Page 101 - Handbook of Materials Failure Analysis

96 CHAPTER 5 Failure analysis of reinforced concrete structures

Some numerical studies using finite element method (FEM) were already
presented in literature [31–33]. These studies analyze the mechanical problem of
reinforcements corrosion penalizing the reinforcement area and modeling the con-
crete damage by empirical/analytical approaches. The researches cited above pre-
sented theoretical/numerical/empirical approaches that allow the mechanical
modeling of reinforced concrete structures subjected to reinforcements corrosion.
Nevertheless, a numerical approach that accounts realistically for both steel and con-
crete mechanical degradation along time coupled to a numerical method capable to
general structural modeling is still a challenge in this important scientific domain.
In this regard, a numerical mechanical model for structural analysis of reinforced
concrete frames subjected to chloride penetration and reinforcements corrosion
based on FEM is proposed in this chapter. The nonlinear mechanical behavior of
steel and concrete are modeled considering elastoplastic criterion and damage
mechanics approach, respectively. Geometric nonlinearity is considered by the
updated Lagrangian description, which allows writing the structural equilibrium con-
ditions on the last equilibrium configuration. To improve the modeling of shear influ-
ence, concrete strength complementary mechanisms, such as aggregate interlock and
dowel action are accounted. It is worth to mention that the modeling of such non-
linear phenomena is one contribution of this study. Fick’s law is adopted to deter-
mine the chloride concentration growth at the structural cover along time. The
loss of rebar’s area along time due to corrosion process is calculated using the model
proposed by Val and Stewart [17], Val and Melchers [34], and Vu and Stewart [35],
which is based on experimental data.
In this study, bended structures are analyzed considering the proposed nonlinear
numerical formulation. The results provided by the proposed model are compared
with responses available in literature. The proposed nonlinear FEM formulation
allows the assessment of the residual structural resistance along time accounting
the chloride penetration and the structural loss resistance due to corrosion phenom-
enon. This is one contribution of the present study. In addition to that, this model also
allows the determination of the structural failure mode and its change along time,
which is the main contribution of this work.

2 PHYSICAL NONLINEARITY OF MATERIALS
2.1 DAMAGE MECHANICS MODEL FOR CONCRETE
The nonlinear mechanical behavior of concrete originates from the crack growth
along the concrete mass [36,37]. To represent this singular mechanical behavior,
damage models are particularly suitable, because this approach allows the consistent
representation of material degradation by penalizing the material stiffness as a
function of strain increase. In this study, the Mazars’ damage model [38] was
adopted, which is based on the following hypotheses: damage is an isotropic and
scalar variable, the residual strains are totally neglected and damage occurs only
by elongation strains.