Geoscience Reference
In-Depth Information
Table 12.1. Inertial coefficientsfor BNWF SD analyses ofliquefaction cases
Motion
∗
(
Sa
T
=
1s
/
ZPA
)
Pile cap
Superstructure
C
liq
C
cc
C
liq
C
cc
Long period (1.7-2.4)
1.4
0.85
0.75
0.65
Mediumperiod(0.5-1.6)
0.75
0.85
0.55
0.65
0.35 0.85 0.45 0.65
∗
See Figure 12.9 for examples of long-period,medium-period, and short-period input motions.
Short period
(
≤
0
.
4
)
2.4.3. Perform the BNWF analysis
The BNWF analysis for the liquefaction case involves the simultaneous application of
soil displacements to the free-field ends of the p-y springs and inertia loads to the pile
cap and superstructure as illustrated in Figure 12.4(a). Guidance regarding appropriate
combinations of these loads and soil displacements was developed from the results of
dynamic centrifuge model tests, dynamic finite element analyses, and equivalent static
BNWF analyses.
The dynamic FE analyses showed that the critical loading condition for the pile founda-
tionscorrespondedmostcloselytotheoccurrenceofpeakornear-peaklateralgrounddis-
placements in conjunction with significant inertia loads for a wide variety of soil profile,
pile foundation, superstructure, and ground motion characteristics. This observation is
consistent with the experimental observations from: (1)centrifuge models of pile-group-
supportedstructuresinprofilesofslopingground,likethatshowninFigure12.2,wherein
thecriticalloadingcycleinvolvedalocalpeakinthetransientgrounddisplacementsplus
a local peak in the inertia load (Brandenberg et al., 2005; Chang et al., 2005) and (2)
large-scale shaking table tests of structures supported on pile groups in level soil pro-
files having a dry sand crust over saturated sand, wherein the peak bending moments
occurred when the lateral ground displacements and inertia loads were both large and
acted in the same direction (Tokimatsu et al., 2005). Both of these experimental studies
involvedstructureswithnaturalperiodsof0.8sorlessandsoilprofileswhoseequivalent
natural periods after liquefaction were in the range of 1 to 2s. Tokimatsu et al. (2005)
suggested that the lateral soil displacements and inertia loads would be out-of-phase if
the structure's natural period was larger than the liquefied ground's natural period, based
on their observations from tests involving dry sand profiles with much smaller natural
periods.ThedynamicFEanalysesbyChang(2007)did,infact,showthatthestructure's
inertia load became more out-of-phase with the lateral ground displacement when the
superstructureperiodwas3sandtheliquefiedground'snaturalperiodwasabout1to2s.
The superstructure inertia load was relatively small for this long-period structure, such
that the pile-cap inertia (which was more in-phase with crust displacements) became a
larger fraction of the total inertia load imposed on the pile foundation. Consequently, the
critical loading condition for the pile foundation of this structure with a natural period
of 3s and subject to lateral spreading was still reasonably approximated by a near-peak
lateral ground displacement withasignificant fraction of thepeak total inertia load.
