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 592

pseudo-static interaction between pile and soil is the Winkler model
(Matlock and Reese, 1960) in which the soil reaction to pile movement is
represented by independent (linear or non-linear) unidirectional transla-
tional spring elements distributed along the pile shaft to account for the
soil response in the elastic and inelastic range, respectively (Fig. 22.1).
Although approximate, Winkler formulations are widely used not only
because their predictions are in good agreement with results from more
rigorous solutions, but also because the variation of soil properties along
the pile length can be relatively easily incorporated. Moreover, they are
signifi cantly more effi cient in terms of computational time required, espe-
cially compared to continuum fi nite element (FE) or fi nite difference
methods, thus permitting focus to be placed on the structural inelastic
response.
The mechanical parameters for the spring elements are frequently
obtained from experimental results (leading to P - y curves for lateral and
T - z curves for axial loading) as well as from simplifi ed models. An expres-
sion that is still widely used for the lateral soil resistance-defl ection rela-
tionship is (API, 1993):

⎡
⎢

kH
p

⎤
⎥

Pp = 09 . tanh y [22.1]

u

09 .

u

Deck

Deck mass

Pier

Pile cap

Shell elements

Force-delection
curve for the soil

P k /4

Nonlinear uniaxial
soil springs

k

2.5 cm

y

Pinned supports

22.1 Overview of fi nite element (FE) modeling of pile groups using
uniaxial soil springs.