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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the highest concentration about 1400 kg/m 3 . Conversely, in the case of CB members, this information is very often omitted and, therefore, an average value of g m equal to 1700 kg/m 3 is considered in the analyses; therefore, it is trivial to state that the datasets are mostly concentrated about the value of 1700 kg/m 3 set by the authors, since only for one dataset related to the C-FRCM system and for another one related to the G-FRCM system the scientific papers provide g m = 1700 kg/m 3 (Napoli and Realfonzo 2022). This consideration is useful for the analytical study presented in §3. 3. The analytical study In the previous study (Napoli and Realfonzo 2022), the authors developed new relationships for the estimate of the compressive strength of masonry confined by FRCM,   , suitable for any fiber mesh (B, C, G, PBO, S) and nature of masonry (natural or artificial). These relationships were found by starting from the slightly more general 5 parameter relationship reported in CNR-DT 215 (2018), written here in the following general normalized form: (1) where   = 4 ∙   ⁄ is the geometric strengthening ratio, and   is the dimensionless coefficient of confinement efficiency given by: (2) The parameter   accounts for the influence of the inorganic matrix which in turn depends on both the matrix reinforcement ratio   and the compressive strength of both inorganic matrix and masonry  ,   ⁄ ; it is directly used to reduce the lateral confining pressure exerted by the FRCM system, being:   ≤ 1 . In the estimate of   and in Eq. (2), D represents the diameter of the circular cross-section or the diagonal length of the square or rectangular cross-section. For the expressions of the parameters k h and k v , omitted here for the sake of brevity, reference to DT 215 (2018) and DT 200 R1 (2013) can be made, respectively, as mentioned earlier. In the strength model proposed by DT 215 (2018), the coefficient   can be assumed equal to 0.5 in absence of reliable experimental results, while   and   can be set prudently equal to 1.0, unless experimental results are available to justify different assumptions. For what concerns   , the exponent   is set to 2 while the coefficient   is assumed equal to 1.81 lacking experimental results able to justify different values. Basically, the model described by Eqs. (1-2) is very similar to the formulation proposed by DT 200 R1 (2013) for confinement of masonry with FRP systems, where the coefficients   ,   and   again assume the values 0.5, 1 and 1, respectively, whereas the parameter   is replaced, for design applications, by a term reducing the ultimate strain  , . In Napoli and Realfonzo (2022), a number of best-fit analyses were performed to n = 91 datasets in order to calibrate the values of  i parameters in Eqs. (1-2) minimizing the difference between the predicted and the experimental values of the strength ( ̅ , and ̅    , respectively). From those analyses, two models were finally proposed, which were found by using the mean absolute percentage error (MAPE) as error minimization technique; these models are reported in Table 2, together with the MAPE values (E rr ) m . By focusing on Proposal 2 , and considering that 1.10 ∙ 0.90 /  =    ≈ 1.00 , the model can also be written in a framework very similar to the formulation suitable for FRP systems (Napoli and Realfonzo 2021), where the   coefficient is 2/5 instead of 2/3 and   =    = 1.10 instead of 1.00. Table 2. Strength models published by Napoli and Realfonzo (2022). Masonry n Proposal 1 Proposal 2 Describing Equation     Describing Equation     Any (ALL) 91 ̅  = 1 + 0.40 ∙    1000  . ∙ ̅ , . 13.90% ̅  = 1 + 1.10 ∙ ̅ , . 14.50%   =   = 1.00   =   = 0.90 1  3 1  3  0 f E k , f u 2        , l eff 2         mc f 0 0.5 1000 1 1000 1    f             k k       m mat f h V m m m mc g f g f f 1 4 5     5     0 , mat c 4  0 , mat c 4                mat m mat m mat f f D t f f k