PSI - Issue 62

Giovanna Pappalardo et al. / Procedia Structural Integrity 62 (2024) 460–467 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

463

4

T he evaluation of the landslide body’s vo lume was made possible thanks to the digital model of the landslide. Based on in-situ geomorphological surveying, a sliding surface was hypothesized and inserted into the digital landslide model, yielding a volume of about 13,121 m³ for an area of approximately 3,647 m² (Figure 3b). 3.2. The interaction between the landslide and the structure of the bridge To investigate the non-linear response of the bridge subjected to the thrust of a landslide, a numerical model of the bridge was implemented in the software HiStrA Bridge (Caliò et al. 2015) based on the Discrete Macro-Element Method (DMEM) (Caddemi et al., 2017, Caddemi et al. 2019a), a methodology that has been applied to study the nonlinear behaviour of masonry arch bridges (Caddemi et al., 2019b). The adopted model is based on shear deformable macro-element interacting with other elements through nonlinear zero-thickness spatial interfaces embedding the membrane element deformability. Each element is governed by seven degrees of freedom only, namely six associated with the rigid body motion plus an additional degree of freedom associated with the shear deformability of the element with respect to plane of the element. The four arches of the bridge have 7.30 m spans length, with average rise of 3.65 m. The heights of the masonry piers are Hi = {5.97; 6.08; 6.20} m from the base foundation. A comprehensive description of the bridge in its original configuration, based on the geometrical survey and on the analysis of the available documentation, can be found in (Rapicavoli et al. 2023). Based on the geometry of the bridge and of the observed masonry typologies, in the same study a numerical model was implemented and the effects of vertical settlements in the central pier were investigated to interpret the severe crack pattern observed in the eighties at the intrados of the arches. Due to the observed damage, the bridge was consequently subjected to a strengthening intervention consisting in the enlargement of the foundation and in a thick concrete layer at the intrados of the arches with corrugated steel formworks. Here both configurations (the ‘unstrengthened’ and the ‘strengthened’ ones) were analyzed. In Figure 4a, an exploded view of the bridge in the strengthened configuration shows the composition of the bridge in terms of materials, depicted with different colours, the backfill, the zero-thickness friction interfaces connecting the fill to the other components of the bridge, the stone volcanic arches and spandrel walls, the concrete layer and the steel formwork. The corresponding mechanical properties are summarized in Table 1. The arches and spandrel walls are characterized for the flexural behaviour by a parabolic constitutive law in compression and exponential softening in traction; the shear-diagonal behaviour is assumed elastic while the shear sliding is ruled by a Mohr-Coulomb criteria. The fill is considered as elasto-plastic with almost zero tensile strength and membrane behaviour lumped in the interfaces; an elasto-plastic constitutive law, associated with a Turnsek Cacovic yielding criteria, is adopted for the generalized shear diagonal behaviour, at the macro-scale. The interaction of the fill with the arches and the spandrel walls are ruled by ad hoc interfaces with zero cohesion. For the concrete layer, only for the flexural behaviour a nonlinear constitutive law is considered, which is assumed analogous to that adopted for arches and spandrel walls. Finally, the steel is assumed with an elastic perfectly plastic behaviour.

Table 1. Mechanical parameters. E ( MPa )

G ( MPa )

f c ( MPa )

f ct ( MPa )

G fc ( N/mm )

G ft ( N/mm )

c ( MPa )

w (kN/m 3 )

 c (-)

  ( MPa )

   -  

Arches

1800 1800

600 600 115 115

3.0 2.0 0.5 1.0

0.02 0.05 0.01 0.01

4.0 1.5

0.001 0.001

0.01 0.01

0.6 -

-

22

Spandrel walls

0.6 0.3

0.4 22

Fill

300 300

∞ ∞

∞ ∞

-

-

0.0005

- - - - -

18

Friction interfaces

0.0

0.6 -

-

Concrete Steel bars

9798

4083

11.76 273.9 235.0

1.057 273.9 235.0

19.6

0.028

- - -

- - -

- - -

25

206000 206000

85833 85833

∞ ∞

∞ ∞

78.5

Corrugated Steel 78.5 where E = normal elastic modulus; G = shear elastic modulus; f c = compressive strength; f ct = tensile strength; G fc = compressive fracture energy; G ft = tensile fract. energy; c = sliding cohesion;  c  sliding frict. ratio;   = diagonal shear strength;   = diagonal shear frict. ratio; w = self-weight.