## 1 Introduction  
Ground transport networks have steadily developed worldwide, aiming to foster economic growth and development, link regions and communities separated by geography and create new opportunities for people. Technological advances in recent decades have turned into standard engineering practice former challenges, such as building bridges with spans well above 1 km. Nowadays, the engineering challenges in the design of long-span suspension bridges are in the range above 2000 m, while, for cable-stayed bridges, the equivalent mark could be set in span lengths above 1000 m.  
Due to the exceptional flexibility of such long-span structures, safety with regard to aeroelastic effects becomes the dominant design factor, at least from a wind engineering perspective. Focusing on flutter performance, the safe design of ultra-long span bridges certainly benefits from twin-box deck design. Examples of long span suspension bridges constructed adopting a twin-box arrangement are the Xihoumen Bridge in China, with a main span of 1650 m [1], the Yi Sun-Sin Bridge in South Korea, featuring a 1545 m central span [2], or the 1915 Canakkale Bridge in Turkey with a main span of 2023 m, which is the longest in the [3]. It can be noted that all of them, with main spans above 1500 m, must resort to the twin-box arrangement to meet the critical flutter speed requirements. At a fundamental level, the slot between boxes favours a higher flutter critical wind speed, as the gap between boxes is intended to decrease the slopes of lift and moment coefficients, reducing aeroelastic coupling between the torsional and vertical modes [4] causing, in general, a decrease in the \(A_{2}^{*}\) flutter derivative [5]. Research addressing the aeroelastic performance of twin-box cable-supported bridges has mainly focused on parametric variation studies considering a small number of design variables. In [6], a parametric study based on the sensitivity of the flutter derivatives with respect to the gap distance was conducted for the box geometry of the Stonecutters bridge, finding a higher torsional damping ratio for larger gap widths. In a subsequent work [7], the authors studied several configurations with different gap widths and torsion-bending frequency ratios without introducing changes in the box geometry. Another parametric study based on wind tunnel testing is reported in [8], who studied two 20:1 side ratio rectangular cylinders in tandem arrangement, considering different gap distances along with gratings and vertical plates, demonstrating that the \(A_{2}^{*}\) flutter derivative is the one featuring a dependence on the gap length. More recently, additional design variables have been considered in parametric studies dealing with the flutter performance of cable-supported twin-box deck bridges. In [9], two different wind fairing shapes, symmetric and asymmetric, were considered along with several gap widths to investigate torsional divergence and flutter performance. The main conclusion of this study was that _\"the favorable aerodynamic effects of the center slot on bridge decks depend on the aerodynamic shape of the box girders and on the slot widths rather than unconditionally improving the aeroelastic stability\"_. Similarly, in [10], the authors adopted an experimental approach to analyse the effect of several vertical central stabilizers (VCSs) for a twin-box deck considering different gap distances. However, in [11], it is shown how minimal changes in the geometry of the deck, such as introducing a cut in the internal lower corner of the boxes facing the gap, produces a strong non-linear response affecting the aeroelastic torsional damping. The review of the literature addressing the design of twin-box decks based on experimental testing shows the complex relationship between aeroelastic response and the deck shape, remarkably gap distance and box geometry. In addition, the large number of deck shape design variables precludes a thorough analysis based only on wind tunnel testing.