PSI - Issue 78

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

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Three distinct backfill modeling strategies were developed to evaluate their influence on the seismic response of the bridge structure and to validate the assumptions adopted in the full-bridge numerical model. Specifically, the backfill was represented as: (i) a single deformable continuum block (model SUB-D); (ii) an assembly of rigid blocks (model SUB-R); and (iii) a Voronoi-tessellated block system (model SUB-V). To ensure consistency across the three approaches, comparable discretization criteria were applied. In model SUB-D, the deformable block was discretized using constant-strain tetrahedral elements with a maximum edge length of 0.2 m (Itasca Consulting Group Inc. 2024). For SUB-R and SUB-V, the rigid block size ranged between 0.2 m and 0.3 m. These dimensions were selected to be approximately half the size of the masonry units, to more accurately reproduce backfill-induced pressures on the masonry components. The resulting models included approximately 2430 blocks and 88,042 sub-contacts in SUB-D, 9218 blocks and 390,682 sub-contacts in SUB-R, and 10,083 blocks and 599,134 sub-contacts in SUB-V. A visual comparison of the three discretization strategies is provided in Fig. 5. To investigate and compare the response of the substructural models, quasi-static analyses were performed. For each model, three simulations were carried out to assess structural stability under in-plan and vertical distortion scenarios. The numerical analyses were conducted using the commercial software 3DEC, which employs a dynamic time-integration scheme based on an explicit finite-difference method to solve the equations of motion. In this study, quasi-static conditions were achieved by applying adaptive global damping to suppress dynamic effects and rapidly reach force equilibrium (Damiani et al. 2023). Lateral displacements were imposed by incrementally applying multi step velocity histories to one of the two supporting piers, along the x-, y-, or z-direction depending on the loading scenario, as illustrated by the red arrows in Fig. 6. The velocity was gradually increased to induce a total displacement of 2.5 cm over 1.0 second. Following each 2.5-cm displacement increment, an equilibration phase was introduced. The opposite pier, shown in grey, was fixed throughout the analysis.

Fig. 6. Imposed velocity directions for the quasi-static simulations: (a) x -direction; (b) y -direction; (c) z -direction.

4.2. Results Fig. 7 shows the damage mechanisms and shear force–displacement responses for all three substructural models (SUB-D, SUB-R, and SUB-V) under quasi-static loading. Each row corresponds to a different modeling strategy, while each column refers to a different loading direction. The top panels display the deformed configurations at near collapse conditions, while the bottom panels show the corresponding base shear versus imposed displacement curves. Note that for SUB-D model, the backfill block was hidden for visualization clarity. Under x -direction loading, all models exhibit a similar collapse mechanism characterized by the formation of two hinges within the arch barrel, leading to a progressive loss of stability. Under z -direction loading, a comparable failure mechanism is observed. In contrast, the y -direction loading scenario results in a different failure mode: diagonal cracking initiates within the arch and backfill, followed by the out-of-plane overturning of the spandrel walls. In this