PSI - Issue 44

Annalisa Napoli et al. / Procedia Structural Integrity 44 (2023) 2182–2189 Annalisa Napoli, Roberto Realfonzo / Structural Integrity Procedia 00 (2022) 000–000

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3.1. Considerations from the previous study and new analyses In Table 2, Proposal 1 was derived by considering the variability of the five   in the MAPE minimization procedure with the purpose to provide an updated version of the model suggested by DT 215 (2018). This model highlights a negligible influence of the matrix properties in the ̅  value, being   equal to 0 and   equal to 1. Furthermore, the value obtained for   , equal to 2.00, might let seem that the masonry mass density g m affects the masonry performance; however, in light of the considerations made before about the poor availability of g m values in the scientific papers for the CB masonry, and being the number of datasets related to the CB masonry 3,5 times the number available for NM (i.e., 77 vs 22 datasets), the term   /1000 . is almost constantly equal to 1700/1000 . = 2.89 that, multiplied by   = 0.40 , yields a value very similar to   = 1.10 in Proposal 2. Therefore, based on the experimental datasets, it is quite trivial to monitor the contribution of the masonry mass density g m except for the 22 datasets related to masonry columns made of natural masonry. Proposal 2 was derived by considering in the MAPE analysis the variability of   ,   ,   while keeping   and   set to the values found by the authors in the case of masonry confined by FRP (Napoli and Realfonzo 2021), i.e.,   = 1.10 and   = 0 . Setting   = 0 means that, already in the case of FRP confinement, it has been found that the masonry mass density g m seems to have a negligible influence on the strength performance. In this study, new best-fit analyses were performed by considering the 99 experimental datasets. The general 5 parameter relationship described by Eqs. (1-2) was again taken into account, where the   parameters were calibrated by considering the MAPE error minimization technique. All the 8 analysis cases described in Napoli and Realfonzo (2022) were generally considered and applied, one at a time, to three different groups of datasets, i.e.: • Group 1 : all datasets together ( n = 99), with the aim to find strength models suitable for any masonry type (NM and AM); • Group 2 : datasets related to AM only ( n = 77); • Group 3 : datasets related to NM only ( n = 22). Based on the considerations above it can be stated that, in the case of Group 1 , considering the influence of masonry mass density g m through the calibration of   loses of significance, as well as for Group 2 , while it can be useful to examine the results of the best-fit analyses in the case NM, for which the experimental values of g m are available. Finally, by setting   = 0 , a further 4 - parameters analysis is performed with reference to all the groups of datasets with the purpose to compare the calibrated value for   with respect to   = 1.10 obtained for the case of FRP confinement (Napoli and Realfonzo 2021). Table 3 provides, for each group of datasets, the best analytical solutions obtained from the application of the MAPE minimization technique, labelled Proposal 1 , Proposal 2 and Proposal 3 . In particular, Proposals 1 and 2 account and do not for the contribution of the masonry mass density ( Proposal 1 is not taken into account for AM), respectively; Proposal 3 is the result of the new best-fit analysis obtained by setting   = 0 and calibrating   together with   ,  ,   . As noted, in the case of the Group 1 (all datasets), the new relationships basically confirm the best-fit models found in Napoli and Realfonzo (2022), with very slight modifications of   coefficients; also, the new formula labelled Proposal 3 is very similar to Proposal 2 , with only a small reduction of the coefficient   (from 1.10 to 1.05) and a slight increase of   (from 0.90 to 0.95). In the case of Group 2, it has been found that Proposal 2 is the model yielding the lowest error since it exactly coincides with Proposal 3 . Table 3. New proposals. Masonry n Proposal 1 Proposal 2 Proposal 3 Describing Equation     Describing Equation     Describing Equation     Any (ALL) 99 ̅  = 1 + 0.35 ∙    1000  . ∙ ̅ , . 13.21% ̅  = 1 + 1.10 ∙ ̅ , . 13.67% ̅  = 1 + 1.05 ∙ ̅ , . 13.64%   = 1.00   = 0.90   = 0.95 ̅  = 1 + 1.10 ∙ ̅ , . 12.73% = Proposal 2 12.73% 11.95% ̅  = 1 + 1.10 ∙ ̅ , . 12.05% ̅  = 1 + 1.05 ∙ ̅ , . 11.95% Artificial Masonry (AM) Natural Masonry (NM) 77 ⁻   = 1.00 22 ̅  = 1 + 1.00 ∙    1000  . ∙ ̅ , . .

.   = 0.40 ∙   ∙  ,    .

  = 0.40 ∙   ∙  ,   

  = 0.35 ∙   ∙  ,   