Effect of soil–structure interaction and spatial variability of ground motion on seismic risk assessment of bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 595

• inelastic dynamic analysis is conducted in the time domain but the
energy absorption is expected to be mainly concentrated on the super-
structure (i.e., through bearings or other dissipating devices) while the
material and radiation damping at the soil-foundation interface is a-
priori judged of secondary importance (i.e. in cases where the underly-
ing soil formations are stiff and uniform with depth).

Dynamic loading

Owing to the large dimensions of bridge structures, consideration of SSI
effects is often made by implementing fi nite element discretization, either
through a complete FE or substructure approach. The complete FE approach
is primarily used when the overall wave propagation in 2D or 3D space is
of primary interest and the response of the soil-foundation-superstructure
is mainly linear elastic. It permits modeling of the entire bridge-soil system
and a balanced refi nement between the numerical representation of the
structure and the subsoil domain; however, it has signifi cant limitations
as regard to the accuracy of seismic wave propagation especially in cases
of inhomogeneous media where the fi nite difference method is deemed
preferable. Realistic boundary conditions (Novak and Mitwally, 1988)
and optimal mesh dimensions (Lysmer and Kulemeyer, 1969) are also a
prerequisite.
On the other hand, according to the substructure method, the soil-
foundation-bridge system is divided into distinct substructures, typically the
superstructure, near fi eld soil domain inclusive of the foundation, and far
fi eld domain. Owing to considerably reduced computational cost, the sub-
structure method has been extensively used in the past in one of the fol-
lowing forms:

• Coupled fi nite element method/boundary element method (FEM/BEM)

approaches (Renault and Meskouris, 2005): the advantage of this
approach is that the soil can be discretized only in the interaction
horizon, while the boundary conditions are consistent and hence, the
wave propagation in the free-fi eld can be accurately calculated consider-
ing non-relaxed boundary conditions.

• Uncoupling and superposition of kinematic and inertial interaction

(Makris et al. , 1996; Mylonakis et al. , 1997): the dynamic stiffness matrix
of the superstructure is attached to an additional impedance matrix
representing the underlying unbounded soil region and the superstruc-
ture is then excited by the response history (denoted as foundation input
motion - FIM) of a hypothetical soil-foundation subsystem without
superstructure mass. In case of deep (pile) foundation, the procedure
can be summarized in four independent steps: