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is considered by two additional circular
layers of rebars.
4.
Abutments:
The bridge abutment is modeled
using a rigid element with a length equal to
the superstructure width, connected to the
superstructure centerline through a rigid
joint. This element is supported at each end
by three springs in longitudinal, transverse,
and vertical directions. While an elastic
spring is used for the vertical direction, the
longitudinal and transverse springs are ex-
pected to present a nonlinear behavior. For
this purpose, nonlinear zero-length elements
are placed in the perpendicular horizontal
directions with the properties determined
from the Caltrans seismic design criteria
(SDC, 2006). The abutment stiffness and
maximum resistance are dependent upon the
material properties of abutment backfill and
account for an expansion gap, here assumed
to equal 5 cm.
=
4700
'
(ACI-318, 2008). To capture
the effects of confinement in columns, the
properties of confined and unconfined con-
crete are both taken into account following
the equations given by Mander et al. (1988).
For the reinforcing bars, the yield strength
is assumed to equal 470 MPa before corro-
sion begins. As discussed in the previous
section, the steel yield strength decreases
over the time due to the corrosion progress
(Equation 10).
2.
Superstructure Model:
The bridge super-
structure has been designed for four traffic
lanes, two in each direction (as it can be seen
in Figure 4). The roadway width is equal
to 23.0 m and the concrete cross-sectional
area is 12 m
2
. The bridge deck is modeled
by linear-elastic beam-column elements
placed at the centroid of the deck cross sec-
tion. These elements are subjected to linear-
distributed loads which represent the bridge
mass per unit length. Since the columns and
abutments are designed to experience the
nonlinear behavior, no nonlinear properties
are assigned to the superstructure elements
and they always remain in the elastic range.
Furthermore, because the concrete super-
structure always experiences some cracks
due to loading conditions, the flexural stiff-
ness of deck section is modified by a factor
of 0.75 according to the recommendation
of Caltrans seismic design criteria (SDC,
2006).
3.
Pier Columns:
A nonlinear three dimen-
sional beam-column element is used to
model the bridge columns. This element
is based on the iterative force formulation
and considers the spread of plasticity along
the column (OpenSees, 2009). The concrete
cross section is discretized into a number
of fibers (total of 18 wedges and 20 rings)
defined by the fiber module available in
OpenSees (2009) and the steel reinforcement
E
f
c
c
As discussed earlier, the corrosion process may
cause a significant structural capacity loss which
directly affects the bridge performance under any
service and extreme loading conditions. From a
multi-hazard point of view, the combined effects
of a natural event, here an earthquake, and an
environmental stressor, here chloride-induced
corrosion, are studied over the time and the vulner-
ability of bridge as one of the key infrastructure
components is evaluated. Towards this goal, the
nonlinear time-history analysis is employed to
estimate the seismic response of various bridges at
different ages. Obtained results will be used later
for the probabilistic life-time fragility analysis.
In order to perform nonlinear time-history
analysis, a suite of 60 earthquake ground motions
is selected. These ground motions were originally
generated through the FEMA/SAC project (1997)
for the Los Angeles area and include records from
historic earthquakes as well as artificially-gener-
ated time histories. The selected suite consists of
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