PSI - Issue 84

Francesco Cannizzaro et al. / Procedia Structural Integrity 84 (2026) 874–881

875

Keywords: Scour; Masonry Arch Bridges; Discrete Macro-Element Model; Piers; Settlements; Modal analysis

1. Introduction Masonry arch bridges represent a significant portion of existing road and railway infrastructures, particularly in Europe, where many of these structures are still in service after more than a century. Despite their apparent robustness and redundancy, masonry arch bridges are vulnerable to a number of deterioration mechanisms, among which scour at foundations was recognized as one of the most critical and insidious causes of structural damage and collapse by Melville and Coleman (2000). Scour is induced by the erosive action of flowing water during flood events, which progressively removes soil material around the foundations of piers and abutments, leading to a reduction of support conditions and to a modification of the soil–structure interaction. Historical evidence and post-event inspections have repeatedly shown that scour-related failures often occur suddenly and without clear warning signs, since the erosion process typically develops below the water level and remains hidden until severe damage has already occurred, Richardson and Davis (2001). The consequences of scour include excessive settlements, rotation of piers, redistribution of internal forces within the arch barrels, and a substantial loss of global load-carrying capacity, potentially triggering progressive collapse mechanisms, Zhang et al. (2023). For these reasons, the assessment of scour effects is now considered a key aspect in bridge safety evaluation and asset management strategies. Over the last decades, extensive research has been devoted to the hydraulic aspects of scour, leading to empirical and semi-empirical formulations to predict the depth and shape of scour holes, Hoffmans & Verheij (2017). However, the translation of these hydraulic predictions into reliable structural assessments remains a challenging task, especially for masonry arch bridges, whose behaviour is strongly nonlinear and governed by the limited tensile strength of masonry and by the activation of local failure mechanisms. From a structural modelling perspective, limited investigations have been conducted to experimentally investigate the response of masonry arch bridges subjected to scour in controlled laboratory conditions, Invernizzi et al. (2011). On the other hand, several numerical approaches have been proposed to simulate such a phenomenon. Finite element models, often coupled with advanced constitutive laws and contact formulations, have been employed to simulate the progressive loss of support and the resulting stress redistribution in the masonry. Planar numerical models were employed in Zampieri et al. (2017) However, the complex interaction of the masonry pier with the scour hole, often requires the implementation of three-dimensional models. Within this context and with regard to refined approaches, both meso- and macro-scale strategies were applied, respectively in Tubaldi et al. (2018) and Scozzese et al. (2019). While these models can provide highly detailed insights into local damage patterns, they are usually associated with a high computational cost and require a significant modelling effort, which limits their applicability in routine assessment and large-scale network analyses. Discrete approaches, such as distinct element methods and block-based models, have also been adopted to explicitly represent the discontinuous nature of masonry and the opening and sliding of joints under altered boundary conditions, Tòth et al. (2009), Sarhosis et al. (2020). Although particularly effective in capturing collapse mechanisms, these approaches similarly suffer from computational complexity and may be impractical for rapid evaluations or parametric studies required by infrastructure managers. Limit analysis can offer a fast tool for preliminary evaluation of the load capacity of scoured masonry arch bridges, George & Menon (2022). However, such an approach does not provide detailed information on the evolution of the damage and on the residual displacement capacity of the structure. In this context, simplified yet mechanically sound modelling strategies are increasingly sought to bridge the gap between accuracy and efficiency. Among them, macro-element approaches have proven to be particularly attractive for the analysis of masonry structures. These methods idealize masonry assemblages through equivalent mechanical elements able to reproduce the dominant deformation and failure modes with a limited number of degrees of freedom. The Discrete Macro-Element Model (DMEM), Caddemi et al. (2017), Cannizzaro et al. (2018), belongs to this class of approaches and was originally developed for the nonlinear in-plane analysis of masonry walls under static and seismic actions, Caliò et al. (2012). Subsequent developments of the DMEM framework have extended its applicability to masonry arches and arch bridges, enabling the interaction between piers, arches and spandrel walls, Caddemi et al. (2019), and to account for