PSI - Issue 84

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

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Fig. 7. Spatial distribution of horizontal and vertical accelerations for Test D with a 45° impact.

By analysing the wave propagation in the structure over time, in the Test D with α=45° (Figure 7), we observe that the initially negative horizontal component in the impact zone is progressively reflected in the lower part of the left pier, due to the constraint. On the other hand, the vertical component, that is initially facing downwards in the impact zone, propagates very quickly towards the left pier and is reflected, until it reaches the keystone of the central arch with an opposite sign, producing the collapse mechanism shown in Figure 6, centre, with the rigid elements projecting upwards. By analysing the dynamic response of the system in the frequency domain, and with specific reference to the vertical acceleration evaluated at control points coinciding with the impact points (as shown in Figure 1), it emerges that the in the Test D with an angle of 45°, the impact exhibits frequency peaks very close to those of vibration modes 1, 5 and 10, which in fact have a modal shape close to the deformation obtained from the impact test.

Fig. 8. Fast Fourier Transform (FFT) analysis results obtained for Test D with a 45° impact varying the control point adopted.

6. Final remarks In this work, we have proposed a specific numerical strategy for assessing the damage caused to a masonry arch bridge by projectiles impacting the upper surface. Using a specific RBSM numerical model implemented in MatLAB, we investigated how the position and angle of impact of affect the dynamic response of the system, the damage caused and the resulting collapse mechanism. The modelling of masonry arch bridges subject to dynamic in-plane actions is an open issue in scientific research, requiring comprehensive, efficient and effective computational tools. However, masonry arch bridges are characterized by complex behavior due to the mechanical characteristics of the constituent materials, the presence of texture-bond phenomena in the masonry composite and the interaction between masonry and infill. In the analysis of such infrastructures, therefore, it is necessary to adopt computationally convenient modelling strategies that are nevertheless capable of taking all these complexity factors into account. To this aim, we proposed an RBSM computational strategy based on the concept of Heuristic Molecules (Casolo, 2021a), adopting the San Marcello Pistoiese Bridge as case study. An RBSM model was implemented in a specific MatLAB code, and several non-linear dynamic analyses were performed by simulating the impact of individual spherical elements with a diameter of 1.50 m, in a time ∆ = 0.01 . The position of the point of impact and the inclination of the load direction was varied by adopting five different positions and two inclinations (α=45° and α=90°), investigating the effects of the angle of incidence. In Test C, a significant difference in the response to ballistic impact was observed when varying the inclination, and in Test D, the impact even activates resonance with the natural vibration modes of the structure and the upward projection of the rigid elements. The results obtained have shown that the numerical model developed is well suited to the analysis of large infrastructures, as it can manage complex structural problems with a very small number of degrees of freedom (in the case in question, the entire structure was discretized into only 1,232 rigid elements). Furthermore, it allows the modelling of local collapse mechanisms (such as those observed on the abutments, lateral arch and keystone of the central arch), global collapse mechanisms (such as those observed in cases of impact on the abutments and ribs of the central arch) and debris projection phenomena, that are difficult to model with FE methods.