PSI - Issue 84

Alessandro De Iasio et al. / Procedia Structural Integrity 84 (2026) 952–958

955

Fig. 2. (a) Pier model, (b) focus on the impact zone, (c-d) equivalent wall models with different boundary conditions.

Two equivalent wall models are extracted from the main structure by considering the pier portion impacted by the debris with fully fixed (Fig. 2-c) and mixed fixed-supported (Fig. 2-d) boundary conditions. The bottom side is always considered fixed, consistent with the pier fixed base. The top and side sides are assumed either fixed or supported to investigate the effects of the degree of reattainment given by the rest of the pier structure. The width of this wall is the same as the pier side, while the height is defined based on the impact simulation outputs on the entire pier. The entire and equivalent wall models are compared in terms of impact force and structural displacements . The value of is measured as the contact force between debris and structure. The value of is measured as the horizontal displacement of the structure at the impact point along the impact direction. 3. Results and discussions The time histories of and for the impact simulation on the entire pier are presented in Fig. 3-a. The F-t diagram is rectangular, with average impact force at the plateau equal to ≅ 743 and impact duration equal to ≅ 0.0051 (Fig. 3-a). These values convey that a rigid impact occurs, i.e. the structure does not displace significantly during the impact due to its high stiffness and mass (Paczkowski et al., 2012; De Iasio et al., 2024). In rigid impacts, the F-t diagram is rectangular, with plateau force ̅ =v √ and impact duration =2√ / . In the studied scenario, ̅ = 739.03 and = 0.0054 , which align with the simulation outputs and demonstrate that a rigid impact occurs. Moreover, the impact causes a maximum displacement = 1.88 , which quickly vanishes after the impact (Fig. 3-a). Finally, global displacement analyses of total displacements, i.e. the absolute value | | , highlight that the pier deformations are initially concentrated at the impact location (Fig. 3-b, = 0 − 0.005 ). The rest of the structure, which displaces in different phases as stress waves spread at finite speed ≅ √ / (De Iasio et al., 2025b), is affected by the impact, but displacements remain limited, i.e. up to two orders of magnitude lower than maximum displacement at the impact location (Fig. 3-b, = 0.005 − 0.01 ). This is expected given the significantly bigger dimensions of the pier compared to the debris.