Stochastic modeling of deterioration in buildings and civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 404

of the system behavior (e.g., Stewart, 2001; Melchers, 2005; Choe et al. , 2009;
Pillai et al. , 2010; Simon et al. , 2010). However, typically such studies do not
completely model the time-dependence of a stochastic deterioration process
and its interaction with the process of loading. Therefore, the results might
not be adequate to conduct life-cycle analysis of a deteriorating system (e.g.,
predicting lifespan and life-cycle costs). The second type of studies focus on
stochastic modeling of deterioration processes to conduct life-cycle analysis
of systems (e.g., Esary et al. , 1973; Ellingwood and Mori, 1993; Mori and
Ellingwood, 1994; Klutke and Yang, 2002; Noortwijk et al. , 2005; Wortman
et al. , 2006; Kumar et al. , 2009; Sánchez-Silva et al. , 2011; Kumar et al. , 2012).
However, owing to the complex nature of deterioration processes, there are
challenges in certain aspects of modeling such as the dependence between
deterioration and loads, the interaction between different failure modes of
a system and non-stationary behavior of a damage accumulation process.
This chapter uses the stochastic semi-analytical approach (SSA), which
is a general stochastic formulation originally proposed by Kumar et al.
(2012), to model the deterioration of civil engineering systems and account
for the effects of deterioration on their reliability over time. We use the
SSA formulation to forecast the lifespan of a reinforced concrete (RC)
bridge bent subject to earthquakes and a corrosive environment. The SSA
formulation is selected here because it addresses the following important
issues typical of other available models:

• modeling the effect of deterioration on both capacity and demand;
• modeling the dependence between the deterioration process and
demand;
• modeling the combination of shock and the gradual deterioration
process;

• accounting for different failure types; and

• having accurate and time-effi cient solution strategies.

The rest of the chapter has four sections. In the next section, the chapter
describes the characteristics of a general deterioration process. The follow-
ing section summarizes the SSA formulation. Next, the chapter describes
the methodology to model deterioration in RC bridges and presents a case
study consisting of an RC bridge subject to deterioration due to earth-
quakes and corrosion. The last section summarizes the chapter and draws
some conclusions.

16.2 A general deterioration process

A deterioration process can be distinguished into two types: shock and
gradual deterioration. A shock deterioration is an instantaneous change
in a system's properties due to the action of external loads (e.g., sudden