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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curves emerged in both cases. Sample vRI-C reached maximum load values equal to +7.3 kN, at +19.6 mm, and -8.2 kN at -27.9 mm; the load was then approximately maintained in the positive direction, up to about +105.3 mm, while it gradually decreased in the negative one. The test was then stopped at high values of displacement (~110 mm) without reaching the breaking of the GFRP mesh. Sample vRI-F attained to +9.5 kN at +37.7 mm (and then almost maintained the load till +74.2 mm) and to -6.5 kN at -23.7 mm (followed by a gradual resistance decrease); in the positive loading direction, the tensile failure of the carbon grid was reached. The graphs unsymmetry was likely related to the different entity of inward slip associated to the partial efficiency of the fiber-based connectors at the extremities, whose damage appeared with evidence in the last cycles of the tests. Also some progressive debonding of the FRCM layer was noted in vRI-F. These tests evidenced the need of a stronger connection to exploit the whole benefits of the reinforcement. However, a consistent effectiveness of both the reinforcement techniques applied at the intrados emerged, when comparing with the plain configuration. The global view of the vaults at ultimate displacement and some crack details at the haunch section, where the fibers damage localized, are illustrated in Fig. 6.

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b c Fig. 6. Global view at ultimate displacement in vRI-F (a) and some cracks details in (b) vRI-C and (c) vRI-F.

4. Numerical modelling The numerical simulations of the masonry vaults were developed in the context of the “conFiRMa” project (EU, 2020), whose main goal is the calibration of reliable numerical models for the assessment of the structural performances of historic masonry buildings strengthened with TRM. A multi-level approach has been pursued, starting with the detailed modelling of components (Boem, 2022; Boem et al., 2022a), followed by a more computationally efficient intermediate level model, based on layered elements (Boem at al., 2022b) and the calibration of lumped plasticity models for global analysis. For the simulations of the vault samples, the intermediate level numerical model is adopted. The models were developed by using the free, open-source finite element code OOFEM (Patzák, 2002; Patzák, 2012) and are based on twenty-node brick elements (167x154xt mm 3 , being t is the overall vault thickness), set-up with layered stacking sequence of plies oriented along the vault thickness, representing the different materials: the masonry, the mortar of the coating and the embedded reinforcement. Simplified assumption is that the layers are perfectly bonded each other. The Gauss integration rule is used for setting up integration points through the thickness of each layer: in the performed analysis, the number of Gauss points was equal to 12 for masonry layer, 6 for the mortar coating and 1 for the fiber based reinforcement. The model is schematized in Fig. 7: rigid, fixed brick elements were provided in correspondance of the abutments and rigid truss elements served for the application of the horizontal load in correspondance of the experimental loading points. 2D interface elements connected the vaults with the rigid elements at the abutments, so to consider the tensile failure at the spring sections. In particular, the same tensile strength of the bare masonry was considered, since the CRM layer was interrupted at the vaults extremities; the occurrence of possible slippage at the interfaces was neglected in this simplified modelling. Truss elements, crossing the interfaces, were introduced to consider the steel bars used for connection. Nonlinear-static analyses at displacement control were performed (Newton-Rapshon solver). The material parameters are resumed in Table 1; all materials were assumed homogeneous and isotropic. For the masonry layer, the Concrete-Damage Plasticity material model “Cdpm2” (Gassl et al., 2013) was considered, with the parameters set previously in accordance to experimental characterization tests on plain masonry elements, so to account for both crushing and cracking. A unitary thickness was assigned to the reinforcement layer, with an elastic-brittle tensile