Titel_SS06

lead to significant reductions in the probability of failure.

Example 12.7 – Reliability updating by inspection of deterioration

For some structures degradation such as fatigue crack growth and corrosion are important

issues. In order to ensure that such structures remain safe throughout their service life the

degradation must be controlled. Normally the degradation processes can be controlled

efficiently by regular inspections but other approaches such as monitoring of the loading or

monitoring of the response characteristics of the structure can be effective alternatives.

Inspection results can be used to update the safety of the structure. Considering the example

with the steel bar subject to tension loading it is now assumed that the steel bar is subject to

fatigue loading. The fatigue loading is represented in terms of a normal distributed equivalent

constant stress range S with parameters SS 30 MPa,  5 MPa

A 0

. The corresponding
number of stress cycles per year is. The quality control procedure applied when the steel
bar was manufactured implies that an initial defect may be present in the steel bar. The
initial defect is modelled as an exponential distributed random variable with
parameters

105

AA 00   1 mm. It is for illustrative purposes assumed that the crack growth due

to the stress cycles can be modelled to the following simple crack growth model see Madsen

et al. (1986):

2

an a() 0 exp(C sn ) (12.23)

where C is a material parameter equal to 510  ^10. It is assumed that the steel bar fails when

the crack has reached a length of 40 mm.

Based on the simple crack growth model the annual probability of failure is calculated using

FORM/SORM analysis. The result is seen in Figure 12.14 as the dotted line.

234 56

Updated probability

of failure

Original probability

of failure

0

Years in service

1

1.00E-01

1.00E-02

1.00E-03

1.00E-04

1.00E-05

1.00E-06

1.00E-08

1.00E-07

7 8 910111213 14 1516 17 18 19 20 21

Figure 12.14: Inspection plan for a service life of 20 years assuming no findings at inspections.

Now assume that the requirement to the safety of the steel bar is a maximum annual failure

probability of 10-4. Then an inspection is planned the year just before this acceptable

probability level is exceeded, in this case at year 6. The inspection, which is performed, is

uncertain in the sense that that it may fail to detect a crack and further if a crack is detected it

may assess the size of the crack inaccurately.