PSI - Issue 78

454 Matilde Natalizi et al. / Procedia Structural Integrity 78 (2026) 449–456 Finally, to perform cost-benefit analysis the amortization time (in years) of the intervention costs should be estimated as follows (Bhandari S. B, 2009): = − (1 − ⋅ )⁄ (1 + ) (8) where is the saving given by the difference between pre-intervention and post-intervention. is the interest rate assumed equal to 5%. In Appendix (Table 6) are summarized the variables adopted for the cost-benefit analysis. Table 3 presents an example of a consolidation intervention matrix for typology 4B (Table 1), which illustrates the possible interventions, the resulting transition to a new structural typology, and the corresponding reduction in vulnerability, expressed in terms of ∆ ( ) and ∆ . Moreover, Table 3 reports the amortization time and the total intervention costs % , expressed as a reconstruction cost percentage for the considered typology, calculated as follows: % = ⁄ (9) Table 3. Matrix of intervention for the 4B typology 4B typology Interventions Tie rods Slab CRM Tie rods +Slab Tie rods +CRM Slab +CRM Tie rods+ Slab+CRM Typology transitions 4C 6B 4D 6C 4E 6D 6E ∆ ( ) 8.0% 22.3% 17.4% 38.9% 27.4% 45.4% 55.3% ∆ 0.28% 0.59% 0.71% 0.86% 0.83% 1.01% 1.13% % 1.6% 4.4% 11.4% 6.0% 13.0% 15.8% 17.4% (years) ≈7 ≈10 ≈34 ≈9 ≈31 ≈31 ≈30 This approach can be extended to the entire municipality of Arquata del Tronto to implement a large-scale intervention plan designed to minimize the cost-benefit ratio, effectively supporting the allocation of public resources toward the most efficient interventions. The results, summarized in Figure 3 in the form of histograms, can be obtained with a low computational burden simply by modifying the combination of structural typologies into which the sample was initially divided (Plan 0), representing the current situation without interventions. Each intervention plan may provide, for each typology, the application of one or more interventions, or no intervention at all, so that each typology may eventually change to another, generating a new combination. Various intervention strategies (the combinations of which are listed in Table 4) were considered and divided into two main categories. The first, which includes plans from 1 to 7, involves uniform interventions on the entire municipal area, for example, plan 4 involves the insertion of tie rods and the stiffening of floors in all buildings, except, of course, those where these elements are already present. The second category (plans 8 to 10) considered different interventions for each typology.

Table 4. Combination of structural typologies following intervention plan Uniform interventions

Differentiated interventions

No intervention

Tie rods +Slab

Tie rods +CRM

Slab +CRM

Tr+Slab +CRM

Tie rods Slab

CRM

0

1

2

3

4

5

6

7

8

9

10

4B 5B 6B 4C 5C 6C 4D 5D 6D 4E 5E 6E

4C 6B 5C 6B 6C 6B 4C 6C 5C 6C 6C 6C

4D 5D 6D 4E 5E 6E 4D 5D 6D 4E 5E 6E

6C 4E 6C 5E 6C 6E 6C 4E 6C 5E 6C 6E

6D 6E 6D 6E 6D 6E

6E 5E 6E

6C 6C 5C 6C 6C 6E

6E 6E 6E

6E 6E 6E

6C 6C 6C 6C 5C 5C 6C 6C 6E

4E 5E 6E 4E 5E 6E

6D 6D 6D 6E 6E 6E

6E 6E 6E 6E 6E 6E

4E 5E 6E 4E 5E 6E

6D 6E 6D 6E 6D 6E

4E

4E

4E

5D 5D 5E

6D 6E

6E 4E 5E 6E

6E 6E 6E

6E 6E 6E

4E 5E 6E

4E 5E 6E