Civil Engineering Reference
In-Depth Information
deterioration of a bridge due to an earthquake). A gradual deterioration is
the wear and decay of the system over time due to prolonged use (e.g.,
fatigue in machine parts during regular operation), aging, and exposure to
unfavorable environment (e.g., corrosion of steel reinforcement bars in RC
structures from exposure to chlorides). Figure 16.1 illustrates a general
deterioration process in a system.
During the service life, a system is typically subject to a sequence of loads
{
S
t
n
}
{
t
1
,
t
2
, . . .}. The sequence of loads
{
S
t
n
} induces a sequence of demands {
D
t
n
}
=
{
S
t
1
,
S
t
2
, . . .} at time instances {
t
n
}
=
D
(
x
t
−
,
S
t
n
),
x
t
represents the properties of the system at time
t
, and
t
−
is the time
instant just before
t
n
. The capacity of the system at time
t
is written as
C
t
=
{
D
t
1
,
D
t
2
, . . .}, where
D
t
n
=
=
C
(
x
t
). Figure 16.1 shows that the system experiences shock deteriorations
at
t
n
−1
and
t
n
. The capacity
C
t
instantaneously changes from
C
t
n
−1
to
C
t
n
−1
and
from
C
t
−
to
C
t
+
(
t
i
is the time instant immediately after
t
i
). The fi gure also
shows the process of gradual deterioration after the shocks at
t
n
−1
and
t
n
in
which
C
t
gradually decreases over time.
Typically, a system has multiple modes of failure (e.g., an RC column can
fail in shear, deformation, or axial compression). For a given mode of failure
k
, failure can be of two types: excessive demand and excessive deterioration.
In the former type, the demand is greater than the capacity corresponding
to a particular performance level, i.e., [(
C
t
−
D
t
n
) < 0]. In this type, the failure
occurs at the time of occurrence of the load. In the latter type, a system is
considered as failed at a time
t
when the total deterioration
W
t
crosses a
−
C
t
-
n
-1
C
t
+
n
-1
C
t
-
n
C
t
+
n
D
n
-1
D
n
t
n
-1
t
n
Time (
t
)
16.1
A general deterioration process.
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