PSI - Issue 84

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

878

centroid coincides with a prescribed point s x representing the initiation location of scour. The scour depth is discretised into a sequence of constant increments and, at a generic step k , is represented by the pyramid height k s y defined as follows

k y k h = 

0,1,...,

k

N

(1)

=

s

s

s

where s h  is the user-defined scour step and N s is the total number of stages of the scour evolution. For each increment k s y , the subset of restraints that become fully exposed is identified. These restraints are grouped and associated uniquely with the corresponding scour stage k . In Fig. 2 this procedure is depicted for the case of a parallelepiped foundation with regular mesh of the restraints. Each rectangular patch corresponds to a restraint; the colored patches correspond to restraints completely uncovered at the current stage of the scour progression, whose hole volume is represented with the light blue inverted pyramid. Each color of the patches corresponds to a step of the scour progression, and the relevant restraints are conveniently grouped to be simultaneously removed at the corresponding step of the analysis.

Fig. 2. Scour progression modelling.

The structural response is computed through a staged degradation procedure for each th k − scour increment, which rules the sequence of restraint removals. Step 0 corresponds to the application of the gravity loads, and the structure is assumed to be intact, with all restraints active. The gravitational loads are applied, and equilibrium is established. At each step, the restraints belonging to the corresponding scour depth are removed by deactivating the corresponding interface links. This operation modifies the system stiffness and generates an unbalanced residual force vector, which represents the forces previously carried by the removed restraints. The residual forces are automatically redistributed over the remaining active structure, and the equilibrium problem is solved again to obtain the updated displacement vector. This redistribution may activate additional nonlinear mechanisms, such as interface opening, sliding or pier rotation, which are fully captured by the DMEM formulation. 3. Applications This section presents an application concerning a three-span masonry arch bridge previously investigated under scour conditions using a Finite Element approach by Scozzese et al. (2023). Although the bridge geometry does not refer to a specific real structure, it is representative of a typical European construction typology. The three spans are identical, each with a length of 16.0 m, and the bridge has an overall width of 6.82 m. The barrel vaults have a thickness and a radius equal to 0.95 m and 11.58 m, respectively, resulting in a rise of 3.2 m. The spandrel walls have a thickness