Seismic risk models for aging and deteriorating buildings and civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 393

common. Corrosion is a form of steel deterioration that consists of material
disintegration as a result of chemical or electrochemical actions. Most
metals corrode on contact with water (or moisture in the air), acids, bases,
salts, and other solid and liquid chemicals. Metals will also corrode when
exposed to gaseous materials like acid vapors, formaldehyde gas, ammonia
gas, and sulfur containing gases (Jones, 1992). Depending on the case, cor-
rosion can be concentrated locally to form a pit, or it can extend across a
wide area to produce general wastage (Vu and Stewart, 2000; Martín-Pérez
et al. , 2001; Val and Stewart, 2003, 2009). On the other hand, fatigue is the
damage of a material resulting from repeated stress applications (e.g., cyclic
loading). Fatigue is conditioned by many factors such as high temperature,
i.e., creep-fatigue, and presence of aggressive environments, i.e., corrosion-
fatigue (Schijve, 2003; Suresh, 1998). Coupled corrosion-fatigue deteriora-
tion results from the combined action of cycling stresses in corrosive
environments. Localized corrosion leading to pitting may provide sites for
fatigue crack initiation. Several experimental studies have shown that
pitting corrosion has been responsible for the nucleation of fatigue cracks
in a wide range of steels and aluminum alloys (Kondo, 1989; Ahn et al. , 1992;
Chen and Duquette, 1992). In such studies, pits are usually found at the
origin of the fracture surface.

15.4.2 Approximation to graceful deterioration

In modeling graceful (continuous) deterioration it is frequently not possible
to evaluate the time-dependent nature of the degradation rate (Kiessler
et al. , 2002) (equation 15.3). Thus, alternative models focus on evaluating
progressive deterioration discretely. These models use stochastic processes
in which the loss of remaining life (i.e., deterioration) occurs only at dis-
crete, and frequently, deterministic times. Therefore, most of these models
are limiting solutions of shock models. In this section two shock-based
approaches to graceful deterioration are presented. In both cases, progres-
sive deterioration is caused by random shock occurring at fi xed time
intervals.

15.4.3 Gamma process

If the Gamma process (Abdel-Hameed, 1975) is used for modeling graceful
deterioration, it is assumed that shocks follow a Gamma distribution with
identical scale parameter and occur at small, deterministic and equally
spaced time intervals (Noortwijk 2009). A continuous-time stochastic
process { X ( t ), t 0} is said to be a Gamma process if it has non-negative

independent increments and X ( s )

≥

− X ( t ) ∼ Gamma [ ν ( s ) − ν ( t ), u ]; ∀ 0 ≤ t <

s .; where Gamma [ ν ( t ), u ] is the Gamma distribution function with param-