PSI - Issue 62

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Mattia Zizi et al. / Procedia Structural Integrity 62 (2024) 430–437 M. Zizi et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 6. Visualization of the first four mode shapes obtained by FDD in axonometric and plan view: (a) at 1.66 Hz, (b) at 2.54 Hz, (c) at 3.52 Hz, and (d) at 5.47 Hz. 4. Numerical analysis 4.1. The adopted numerical model A numerical model was realized in Abaqus software (Dassault Systèmes Simulia Corp., 2023). The model did not include the wing walls. To simulate their presence, total restraints in the longitudinal and transversal directions were introduced in the external surfaces of the abutments, while the vertical displacements were left free. Fully-fixed constrained conditions were instead assumed at the base of the piers. The model was assembled with 2 nd order 10 node tetrahedral elements (C3D10), whit an average mesh size of 0.30 m. The model consisted of about one million of computational elements. Two different materials were preliminary considered: regular tuff masonry and backfill material. For masonry material, a modulus of elasticity E=1600 MPa and a density γ =1600kg/m 3 were defined, according to the range proposed for regular tuff masonry in the Italian code (Ministero delle Infrastrutture e dei Trasporti, 2019). As for backfill material, E=500 MPa and γ =1500kg/m 3 were tentatively fixed. Neither additional masses, nor stiffness were