PSI - Issue 78

Alessia Furiosi et al. / Procedia Structural Integrity 78 (2026) 753–760

756

Based on the case study presented in Section 2, a substructural numerical model was developed. As shown in Fig. 3, the central portion of the bridge, located between the two piers, was isolated. Although the piers were not explicitly modeled, their influence was accounted for through the application of appropriate boundary conditions. Structural components, such as arches, backing and spandrel walls, were discretized as assemblies of rigid blocks, each with six degrees of freedom. This substructural approach enabled the use of block elements consistent with the actual masonry unit dimensions (i.e., 78 × 60 × 50 cm), while ensuring computational efficiency. The interfaces between adjacent blocks, either rigid or deformable, were represented by zero-thickness interfaces, characterized by normal and shear stiffness parameters ( k n , k s ), as shown in Fig. 4. The shear response was governed by a Mohr-Coulomb slip criterion, defined by cohesion ( c ) and friction angle ( ϕ ), while the normal response was regulated by a finite tensile strength ( f t ) with an associated tension cut-off. Compressive failure was not considered in the modeling framework.

Fig. 4. Distinct element modeling strategy for masonry and backfill material (Furiosi et al. 2025).

The backfill material was simulated using three different modeling strategies: as a deformable continuum discretized into tetrahedral finite elements and described by a Mohr-Coulomb plasticity model with tension cut-off (Pulatsu et al. 2019, Furiosi et al. 2025); as an assembly of rectangular rigid blocks; and as an assembly of Voronoi blocks. For both rigid block-based approaches, the behavior of contact interfaces was governed by a Mohr-Coulomb constitutive model (Fig. 4). A detailed description of these alternative modeling options is provided in Section 4.1 Regarding the boundary conditions, four rigid blocks, highlighted in red in Fig. 3, were employed. Specifically, two vertical blocks were placed along the lateral edges of the substructural model, while two additional blocks, were introduced at the base of the modeled bridge segment to represent the supporting piers. In-situ core drillings were conducted to identify the type of masonry units and reconstruct the stratigraphy of the investigated structure. However, no material characterization tests were performed for either the masonry or the backfill material. Parameters such as density ( ρ ), elastic modulus ( E ), shear modulus ( G ), tensile strength ( f t ), cohesion (c), and friction angle ( ϕ ), were estimated in accordance with the values suggested by the Italian building code (MIT 2018) for existing, regular soft-stone masonry. The mechanical properties of the backfill material were assigned based on the recommendations of recent research studies on similar structures (Pulatsu et al. 2019). The assumed properties for both masonry and backfill are summarized in Table 1.

Table 1. Mechanical properties of masonry and backfill material (Pulatsu et al. 2019, MIT 2018, Furiosi et al. 2025)

ρ [kg/m 3 ]

E [MPa]

G [MPa]

f t [MPa]

c [MPa]

φ [°]

Material Masonry Backfill

1600 1600

1692

540

0.10

0.15 0.02

30 40

100

42

0

The use of rigid blocks required the calculation of equivalent joint stiffness values. Based on the assumed elastic and shear moduli ( E , G ), the normal and shear stiffnesses of the interfaces were computed using Equation 1, where d c is the centroid-to-centroid distance between adjacent blocks. For contacts between masonry units, an average value of d c was adopted. For the backfill material, the same equation was applied in the models built using either Voronoi or rectangular rigid blocks. In the model where the backfill was represented as a single deformable block, the mechanical properties were directly assigned to the block itself, without the need to compute contact stiffnesses.