Page 114 - Handbook of Materials Failure Analysis

7 Applications 109

d initial if t t 0
dtðÞ ¼ (5.32)
ð
d initial 0:0232i CORR t t 0 Þ if t > t 0
in which d initial is the reinforcement diameter before depassivation in mm, t 0 repre-
sents the time of corrosion initiation in years, and i CORR indicates the corrosion ratio
2
given by μA/cm .
The corrosion rate is calculated using the expression presented in Ref. [35], which
was also determined empirically.
1:64
ð
37:81 w=cÞ 2
i CORR ¼ μA=cm (5.33)
cvr
in which w/c indicates the water/cement ratio and cvr represents the concrete cover
thickness in cm.
On the other hand, when pitting corrosion is considered, nonuniform corrosion
model is assumed. The corroded diameter of reinforcements is determined using
the following expression:

d initial if t t 0
dtðÞ ¼ (5.34)
ð
d initial 0:0116Ri CORR t t 0 Þ if t > t 0
where R represents the ratio between steel corroded thickness calculated using uni-
form and pitting corrosion approaches. The value 5.65 may be adopted for R variable
according to Vu and Stewart [35]. It is important to mention that Equations 5.32 and
5.34 were determined considering experimental results. Therefore, such equations
are suitable to inherent errors associated with equipment of measure and/or human
errors. However, in spite of their inherent limitations, models better than those are
not available in literature.
Reinforcements corrosion induces longitudinal cracking due to the expansive
products of corrosion, which leads to spalling and/or delamination phenomena. In
such case, experimental results suggest that structural mechanical capacity is
reduced due to the concrete compression zone being reduced by the depth of the
spalled/delaminated cover. In this regard, it is important to mention that the equa-
tions presented in this section accounts only the steel loss itself, along time, after
the time of corrosion initiation. Complementary mechanical degradation effects
due to corrosion such as reduction of steel strength and ductility along time, spalling
and delamination of concrete, and adherence loss among concrete and reinforce-
ments are not considered by the equations adopted in this study.

7 APPLICATIONS
Two applications are considered in this study. The first application concerns the
mechanical analysis of a two-dimensional frame where the results achieved by
the nonlinear FEM model are compared with experimental results available in liter-
ature. In the second application, the proposed formulation is used to model the
mechanical behavior of two simple supported beams subjected to chloride