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capacity, and nonlinear shape of these spring elements may be made from estimates of
the soil strength and stiffness parameters, from correlations to in situ test results (e.g.,
SPT or CPT), from analysis of dynamic monitoring records (e.g., CAPWAP analyses),
or from results of pile load tests. These estimates may require further adjustments for
pilegroupeffectsandpileset-upwithtime.Theuncertaintyintheestimatedspringpara-
meters depends on the approach taken. For seismic design, it is important that this step
identify best estimates and some measure of uncertainty for these different spring para-
meters (e.g., upper and lower design values) because it is not always evident whether
a conservative design will correspond to underestimating or overestimating the spring
parameters.
Some existing expressions for p-y curves in sand (e.g., API, 1993) overestimate the p-y
stiffness at depths greater than several pile diameters, which is not a concern for inertia
loading cases but can be significant for the lateral spreading cases. The initial stiffness
parameter in the API relationship for sand was modified to be proportional to the square
root of effective overburden stresstocompensate forthiseffect (Boulanger et al., 2003).
2.2.2. Estimate loads from the superstructure
Seismic displacement and associated internal force demands on the global bridge struc-
ture or its local subsystems may be estimated in different ways, often starting with an
estimate of the “elastic” response from the design linear-elastic acceleration response
spectra (ARS) for the site or from a dynamic elastic analysis of the structure (e.g.,
Caltrans, 2006). Displacement capacities and their associated internal forces within the
bridgestructuremaythenbedeterminedfrominelasticstaticpushoveranalyses.Thus,the
lateral loads and overturning moments imposed on the foundation by the superstructure
may be limited by the lateral strength (with allowance for over-strength) of the support-
ing columns or piers. The analysis of the pile foundation may be directly coupled to, or
separated from, the analysis of thesuperstructure.
2.2.3. Perform BNWF analysis
The pile foundation is then analyzed for the lateral loads and overturning moments that
are produced by the superstructure's dynamic response, both transversely and longitudi-
nally.Kinematicloadingfromgrounddeformationisgenerallynotincludedinthisanaly-
sis; special analyses are required in cases where ground deformations may be significant
(e.g., in soft clays or liquefiable soils). An estimate of the pile foundation stiffness may
havebeenneededforestimatingthesuperstructure'sdynamicresponse,suchthataround
of iteration may be required between these two steps. It is often preferable to have the
piles remain elastic because subsurface damage is difficult to assess or repair, but there
arecaseswhereallowingalimitedamountofyieldinginthepilescanprovidesignificant
economy. Piles are also checked for their maximum uplift and compressive axial loads.
Uplift or plunging of the outer piles under the imposed overturning moments can con-
tribute to the cyclic accumulation of permanent displacements and rotations at the pile
cap, which should be evaluated.
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