Geology Reference
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Figure 3. Estimation of corrosion initiation time for the cover depths of 40, 50, and 60 mm
m ( t ) is equal to the consumed mass of steel per
unit length divided by the original steel mass.
The reduced diameter and the remaining yield
strength of rebars are calculated at different time
steps during the life-cycle of the bridge (Table 2).
These values are used to update the characteristics
of bridge models during the structural capacity
estimation and seismic performance evaluation
of corroded bridges.
Through a step-by-step analysis, the time in
which the concrete starts cracking is determined
as the time when the percentage of steel mass
loss, m ( t ), becomes equal to a critical level, m critical .
The m critical which can be defined as a function of
rebar dimensions and concrete properties (El
Maaddawy and Soudki, 2007) is calculated in the
present study equal to 20%. Based on this critical
level, the crack initiation time is found to be 51
days (0.14 year) for the structures under consid-
eration. To calculate the crack width after crack
initiation, w crack (mm), the analytical equation
proposed by Vidal et al. (2004) can be used:
D t
( )
=
D
2
4
V t
loss
( ) /
π
(9)
0
where D 0 is the initial diameter of the rebar.
The residual strength of corroded reinforcing
bars was investigated experimentally by Du et
al. (2005a and b). They conducted both acceler-
ated and simulated corrosion tests on the bars
embedded in the concrete and concluded that
the strength of steel bars decreases significantly
with chloride penetration. Their test results are
in reasonable agreement with other studies, such
as Andrade et al. (1991), Lee et al. (1996), and
Morinaga (1996). Therefore, the below empirical
equation proposed by Du et al. (2005a and b) is
used to estimate the time-dependent loss of yield
strength in corroded reinforcing bars:
)
(
( ) = −
( )
f
t
1
0 005
.
m t
f
(10)
y
y
0
where f y ( t ) is the yield strength of corroded rein-
forcement at each time step, f y0 , the yield strength
of non-corroded reinforcement, t , the time elapsed
since corrosion initiation (year), and m ( t ), the
percentage of steel mass loss over the time. The
(
)
w
( )
t
=
K
A t
( )
0
A
(11)
crack
crack
s
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