PSI - Issue 84

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

876

the effect of settlements at the base of the piers, Rapicavoli et al. (2023). Thanks to its reduced computational demand and clear mechanical interpretation, the DMEM has been successfully applied to seismic assessment, pushover analyses and assessment of retrofitting strategies of masonry arch bridges, showing good agreement with experimental data and refined numerical models. Despite these advances, the explicit modelling of scour within the DMEM framework has not yet been addressed. Existing applications generally account for foundation degradation through simplified assumptions, such as uniform reduction of stiffness or prescribed settlements, which may not adequately capture the progressive nature of scour and its influence on the activation of failure mechanisms. In reality, scour develops gradually, modifying the support conditions of piers in a non-uniform manner and leading to a staged evolution of the structural response. The present study aims to fill this gap by proposing a novel procedure to model scour in masonry arch bridges within the DMEM framework. The key idea is to represent scour as a progressive removal of restraints at the base of bridge piers, according to a predefined geometry of the scour hole and its expected evolution with increasing flood severity, similarly to what was proposed in Tubaldi et al. (2018) within a Finite Element environment. This is achieved by introducing a staged degradation procedure into the DMEM, allowing the structural configuration to be updated incrementally as the erosion process advances. The proposed approach enables the simulation of pier rotation, redistribution of internal forces and degradation of global capacity as a function of the scour depth, while maintaining a reasonable computational cost. Moreover, the staged nature of the analysis makes it possible to investigate intermediate conditions, which are particularly relevant for monitoring and early-warning purposes. The procedure is validated against results available in the literature obtained through more refined numerical techniques, demonstrating its ability to capture the essential features of the structural response under scour conditions. Overall, the proposed methodology represents a practical and reliable tool for the assessment of masonry arch bridges affected by scour, supporting informed decision-making in bridge management and risk mitigation. 2. Scour modelling within the Discrete Macro-Element Method 2.1. Brief recall of the DMEM The Discrete Macro-Element Model (DMEM) is a modelling strategy specifically developed to analyse the nonlinear behaviour of masonry structures through a reduced number of degrees of freedom while preserving a clear mechanical interpretation of the structural response. The method is based on the idealisation of masonry assemblages into an equivalent discrete system, where each macro-element represents a portion of masonry and its dominant deformation and failure mechanisms. This approach allows capturing the inherently nonlinear and heterogeneous behaviour of masonry, governed by low tensile strength, limited shear capacity and frictional sliding, with a computational effort significantly lower than that required by refined continuum models. The DMEM was originally conceived for the in-plane analysis of masonry walls subjected to static loads. In its initial formulation, a wall is discretised into macro-elements connected by nonlinear interfaces that govern axial, sliding and rotational interactions. Each macro-element is characterised by an in-plane shear deformability governed by a nonlinear diagonal link. The activation of typical in-plane failure mechanisms, such as rocking, diagonal cracking, sliding, is captured through suitably calibrated constitutive laws at the interfaces. This formulation proved effective in reproducing the global force–displacement response and collapse mechanisms of masonry walls under monotonic and cyclic loading, providing a reliable alternative to more computationally demanding finite element approaches, Caliò et al. (2012). A subsequent and significant evolution of the DMEM framework addressed the modelling of the out-of-plane response of masonry walls. Out-of-plane failure mechanisms are particularly relevant for existing masonry structures, as they are often governed by local instabilities and overturning phenomena. The macro-element formulation was extended to account for rocking modes perpendicular to the wall plane, enabling the simulation of wall overturning, interaction between orthogonal walls, and the stabilising role of boundary conditions and horizontal diaphragms. This extension, which required the introduction of three additional out-of-plane degrees of each element (that is a total amount of seven degrees of freedom per element), further demonstrated the flexibility of the DMEM in representing different structural behaviours within a unified modelling philosophy.