PSI - Issue 11

Pablo Benítez et al. / Procedia Structural Integrity 11 (2018) 60–67 Benítez et al./ Structural Integrity Procedia 00 (2018) 000 – 000

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Another meaningful parameter is the effectiveness of the inspection technique for detecting damage. For an illustrative example, three different inspection technique has been selected in order to assess its probability of detection a corrosion damage. In this case, these techniques have been nominated generically as technique A, B and C . Nevertheless, these techniques can be whatever technique capable of measuring the corrosion probability in the reinforcement, or even, the intensity and/or corrosion rate. In this way, each technique will have its own operation cost and detectability related to its quality. Considering the values of Table 3 and assuming the inspection technique A and C applied five years after the corrosion initiation in a RC structure whose damage degree caused by corrosion is = 0.0556 , the detectability can be calculated in order to quantify the inspection quality. Then, the detectability for the technique A is ( ) = 2.58 × 10 −14 and for the technique C is ( ) = 1.43 × 10 −8 . As can be seen in Figure 3(a), a higher quality technique requires lower corrosion intensity to detect the damage in the structure. Similar to the previous analysis, the probability of damage detection before failure is highly associated with the quality of the inspection technique. By this point, a high-quality technique will need to perform a low number of inspections over the service life of the structure to achieve the maximum probability of detection. In Figure 3(b) can be seen that the propagation of corrosion damage is slow in RC structures and it is unlikely that during the first years of the service life, corrosion damage becomes an issue of structural failure. Therefore, the lower the number of inspections projected during the service of a structure, the lower the probability of detecting the damage in time. In other words, if it is considered to perform only an inspection over the service life of a structure, it is expected that the probabilities damage detection before failure will be lower, although this approach does not necessarily mean that the structure will fail. On the other hand, the expected total cost of the inspection planning is directly proportional to the number of proposed interventions. Clearly, a minimum number of inspections leads to a lower total cost. However, as was found previously, the smaller the number of inspections, the greater the probability that a failure damage will occur in the structure without being detected. In this context, the inspection cost function has an inverse behaviour regarding the failure costs function over the service life of a structure. This means that a trade-off between both functions must be founded in order to achieve an optimal cost of the inspection planning. Figure 3(c) shows the relationship between both functions regarding technique A , where the optimal number of inspection is revealed when the lower expected total cost of the interventions is found. (a) (b) (c)

Fig. 3. (a) Detectability, (b) Probability of detection before failure and (c) Cost analysis.

Whereas for the assumption considered here the technique A is the lowest quality one, the same analysis presents the same behaviour for the inspection technique C , which is the highest quality ones, but with a higher expected cost ( = 340.57 ) and a lowest optimal number of inspections ( = 5 ). Similarly, the cost analysis shows that for the inspection technique B, the minimum expected total cost would be 313.64 when the optimal number of inspection is = 7 . Therefore, the probabilities for the expected corrosion-induced failure are quite sensitive to the environment surrounding the structure. Moreover, the influence of the inspection quality both on the capability to damage detection before failure, as well as on the expected total cost for the inspection planning has been demonstrated. Finally, the parameters assumed above have been considered as a referential cost. This means that the real cost values can be considered with the same approach making use of the market cost for each country. Likewise, the properties of the techniques can be considered with more realistic values through the permanent update of data that are collected after each intervention. The values for these parameters are usually difficult to establish due to the high uncertainty involved in the degradation mechanism, that is, each case should generally be treated as a different case.