PSI - Issue 78

Marina Serpe et al. / Procedia Structural Integrity 78 (2026) 1000–1007

1004

static conditions , with steps of 10 mm up to a maximum of 30 mm and a maximum numerical increment size of 0.1. Pushover analyses were conducted using the Riks method. The seismic action was simulated by applying force controlled horizontal loads , proportional to the wall's mass of the façade. To simulate the presence of a rigid floor slab , equal displacement constraints were imposed at the floor edges. Geometric non linearity is considered during the entire analysis.

a)

b)

f t

f c

E

E

0.2f c

0.30f t

ε tel

ε cel

0.001

ε cu = 3 ε cel

Fig. 3 Compression (a) and tension (b) stress–strain relationships adopted for the material model.

Table 1 Adopted parameters in the numerical analyses.

Eccentricity ε

Viscosity Parameter

Dilatation angle ϕ

f b0 /f c0

Kc

10°

0.1

1.16

0.666

0.002

Density ρ [kN/m³ ]

Young’s modulus E [Mpa]

Poisson’s ratio ν [ - ]

Compressive strenght f c [Mpa]

Tensile strenght f t [Mpa]

18

1500

0.2

6.2

0.18

5. Phase 3: Fragility Curves Derivation Pushover analyses were carried out for all façade configurations, both with and without foundation settlements, to derive capacity curves (base shear vs. horizontal displacement). The comparison focused on evaluating variations in stiffness, strength, and ductility due to settlement-induced damage. The control node was placed at the top of the wall, and analyses continued until a 15% drop in base shear after peak strength, identifying the ultimate displacement. The N2 Method (EC8-1, App. B) was adopted to estimate the seismic response, converting the MDOF system into an equivalent SDOF system through modal participation factors. A bilinear approximation of the capacity curve was applied, ensuring energy equivalence and limiting post-peak strength loss to 15%. The seismic demand was defined using spectra proposed by Eurocode 8, considering both Type 1 (far-field seismic events) and Type 2 (near-field seismic events) events, and various soil classes (A–E). A range of Peak Ground Accelerations (PGA) from 0.05g to 0.5g was used to reflect European variability. Four damage levels (DL1–DL4) were defined on the bilinear curve, corresponding to performance limit states from NTC 2018 ( NTC 2018): • DL1 (SLO) = ⅔ Dy → Slight damage • DL2 (SLD) = Dy → Moderate damage • DL3 (SLV) = ¾ Du → Heavy damage • DL4 (SLC) = Du → Complete damage where D y and D u are the yielding and ultimate displacements, respectively.