PSI - Issue 84

Siro Casolo et al. / Procedia Structural Integrity 84 (2026) 1214–1221

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2.2. A numerical strategy for modelling the behaviour of masonry arch bridges subjected to in-plane impacts

In this paper, we propose a specific methodology for assessing the damage caused to a masonry arch bridge by projectiles impacting the road surface. In the study, the position and angle of each projectile are the two factors varied to understand how they affect the dynamic response of the system, and to evaluate the damage caused and the resulting collapse mechanism. For the case study, a specific RBSM code was implemented in MatLAB, and a plan model with appropriate geometry and materials developed. The mechanical behavior of the materials and the masonry-infill contact were modelled using hysteretic stress-strain laws with decay of stiffness and strength. The analysis is divided into three steps. In the first step, modal analysis is performed to extract the frequencies and shapes of the vibration modes. In the second step, gravity loads are applied to the model to evaluate the stress state prior to impact, which affects the system's response to the transient load and, therefore, the collapse mechanism. The third step involves the simulation of the impact of a single spherical element having a diameter of 1.50 m and a mass of 500 kg, falling from an altitude of 3000 m. An impact time of ∆ = 0.01 is assumed. Several scenarios are considered by varying the position of the impact point and the inclination of the load direction, adopting 5 different positions and two different inclinations (α=45° and α=90°) for each position. The results obtained are analyzed in terms of displacements and collapse mechanisms. Attention is then focused on the load case for which the propagation of the shock wave in the structure has produced a substantial change in the collapse mechanism (Test D with α=45°). In this case, the wave propagation in the solid is qualitatively analyzed and the resonance with the modal shapes is investigated using a Fast Fourier Transform analysis. 3. Presentation of the case study: San Marcello Pistoiese Bridge (Italy) The proposed strategy is presented through the application to the case study of the San Marcello Pistoiese bridge, located in a town of the same name in Tuscany, Italy. The geometrical and mechanical characteristics of the bridge are available in the literature (Leprotti et al., 2010; Pelà et al., 2009; Pelà et al., 2013). The bridge was built using different types of masonry and geo-materials (Table 1). The main structure is composed of three arches (Figure 1) and is characterized by the presence of an infill consisting of waste material obtained from the excavation of the foundations. For further information, the reader is addressed to the above-mentioned works.

Fig. 1. Internal and external geometry of San Marcello Pistoiese Bridge, with indication of the position and inclination assumed for the projectile (left) and constraints; HM Model implemented in MatLAB (right).

Table 1. Structural materials identified in the bridge, with indication of the position and label assigned, as shown in Figure 1. Structural material Position Label Stone and lime mortar masonry Piers, spandrel walls, abutments, parapets Masonry 1 Stone and concrete mortar masonry Arch cornice Masonry 2 Bricks and concrete mortar masonry Vaults Masonry 3 Waste soil-like material Infill above vaults and between spandrel walls Infill