PSI - Issue 44

I. Boem et al. / Procedia Structural Integrity 44 (2023) 1260–1267 Boem I. and Gattesco N. / Structural Integrity Procedia 00 (2022) 000–000

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behavior and parameters set in accordance to experimental tensile tests on bare yarns. For the mortar coating layer, the Concrete-Damage Plasticity material model “Cdpm2” was considered. The Young modulus and the compressive and tensile strengths were obtained from characterization tests on cylinders; the softening in tension was calibrated so to properly reproduce approximately the equivalent behavior of the direct tensile characterization tests on fiber reinforced coupons (Fig. 2). The equivalent behavior assigned to the steel bars (with a softening exponential law) accounted for the occurrence of slippage from the mortar, according to the experimental evidences coming from pull out tests.

Fig. 7. Main features of the intermediate level numerical model for vaults.

Table 3. Main material parameters for the vaults simulations (for unspecified parameters, the OOFEM default values are used (Patzàk, 2002). Masonry Mortar coating Glass FRP Carbon FRP Steel bars Layer thickness 55 mm 30 or 10 mm 1 mm 1 mm - Number of Gauss points 12 3 1 1 - Material type con2dpm con2dpm Idm1 Idm1 Idm1 Self-weight d 18 kN/m 3 20 kN/m 3 - - - Young mod. E 4.27 GPa 14.4 GPa 3.81 GPa 5.71 GPa 170000 Poisson mod. n 0.45 0.25 0.01 0.01 0.3 Comp.strength f c 5.12 MPa 6.29 MPa Equiv. strain type mod.Mises mod.Mises Mazars Tens.strength f t 0.32 MPa 0.85 MPa Comp./tens. ratio 0.00075 0.00075 - Softening law linear bilinear Damage law linear linear exponential Hardening parameters b h , h p 0.003, 0.0 0. 002, 0.0 Peak strain  0 2.0% 1.7% 0.24% Softening parameters w f /h , a soft 0.0001, 5 0.035, 4 Ultimate strain  f 3.5% 3.2% w f 7 f t1 , w f1 /h - 0.45, 0.0045 Dilation ψ 0.58 0.85 The numerical curves are plotted in Fig. 4, in comparison with the experimental results: considering the simplified modelling approach adopted, the models with the reinforcement applied at the extrados (Fig. 4a-b) reproduced pretty well the trend of the samples. Also the damage pattern of the models (Fig. 8a) resulted in accordance with the experiments, evidencing at first the opening of the spring interfaces, then a localized failure at the intrados at one haunch (masonry side) and a wider area with high strain level at the extrados of the opposite haunch (reinforcement side). The beginning of the slip in the steel anchors occurred at about  h = 12-15 mm.

a

b Fig. 8. Numerical simulation of the vault (a) vRE-F and (b) vRI-F: tensile strains in the arch direction before collapse.