PSI - Issue 78

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

719

bridges, consisting of a stiff deck connected to the bottom arch through slender columns , and “Non -Maillart- type” bridges, featuring more massive arches. These structures usually exhibit critical vulnerabilities, due to insufficient ductility, non-uniform pier s’ height, and shear or flexural failure mechanisms [Modena et al., 2015; Crisci et al., 2022]. In recent years, various retrofitting strategies have been proposed. One involves the enhancement of piers’ flexural and shear capacity, as well as their ductility, by applying Fiber-Reinforced Polymer (FRP) strips [Pavese et al., 2004] or jacketing with Ultrahigh-Performance Fibre-Reinforced Concrete (UHPFRC) [Reggia et al., 2020]. Another consists of decoupling the deck motion from the piers using seismic isolators [Lomiento et al., 2024], e.g., Rubber Bearings or Friction Pendulum Isolators, in order to mitigate seismic forces [Guidi et al., 2024]. A further approach integrates viscous or hysteretic dampers at abutments to limit the longitudinal displacements of the deck and reduce flexural demand on piers [Wang et al., 2025]. An alternative to previous strategies is provided by Tuned Mass Dampers (TMDs), introduced in the early 20th century [Frahm, 1909] and consisting of a mass connected to the main structure via an elastic spring and a damping device. During the dynamic excitation, the TMD counterphase-motion effectively reduces the vibrations of the main structure. TMDs were initially used to reduce wind-induced vibrations in tall buildings such as the Toronto’s CN Tower, the John Hancock Building in Boston, and Taipei 101 in Taiwan [Poon et al, 2004]. In bridge engineering, they have been recently applied to mitigate vibrations in lightweight steel pedestrian bridges, like London’s Millennium Bridge [Dallard et al., 2001]. The TMD mass ratio ( ), defined as the ratio between the damper mass ( ) and the modal mass ( ) of the vibration mode to be mitigated, usually ranges between 1% and 10% [Caetano et al., 2007]. For heavy r.c. bridges, low-mass TMDs ( = 0.8 ÷ 1.2% ) have been employed to control the first three vertical bending modes of the 2500 m long Volgograd Bridge in Russia [Weber et al., 2013]. On the contrary, heavier devices ( =7.3% ) were used to reduce lateral vibrations in the pedestrian bridge over the Mondego River in Coimbra, Portugal [Caetano et al., 2007]. Although the control of transverse seismic effects in r.c. arch bridges represents a key concern [Khan et al., 2014], no documented applications of low-mass ( <2% ) TMDs, specifically designed for this purpose, were found by the authors. Nevertheless, profiting of their relatively low weight, these devices may be particular suitable. Within this framework, this study investigates the seismic performance and suggests a (minimally invasive) retrofit intervention of a (“Non -Maillart- type”) r.c. arch bridge designed, in the late 50s, by the internationally renowned Eng. Riccardo Morandi. The solution involves the use of low-mass TMDs ( μ =1.9%) to mitigate the transversal inertia forces at deck level. A parametric non- linear TMDs’ tuning is carried out taking into account of all structural details and defects, such as the presence of half-joints, the rebars ’ corrosion, and the poor shear capacity of short columns at arch mid-span. Once identified the optimal TMDs ’ design parameters , the robustness of this solution is ascertained, by means of non-linear time history (NLTH) analyses, against different scenarios in terms of: (i) level of rebars’ corrosion; (ii) kind of seismic input, i.e., uni-directional (1D) vs. three-directional (3D) ground motion. 2. Case study: Morandi’s bridge in Valvestino The case study bridge (see Fig. 1-a) is a (“Non -Maillart- type”) r.c. arch bridge overpassing the Rio Droanello, a stream supplying the Valvestino lake in Northern Italy. The bridge, designed by the renowned Eng. Riccardo Morandi in the late 1950s, was entirely built with cast-in-place reinforced concrete. The deck is 127.7 m long and 8.6 m wide and is divided into four statically indeterminate segments by a central thermal joint and two lateral half-joints (i.e., deck discontinuities allowing thermal expansions while transferring vertical loads). The two central segments provide four identical spans of about 10 m, while the lateral ones (19.4 m o n the Valvestino side, 24.7 m towards Gargnano) feature two and three variable spans, respectively. The deck consists of three girders with cross- sections ranging from 25×100 cm at mid - span to 70×100 cm at piers’ supports, plus a collaborating slab. The 90 m span arch, with 21 m rise, has a tapered box - section reducing from 10×2.2 m at supports to 7×1.2 m at mid -span. A total of 13 triads (6 on Gargnano side and 7 towards Valvestino - see Fig. 1-a) of tapered piers support the deck. Columns near the abutments feature a cross-section 90 x 80 cm that gradually decreases to 40 x 40 cm for elements located at mid-span. The complete set of construction details are reported in [Gandelli et al., 2025] and were sourced from original technical drawings held in Brescia provincial archive and in Morandi’s family one in Rome (Italy). These were completed by means of a field inspection that revealed several structural issues and functional defects.