PSI - Issue 84

Lorenzo Brezzi et al. / Procedia Structural Integrity 84 (2026) 1159–1166

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through a Monte Carlo approach. For each initiation scenario, 200 simulations were performed by randomly sampling the model parameters from prescribed statistical distributions defined in terms of mean values and standard deviations (Table 1). This strategy allows the variability of runout patterns and dynamic quantities to be systematically explored, reduces user-dependence and provides a robust basis for the assessment of potential interaction scenarios.

Fig. 2. Definition of the triggering areas adopted for the SPH simulations, for the two scenarios considered.

Table 1. Chosen mean and standard deviation values of friction and turbulence for simulations. Parameter Mean value Standard deviation Friction coefficient  (−) 0.3 0.1 Turbulence coefficient  (ms -2 ) 350 120

The numerical outputs of the SPH simulations were subsequently imported and processed in MATLAB to extract landslide thicknesses relative to the digital terrain model, velocity vector components and resultant velocities. These quantities were evaluated both at the final simulated time step and at the instant of maximum interaction with the viaduct. The instant of maximum interaction was identified, for each simulation, as the time step at which the product of flow thickness and resultant velocity reached its maximum at points located in the vicinity of the viaduct, considering the full temporal evolution of the runout process. This criterion provides an objective basis for identifying the most critical conditions for landslide–infrastructure interaction across different simulations. For each scenario, median values and standard deviations of flow thickness and velocity were then computed at both the final time step and the instant of maximum interaction, based on the ensemble of Monte Carlo simulations. This statistical description allows the variability associated with parametric uncertainty to be explicitly accounted for in the subsequent analysis. Finally, the potential impact force acting on the structure was estimated by combining flow thickness and velocity through a simplified hydrodynamic approach (Vagnon et al., 2016), according to: = 1 2 ℎ + 2 (1) where ρ is the density of the sliding mass, h df and v df are the flow thickness and resultant velocity, respectively, and A is the impact area. The impact area was defined by assuming a collision between the landslide material and the viaduct piers, and was approximated as one third of a cylindrical lateral surface, with a base diameter equal to that of the actual piles (3.9 m) and a height corresponding to the flow thickness at the point of interaction. The main outputs of the simulations include time-dependent spatial distributions of flow thickness and velocity, which represent physically meaningful descriptors of landslide dynamics and form the basis for subsequent estimates of potential impact forces acting on the viaduct. Figure 3 illustrates the temporal evolution of the runout process for a representative simulation performed using the mean values of the assigned rheological parameters, highlighting the development of flow thickness over time.