Civil Engineering Reference
In-Depth Information
100
90
80
70
g
(
t
) =
t
2
g
(
t
) = 0.75
t
60
50
40
30
20
g
(
t
) = exp
0.1
t
10
0
0
10
20
30
40
50
60
Time
15.6
Trend-dependent model for graceful deterioration (adapted from
Sánchez-Silva and Riascos-Ochoa, 2012a,b).
are smaller as time increases for the exponential and quadratic functions.
In Fig. 15.6 shocks where assumed to be exponentially distributed with
mean 1/
k
*)/
e
g
(
T
=50)
.
Clearly both models depend on the selected parameters; i.e., shape func-
tion
v
(
t
) (Gamma process) and trend function
g
(
t
) (trend-based approach).
In general, sensitivity analysis show that the latter approach is less smooth
as time increases for non-linear functions since there are more jumps in a
smaller timespan. The only way to validate theses models is by using actual
data, which is usually diffi cult to fi nd. However, if the trend of the deteriora-
tion process is somehow known, these two models can be used to obtain
estimates of the MTTF.
λ
=
(
v
0
−
15.5 Combined progressive and
shock-based deterioration
15.5.1 Basic formulation
There is little evidence of a strong correlation between progressive deterio-
ration and damage as a result of shocks (e.g., earthquakes), therefore, inde-
pendence can be assumed in most cases. If progressive degradation has a
continuous positive rate,
δ
(
t
)
>
0, the remaining life of the structure at time
t
can be computed as:
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