PSI - Issue 78

Samuele Faini et al. / Procedia Structural Integrity 78 (2026) 718–725

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, = , ∙ −(0.0204983∙ [ % ] ) =0.24 (3) being: (i) , = 322.3 , , = 464.1 and , =0.29 the average values of yielding stress, ultimate stress and ultimate strain of uncorroded steel “Aq42” [Verderame et al., 2011]; (ii) [ % ] =10% . The hardening parameter of the “Menegotto - Pinto” model was defined as = ( , − , ) ( , − , ) ⁄ ( , , ⁄ )=0.0028 ⁄ ; being: (i) , =( , ⁄ )=0.0014 the yield strain; (ii) = 200 the elastic modulus. Regarding the non-linear behaviour of concrete, considering the wide stirrup spacing (Φ8 / 12.5 cm), the more conservative “unconfined Mander” model [Chang & Mander, 1994] was enrolled. In order to obtain modal frequencies identical to those estimated processing ambient vibrations records, the elastic modulus of concrete was slightly decreased to = 35770 . The compressive strength was set to that measured from pier s’ specimens (i.e., , = 60.1 ). Due to the lack of experimental data, the peak and ultimate strain of concrete C60/75 [CSLP, 2018], the most similar among modern mixtures, were assumed: 2 =0.22% and =0.29%, respectively. To account for possible shear failures , “elasto - fragile” links [Midas -Support] were placed at column end-nodes. The shear strength, calculated as the maximum obtained from provisions of § 4.1.2.3.5.2 and § 4.1.2.3.5.1 of [CSLP, 2018], ranges from 190 kN, of short mid-span columns, to 612 kN, of taller lateral ones. The frictional response of the half- joints and abutments’ seats was modelled through non -linear link elements [Midas-Support] implemented along both horizontal directions. These links exhibit an elastic – perfectly plastic behaviour with an average yielding (or sliding) force estimated according to EC2-1 (§ 6.2.5) [CEN, 2004]: = ∙ ( ∙ + ∙ ) = 143 (4) being: (i) = (250 ∙ 150) = 37500 2 the beam-support contact area; (ii) =0.35 and =0.60 the adopted intefrace properties (concrete surface without finishing processing after casting); (iii) =2.12 ∙ [1 − ( ⁄10)] = 4.1 the average tensile stregth of the concrete (see EC2-1, § 3.1.6); = ⁄ = 4.0 the average contact pressure ( = 148.8 the average vertical reaction force at supports).

Fig. 2. Set of nonlinear modelling strategies adopted in NLTHs on the “as - built” bridge configuration.

Horizontal and vertical design spectra at the SLV limit state were defined according to the provisions of the Italian Building Code [CSLP, 2018] for: (i) bridge location (lat. 45.69, long. 10.66); (ii) nominal life VN = 100 years; (iii) class of use CU = IV; (iv) foundation soil type A; (v) topographic category T4. This resulted in a horizontal peak ground acceleration (PGA) equal to 0.36g and in a vertical one of 0.25g. Due to the lack of suitable three-components ground-motion records within both the Italian and European databases [ESM, 2025], a single NLTH analysis was performed using earthquake records processed by means of SeismoMatch ® v.2024 [SeismoSoft] in order to fulfil the spectral matching criterion. In particular, Kobe and Northridge records were used in the two horizontal directions (see Fig. 3-a) while Landers in the vertical one. The NLTH analysis allowed to predict this sequence of events: (1) at t = 0.40 s, longitudinal sliding motions starts between abutments and deck; (2) at t = 1.05 s, they are triggered also at half joints; (3) at t = 1.65 s, frictional hinges are fully engaged without support loss or girder pounding; (4) at t = 2.95 s (Fig. 3-b), the collapse occurs due to shear failure of short mid-span spandrel columns; the associated peak lateral displacement is about 8 mm (Fig. 3-c). This brittle failure limited the piers ductility as witnessed by the fact that longitudinal reinforcements remained in their elastic range and peak concrete strains below the ultimate threshold.