Page 525 - Marine Structural Design

Chapter 28 Probability and Risk Based Inspection Planning 501

The detectable crack size aD is related to a specified inspection method and modeled as a
stochastic variable reflecting the actual probability of detection (POD) curve. Among several
formulations of POD available, the commonly used exponential distribution is selected in this
case:
P,(a,) = 1 - exp( -?)

(28.6)
where h is the mean detectable crack size.
Crack Detected and Measured
If a crack is detected and measured for a weld detail i, this inspection event can be written as

1p.i (tr)= am -ai ('1)
= Y(a,)-Y(ao)-Civot,E;A"T(l+~) =O
(28.7)
where, a,,, is the measured crack size at time tI and regarded as a random variable due to
uncertainties involved in sizing. "(a) is a function reflecting the damage accumulation from
zero to crack size a and is defined as (Paris and Erdogn, 1963, Newman and Raju, 1981),

Repair Events
The inspection itself does not increase the reliability of the structures, but it makes possible to
take the necessary corrective actions like repair if a crack is detected. After repair, it is
assumed that the material parameters and initial crack size follow the previous models but are
statistical independent. This repair event based on crack detected and measured is the same as
given by Equation (28.7), i.e. IR=I,,. After repair the failure event also needs to be modified as
discussed below.
Reliability Updating Through Repair
If a crack is detected, measured and repaired, statistical properties of the material are expected
to be the same magnitude but statistically independent. Weld defects, aR, after (underwater)
repair depends upon the repair and post-repair treatment methods (grind, aRg or weld, aRw).
Here it is assumed to follow the same model as a. The new safety margb after repair, MR(t),
becomes

(28.8)

where, fR is the repair time. Parameters aR, CR, mR are assumed to follow the previous models
but are statistically independent.
Updated failure probability for repaired structural details is written as