PSI - Issue 62

Davide Rapicavoli et al. / Procedia Structural Integrity 62 (2024) 476–483 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

480

5

constitutive law in compression and exponential softening in traction; the shear-sliding is ruled by a Mohr-Coulomb criterion, whereas the shear diagonal behaviour is assumed elastic for the arches and elastic-plastic with Mohr Coulomb yielding domain for the spandrels. The fill is considered as elastic perfectly-plastic with almost zero tensile strength and membrane behaviour lumped in the interfaces; an elastic-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. The internal reinforced arch has been modelled by considering two layers of macro-elements, geometrically consistent, whose material parameters are reported in Table 1, assuming an elastic-plastic behaviour for the steel, and a parabolic constitutive law in compression with exponential softening in traction for the concrete. The presence of the rebars has been accounted for by means of conveniently calibrated additional links in the interfaces (Cannizzaro et al. 2024).

(b)

(a)

Fig. 6. (a) Exploded view of the bridge in the strengthened configuration. (b) Adopted locomotive ADe 21-25 associated to the operational loads.

Table 1. Mechanical parameters.

An example of a column heading

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 0.6

-

-

22

Spandrel walls

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 fracture energy; c = sliding cohesion;  c = sliding friction ratio;   = diagonal shear strength;   = diagonal shear friction ratio; w = self weight. The piers are founded on elastic soil foundation whose normal flexibility k n has been assumed equal to 12.75 kg/cm 3 corresponding to a sandy clay soil. The operational load is considered according to the actual locomotive model