PSI - Issue 84

196 Alice Vitaletti et al. / Procedia Structural Integrity 84 (2026) 191–198 containing the two hypothesised non-zero components of the actual displacement ( , ) can be estimated by inverting the 2x2 submatrix of : ̂ = − . (2) 4. Results The FEM-computed displacement field shows that the largest displacements occur in the downslope portion of the unstable area, where total displacements | | reach peak values of about 46 mm (Fig. 4). Additional deformation is also observed in the upper slope, where pore pressure effects result in displacements of up to 20 mm. Overall, the numerical results confirmed a rotational sliding mechanism of the landslide, with deformations affecting the bridge foundations. Although a simplified model of the superstructure was adopted, displacements were extracted at selected control points located at the base (pier-foundation node) and the top (pier-deck node) of Piers 1, 2 and 3 to quantify the effects of landslide-induced forces on the bridge. The recorded horizontal components are summarised in Table 2. The results indicate that Piers 1 and 2, located within the unstable area, undergo notable downslope displacements at their base due to the force exerted by the landslide. By contrast, Pier 3, situated outside the landslide-affected slope, exhibits smaller displacements in the opposite direction, attributable to the restraining effect of the structure. Under compression, the deck behaves as a rigid element and slightly counteracts the forward movement of the heads of Piers 1 and 2. Given the simplified modelling assumptions for the deck, this interaction generates a reaction effect that produces opposite displacements in the piers located on the opposite side of the slope.

Fig. 4. Numerical model showing the total displacements |u| resulting from the FEM simulation.

Table 2. Horizontal displacements at selected control points. Displacement Top Pier 1 Base Pier 1 Top Pier 2 Base Pier 2 Top Pier 3 Base Pier 3 [mm] -5.10 -3.80 -3.37 -2.94 -1.07 0.10 [mm] 2.49 4.97 1.90 5.65 1.86 -0.85 In parallel with the numerical simulations, time series for the vertical ( ) and transverse ( ) components of the displacement were derived for the synthetic PS within the study area following the InSAR data post-processing. The vertical component time series show that the synthetic PS in cell 3, located along the bridge, display a clear seasonal pattern, characterised by downward movement in winter and upward movement in summer, consistent with temperature-related structural deformation. By contrast, the synthetic PS within the vegetated landslide area (cells 6, 7, 10, 11 and 14) do not exhibit a seasonal displacement pattern. Instead, they show a generally stable trend with slight progressive lowering, in agreement with the expected vertical component of the landslide movement (Fig. 5a). The transverse displacement component exhibits greater temporal variability, especially for synthetic PS located within vegetated areas. Several anomalous values are observed, likely associated with temporary variations in radar reflectivity caused by seasonal vegetation changes and wind effects, which reduce signal coherence and potentially lead to outliers unrelated to actual ground deformation. This behaviour is absent in cell 3, where PS lie directly on the