Probabilistic fatigue life updating accounting for inspections of multiple critical locations

Many steel structures contain multiple fatigue sensitive details that have similar geometries and are subjected to similar load fluctuations. Examples are orthotropic (bridge) decks and stiffened (ship) hulls where tens to thousands of similar details are present in one structure. Generally only visual inspections on fatigue cracks are considered for these structures because more accurate techniques are considered to be too expensive and time consuming when so many details need to be inspected. Visual inspections are known to have a low probability of detection. Consequently Bayesian update techniques usually show a marginal effect of the result of visual inspections on the reliability of structures with respect to fatigue failure. On the other hand the inspection result of one location also provides information on similar details at other locations and thus the significance of the inspection result may be larger if multiple potential crack locations occur and cracks are not detected at any of these locations. This paper provides a probabilistic fatigue crack growth (fracture mechanics) model of a system containing a fatigue sensitive detail at multiple locations that accounts for the results of inspections. Spatial correlations of loading, resistance, and uncertainty variables between the different locations are evaluated and estimated through a literature review and are accounted for in the model. The model is demonstrated on a practical example of an orthotropic bridge deck containing a detail at 100 locations. The paper shows that visual inspections may be effective provided that a certain minimum inspection reliability can be guaranteed, that the structure is relatively tolerant to large cracks, and that the geometry and loading conditions are similar for a large number of locations.