Optimal Design of Nonlinear Viscous Dampers for Protection of Isolated Bridges - Structural Seismic Design Optimization and Earthquake Engineering - page 372

Figure 2. Schematic of augmented system and seismic risk description

This chapter presents a methodology that
addresses all aforementioned challenges for the
design of supplemental dampers for seismically
isolated, short-spanned bridges. A probabilistic
framework is proposed for addressing the various
sources of uncertainty and quantifying the overall
performance. This is established by characterizing
the relative plausibility of different properties
of the system and its environment (representing
future excitations) by appropriate probability
models. Seismic risk is then defined as the ex-
pected value of the system performance over these
models. Stochastic simulation is implemented for
evaluation of the multidimensional probabilistic
integral representing seismic risk and an efficient
algorithm (Kleinmann, Spall, & Naiman, 1999;
Spall, 1998) is adopted for performing the as-
sociated optimization and selecting the optimal
damper parameters. This establishes a versatile,
simulation-based framework for detailed charac-
terization of seismic risk that puts no restrictions in
the complexity of the modeling approach adopted.
Thus, the bridge response is evaluated through
nonlinear dynamic analysis allowing for direct
incorporation of all important sources of nonlin-

earities into the model used at the design stage. A
realistic model is also discussed for description of
near-fault ground motions. This model establishes
a direct link, in a probabilistic sense, between our
knowledge about the characteristics of the seismic
hazard in the structural site and future ground mo-
tions. An efficient probabilistic sensitivity analysis
is also discussed for investigating the influence
of each of the uncertain model parameters to the
overall seismic risk.

PROBABILISTIC DESIGN
FRAMEWORK

Evaluation of seismic risk for isolated bridges
requires adoption of appropriate models for (i)
the bridge system itself, (ii) the excitation (ground
motion), and (iii) the system performance (Figure
2). The combination of the first two models pro-
vides the structural response. The performance
evaluation model assesses, then, the favorability
of this response based on the selected performance
criteria.