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43 NACE INTERNATIONAL: VOL. 55, NO. 10 MATERIALS PERFORMANCE OCTOBER 2016
build). Even over 100 years, this would be
negligible compared to the embedded CO
2
used to produce the cement portion of con-
crete (100 to 300 kg/m
3
). A full lifecycle
analysis would also need to include the life-
cycle CO
2
costs associated with items such
as the installation and maintenance of the
system and manufacture of the anodes.
Reinforced Concrete
Durability Predictions
The long-term corrosion behavior of
reinforced concrete structures can be mod-
eled as follows. Generally, a chloride ion or
CO
2
concentration gradient exists between
the outer surface of the concrete and the
surface of the embedded steel rebar. Hence,
reinforced concrete durability predictive
models are mathematically based on the
laws of chloride diffusion. With a focus on
chloride-induced corrosion damage, chlo-
ride-induced corrosion modeling estimates
the time it takes for a significant amount of
chloride ions to reach the steel surface and
initiate corrosion (time of initiation) by
promoting the breakdown of the passive
film. Once corrosion starts, the corrosion
rates and amount of corrosion products
generated can be estimated. The accumu-
lated corrosion products on the steel sur-
face eventually generate stresses greater
than the tensile strength of the concrete,
which results in cracking and/or spalling.
When cracking reaches the concrete sur-
face, these cracks become accelerated chlo-
ride-intrusion paths that lead to the steel;
and corrosion is accelerated.
The time of corrosion initiation (t
i
) in
reinforced concrete structures can be esti-
mated from the error-function (erf ) solu-
tion of Fick's 2nd law,
10-11
with parameters
that include the time and space invariant
diffusion coefficient (D), chloride surface
concentration (C
s
), initial chloride ion con-
centration at the surface of the steel bar
(C
0
), chloride corrosion threshold (C
T
), and
concrete cover thickness (X
c
), as shown in
Equation (2):
(2)
This formula is limited since it is one-
dimensional and does not consider factors
such as chloride binding, the time-depen-
dent diffusion coefficient, and the poten-
tial-dependent chloride threshold.
The estimated impact to t
i
of adding
supplementary cementitious material is re-
flected in the value of the chloride diffusion
coefficient. Previous work has shown that
partially replacing cement in the concrete
mix proportions (i.e., 10 to 50%) with mate-
rials such as fly ash (FA), silica fume (SF), or
metakaolin has resulted in enhanced me-
chanical properties with markedly lower
values of D with consequent long-term en-
hanced concrete performance.
12
An example of how those admixtures
and concrete formulation affect the value of
D is shown by an empirical equation pro-
posed by Sagüés, et al.,
13
based on data from
several bridges, to determine the effective
(time-invariant) chloride diffusion coeffi-
cient (D) for 10-year-old marine structures.
The result is a function of the blended
cement content in the mix (cement factor
[CF]), the water-to-cement ratio (w/c), and
the range of cement replacement by FA, SF,
or blast furnace slag (BFS), as illustrated in
Equation (3):
(3)
where: D is in in
2
/y ; CF is in kg/m
3
(con-
verted from the original lb/yd
3
); CF range =
390