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 594

• Relationships between one-dimensional soil stiffness (expressed in
terms of modulus of subgrade reaction k ) to two-/three-dimensional soil
stiffness, expressed in terms of modulus of elasticity E s and Poisson's
ratio , has not been established. The verifi cation using 2D and 3D FE

analyses is not straightforward. As a result, a set of calibration assump-
tions is required for establishing a correspondence between the Winkler
and plane-strain FE approaches (Kappos and Sextos, 2001) based on
the initial formulations proposed (Vesic, 1961):

ν

065
1

. E

v

ED
vEI

4

s s

kDk = = [22.2]

12

h

( )

( )

2

1 −

2

−

2

pp

where k h is the modulus of subgrade reaction and D the pile diameter.
Moreover, the transformation from one soil parameter to another is
straightforward only in a case where they are assumed constant with
depth; a set of additional and case-dependent calibrations is required to
obtain agreement in the inelastic range.

• Pile group effects are essentially neglected. Even if the piles are stati-

cally connected using appropriate single valued springs to represent the
increased fl exibility of a pile group compared to the summation of the
stiffness of all individual piles, the estimation of the connecting spring
stiffness is highly subjective .

• Use of the (particular statically based) P - y method often leads to the

extension of its application for the case of inelastic dynamic analysis in
the time domain. Such an extension, although tempting for special cases
of structural design (i.e. performance-based design of new or retrofi t of
existing important bridges), leads to the misleading perception of mod-
eling refi nement without proper understanding and consideration of the
complex dynamic nature of SSI phenomena.

It can be concluded that as soil-foundation-structure interaction is a
multi-parametric and strongly frequency-dependent phenomenon, it has to
be investigated from a dynamic point of view, through a very careful selec-
tion of FE models, associated parameters, and modeling assumptions. As a
result, the static Winkler spring approach is deemed appropriate only for
cases where:

• bridges are analyzed linearly solely under static loading and the response
is assessed accordingly;
• (standard or modal) pushover analysis is performed in order to quickly
assess the inelastic mechanisms that are expected to be developed under
earthquake excitation;
• response spectrum analysis and/or linear time history analysis is per-
formed for a relatively low level of seismic forces;