PSI - Issue 44

Elena Speranza et al. / Procedia Structural Integrity 44 (2023) 1784–1791 Elena Speranza et al../ Structural Integrity Procedia 00 (2022) 000–000

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5. Ended seismic upgrading interventions So far, 510 interventions (42% of the building sample) have been concluded: 61 local strengthening, 426 seismic upgrading, and 23 demolitions and reconstructions. As concerns seismic upgrading, according to the NTSC, the assessment of the seismic safety indices αSLV was required not only in pre-intervention condition s (α SLVante ) but also in the post-intervention ones ( α SLVpost ). Furthermore, the NSPP requires the achievement of two different conditions: the attainment of a minimum threshold for α SLVpost , equal to or higher than 60%, and a 20% minimum safety increase ( Δα SLV ), defined as the difference between α SLVpost and α SLVante (Δα SLV = α SLVpost - α SLVante ). The α SLVante and α SLVpost are available for a subset of 353 seismic upgrading interventions, out of the aforementioned 426: 137 r.c. buildings, 154 masonry buildings, and 62 mixed structures, steel structures, and other structural types. The distribution of the number of interventions vs. the percent seismic safety ind ex increase Δα SLV , as well as their cumulative percentages, are reported in Fig. 6 The Δα SLV has been grouped into 9 intervals with a step of 10%, from 20% (minimum allowed) to >100%. The last interval implies the achievement of the full seismic upgrading, although this could have been reached even for lower values of Δα SLV , in all the cases for which α ante is greater than 0. Figure 7 shows that the most populated class of reinforced concrete and masonry buildings is related to that with Δα SLV = 40%–50%. On average, Δα SLV is equal to 71% for reinforced concrete buildings, 61% for masonry buildings, and 63% for buildings with mixed, steel, and other structures, outlining average safety increases largely higher than the minimum allowed. To assess the benefit obtained by the interventions in terms of risk reduction, the marginal cost of the seismic upgrading interventions, MC , can be defined as the ratio between the unitary cost expressed as €/m 3 according to the following equation: MC = c / Δα SLV (4)

(a) Reinforced concrete

(b) Masonry

(c) Mixed, steel or other

Fig. 6. Number of interventions of reinforced concrete (a), masonry (b), and mixed, steel or other structure as function of different ranges of the safety index increment (Δα SLV ).

The marginal cost MC is a very useful metric because it expresses the cost required to increase by one percentage point the safety index of the building. The distribution of MC of the sample, divided into 6 intervals, is shown in Fig. 7 for each structural type. It shows the highest MC ratios for masonry buildings compared to the other two structural types. In fact, on average, the MC is 2.1 €/m 3 /Δα SLV for reinforced concrete buildings, 2.5 €/m 3 /Δα SLV for masonry buildings, and 1.7 €/m 3 /Δα SLV for buildings with mixed, steel or other structures. To evaluate the effectiveness of the seismic strengthening intervention, Fig. 7 shows the distribution of marginal costs associated with interventions of the sample as a function of the total safety increase ∆ α SLV . Coherently with the approach defined in Dolce et al. (2021), to reduce the aleatory and epistemic uncertainties of the dataset and to provide realistic cost estimations the outliers, defined by MC < 0.8, MC > 6, Δα SLV > 100%, are ruled out from the graphs. As a result, the points sketched in Fig. 7 sum up to 111 out of 137 reinforced concrete buildings, 130 out of 154 masonry buildings, and 47 out of 61 buildings with mixed, steel or other structures.