PSI - Issue 84

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

956

Fig. 3. (a) Impact force and displacement , (b) deformed shapes at different times . The results presented above, i.e. the displacement concentration around the impact location, allow to justify the use of an equivalent wall model to simulate debris impacts on bridge piers. This wall is extracted from the pier side (see Fig. 2-c, d). The deformed configuration of Fig. 3-b, particularly at 2 = 0.005 , allows us to estimate such an equivalent wall as a plate having a width equal to the entire side length and a height equal to twice the impact location. The equivalent wall thickness is taken as the pier cross-section thickness. Results compare the entire model and the two equivalent wall models, i.e. with fully fixed and mixed fixed-supported boundary conditions (see Fig. 2-c). A good agreement is found in terms of F-t diagrams (Fig. 4-a), with the equivalent models correctly replicating the rigid impact behaviour of the entire model (see Fig. 3-a and related discussion). It is worth noting that the F-t diagrams of the equivalent wall models differ slightly from that of the entire model (difference ≅ 5%). These differences are due to the effects of different boundary conditions, which modify the dynamic response of the structure (De Iasio et al., 2025b). In contrast, the first peak displacement is accurately captured by the fully fixed equivalent wall model (+1%), whereas the mixed fixed-supported equivalent wall model significantly overestimates it (+21.2%). Note that the displacement time history following the first peak differs considerably between the entire and equivalent wall models. This is likely due to the different dynamic behaviour, including different damping, of the two model typologies. Whilst this is a current limitation of such equivalent models, the accurate estimation of the first displacement peak suggests that the equivalent wall model is a suitable alternative to a model representing the entire pier, provided that appropriate boundary conditions are implemented in the equivalent structure. Such appropriate boundary conditions, here identified as fully fixed based on Fig. 3-a, shall be generalised for different pier sizes and impact locations with further numerical simulations. The efforts to provide appropriate equivalent wall models to study these impact scenarios are justified by the significant computational savings they achieve. Indeed, the simulations carried out in this study