chang,2007).Forexample,thedeformedfiniteelementmeshshowninFigure12.8
is for the centrifuge model shown in Figure 12.2. The finite element platform OpenSees
with the constitutive models developed by Yang et al. (2003) was used. The parametric
FE analyses considered a range of ground motions, pile foundation stiffness, superstruc-
ture elastic period, superstructure mass, crust strength, and other variables. Each case
was analyzed once with liquefaction being possible and once with pore water pressure
generation eliminated. The inertia loads computed with and without liquefaction were
compared as
I
cc liq
=
C
cc
C
liq
I
max nonliq
(12.1)
where I
max nonliq
=
the maximum or peak inertial load in the absence of liquefaction,
C
liq
=
the ratio of maximum inertial load with liquefaction versus without liquefaction,
and C
cc
=
the fraction of the maximum inertial load with liquefaction that occurs at the
critical loading cycle (i.e., when the maximum pile bending moments and shear forces
occur). Values of C
liq
for the superstructure depended on the frequency content of the
inputmotion,asrepresentedbythespectralshapesinFigure12.9andsummarizedbythe
parametric resultsin Figure 12.10. Values of C
cc
varied lesssignificantly.
For design, the values of C
liq
and C
cc
in Table 12.1 were subsequently proposed. The
I
max nonliq
value for the superstructure can be estimated using the procedures discussed
in previous sections, while the I
max nonliq
value for the pile cap can be estimated as
equaltothepeakgroundsurfaceacceleration.Thelateralloadsandoverturningmoments
imposed on the foundation by the superstructure may be limited by the lateral strength
(with allowance for over-strength) of the supporting columns, as noted for the nonliq-
uefaction case. These factors provide an approximate allowance for the fact that inertia
Fig. 12.8. Deformed finite element mesh withpore pressurecontours
