PSI - Issue 84

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

877

Building upon the modelling of planar masonry components, the DMEM was later adapted to represent curved masonry structures such as vaults and arches. In this case, the geometry of the macro-elements follows the curvature of the structural form, while the interface laws govern the opening, closing and sliding of joints along the arch or vault. The method proved capable of reproducing classical collapse mechanisms of masonry arches, including four-hinge mechanisms, as well as more complex interaction effects between axial force, bending and shear, Cannizzaro et al. (2018). This development marked a crucial step toward the application of the DMEM to bridge structures, where arches play a central structural role. The most recent stage in the evolution of the DMEM concerns its application to masonry arch bridges, Caddemi et al. (2019), Rapicavoli et al. (2023). In this context, the method has been extended to model the interaction among arches, piers, spandrel walls and fill material, allowing the simulation of both local and global response under various loading conditions. The discrete nature of the DMEM enables the activation of bridge-specific failure mechanisms, such as pier rocking, differential settlements and redistribution of thrust lines within the arches. An overview of the mentioned subsequent steps of the DMEM is reported in Fig. 1.

Fig. 1. Advances in the mechanical scheme adopted in the proposed macro-element approach: (a) plane element, (b) regular three-dimensional element, (c) irregular 3D element, (d) irregular 3D element with interfaces on all faces.

Within this consolidated modelling framework, a first novelty introduced in the present work is represented by the possibility of forcing the calibration of interfaces according to a material with different mechanical properties with respect to those of the connected elements. More precisely, this feature allows defining and calibrating interface properties between two selected groups of macro-elements by assigning them a material behaviour that is independent of, and different from, the constitutive properties of the adjacent groups themselves. This enhancement is particularly relevant when modelling masonry arch bridges, where the interaction between the masonry structure and surrounding materials plays a crucial role in the overall structural response. A notable example is the interface between the masonry arch or spandrel walls and the backfill material. In such cases, the mechanical behaviour of the interface is predominantly governed by frictional contact and limited cohesion, which cannot be accurately represented by adopting the same constitutive laws used for masonry–masonry interactions. By means of the mentioned feature, frictional interfaces can be explicitly defined to regulate the transfer of normal and tangential forces between the backfill and the masonry structure. This allows for a more realistic simulation of load redistribution, confinement effects and relative displacements, especially under nonlinear conditions such as large settlements, pier rotations or progressive degradation of boundary conditions. The introduction of this feature significantly enhances the modelling capabilities of the DMEM, making it a more versatile and robust tool for the analysis of complex masonry bridge systems. 2.2. Scour modelling The modelling of scour is formulated as a staged degradation problem, in which the progressive excavation of material around bridge piers is represented through the incremental removal of foundation restraints. This approach reflects the physical nature of scour and allows the nonlinear structural response to develop consistently as the support conditions evolve. In the pre-processing phase, the geometry of the scour hole is defined parametrically. In the present application, scour is idealised as an inverted rectangular-based pyramid, Hoffmans & Verheij (2017), whose base