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Nevertheless, a more flexible configuration offers to the deck additional mobility that may result to
undesirable response.
513
Pile Foundation
Approach
E mbanlcmeni
and Pile
Foundation at
Abutment
Approach
JSmbaiikment
and Pile
Foundation at
Abutment
Figure 2. Schematic of an idealized model of the 91/5 Overcrossing
MACROSCOPIC CONSTITUTIVE LAWS OF SUBSTRUCTURE ELEMENTS
The bridge is decomposed into its main substructure components including approach embankments, pile
foundations, center bent and seismic protection system that consists of isolation bearings and fluid
dampers. Simple macroscopic constitutive laws that capture satisfactorily the restoring and energy
dissipation mechanisms of these substructural elements within the deformation levels of interest are
adopted.
Recognizing that soil-structure interaction affects appreciably the earthquake response of conventional
highway overcrossings, a recent study by Zhang and Makris (2001, 2002a,b) developed a simple
procedure to compute the kinematic response functions and dynamic stiffnesses of approach
embankments that has been validated against recorded data from two well-instrumented bridges with
integral abutments, the Meloland Road and the Painter Street overcrossings. That study also indicated
that & although the dynamic stiffnesses of approach embankments and pile foundations are in general
frequency dependent quantities, their low frequency values do not fluctuate appreciably with frequency
and one can replace them with frequency independent springs and dashpots.
For the center bent, the columns are expected to behave inelastically. Therefore, their behavior ^ is
represented by the nonlinear moment-curvature curve, that was computed with the geometry and material
properties of columns.
The mechanical behavior of seismic protection systems is nonlinear since isolation bearings yield or slide,
while fluid dampers deliver forces that depend on a fractional power of the piston velocity. One can use a
bi-directional bilinear model to characterize their behavior. Under shear deformation the elastomeric pads
deform nearly elastically (K eff * 5MN/m) until they develop a lateral force F = pJV, where p, = 0.3 is
the friction coefficient of the pad-deck interface and N is the normal force on the pad. In this study the
force at which sliding initiates is F« 0.3MN and the yield displacement is u y = F/K sff * 0.06m. Each
fluid damper implemented is designed to produce 250kips at a piston velocity of 42in/s. Their behavior is
nonlinear and the force output is proportional to a fractional power of the velocity,
P(/) = C a |w(Ol a sgn[M(0], wk ere fractional power, CL Q IJ taken to be 0.35 in this application.
Accordingly, the damping constant, C a is 1.09MN- (s/m) ' .