Page 100 - Handbook of Materials Failure Analysis

1 Introduction 95

construction and repair/maintenance in some countries in Europe. As observed by
the numbers presented in this table, the cost associated with repair/maintenance can-
not be disregarded.
The corrosion of reinforcements is directly connected to the durability of rein-
forced concrete structures. In addition to that, the diffusion of chlorides is recognized
as one of most important sources that triggers the corrosion process [15,16]. There-
fore, at modeling this phenomenon, the loss of reinforcements, the concrete damage
level and, consequently, the structural durability are efficiently evaluated.
The chloride penetration into concrete pores is controlled by complex physical
and chemical mechanisms. The modeling of this phenomenon is often simplified,
without significant loss of representation, by a process controlled only by the diffu-
sion of chloride ions into concrete pores. The corrosion starts when a threshold level
of chloride concentration is reached at the vicinity of reinforcements, leading to its
depassivation [17,18].
Several models have been proposed in literature to represent accurately such phe-
nomenon. Among them, it is worth to mention [19,20] where Nernst-Planck-Poisson
equation was applied to describe the movement of multispecies in saturated concrete.
Bastidas-Arteaga et al. [21] presented a degradation model for reinforced concrete
structures where mechanical degradation processes are caused by biodeterioration
sources (i.e., action of live organisms), steel corrosion, and concrete cracking. Zhao
et al. [22] analyzed the concrete cover damage induced by corrosion in reinforced
concrete structures using on a simple analytical model. This model was based on
damage and elastostatic mechanics, which considers noncracking and partial crack-
ing stages.
Cellular automata approach was used to model the diffusion mechanism into con-
crete pores by Biondini et al. [23]. The mechanical damage coupled to diffusion is
evaluated by introducing a mechanical degradation law for both concrete matrix and
steel rebar in terms of suitable damage indices. The mechanical model proposed by
Biondini et al. [23] was applied to assessment of reinforced concrete structures dura-
bility taking into account the inherent randomness on the problem variables by
Biondini et al. [24]. The probabilistic analyses were performed using Monte Carlo
simulation and structural maintenance planning based on reliability index were pro-
posed. A case study in cable-stayed bridges using this model is presented in Ref. [25].
The evolution of the lifetime structural performance considering uncertainties is pre-
sented in Ref. [26] using the approaches introduced in Ref. [23–25].
The time-variant reliability analyses of reinforced concrete highway girder bridges
subjected to time-dependent load and resistance is presented in Refs. [27–29]. A sim-
plified mechanical model, which is based on an analytical equation and two random
variables, is used to represent the girders mechanical behavior along time. In these
works, Fick’s law is adopted to determine the time for corrosion initiation and Monte
Carlo simulation applied to calculate the probability of structural failure. Fick’s law
and simplified relations to represent the steel loss along time are adopted in Ref.
[30] to formulate a reliability-based design optimization problem. The total structural
cost is minimized taking into account construction and failure individual cost.