PSI - Issue 78

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

1005

Fragility curves were developed by evaluating, for each damage level, the probability of exceedance using a lognormal distribution. A Damage Index (DI) was defined as the ratio between seismic demand displacement and the displacement at the considered damage level. The relationship between DI and PGA was expressed as (Nielson and DesRoches 2007): ( d )= + ln ( ) where A and B are regression coefficients in the bi-logarithmic space. Dispersion (σ) was derived from the standard deviation of DI values around the mean line. The final expression for the fragility function is: ( > | )= ( > | ) =1 − � ln1 −λ |PGA σ |PGA � where: - Φ[•] is the lognormal standard distribution function; - λ|PGA the mean of the logarithm of the limit state variable DI conditioned on the level of PGA; - σ|PGA is the total model dispersion. 6. Results and discussion The results of the numerical analyses are presented below, starting with a comparison of the capacity curves, represented by their envelopes, obtained from the generated models, followed by the corresponding fragility curves. Specifically, the following figure (Fig. 4) shows the capacity curves derived from nonlinear static analyses. The set of curves corresponding to the condition without vertical settlement is shown in red, while the curves obtained after the application of settlement are shown in grey. The results are presented separately for each applied settlement profile. Analysis of Fig. 4 clearly shows that, in all cases, the structural response is significantly affected. All applied settlement profiles lead to a reduction in both the maximum lateral capacity and the initial stiffness of the wall, accompanied by an increase in the ultimate displacement. This effect is particularly pronounced in the case of a lateral settlement profile involving two piers. Additionally, the horizontal displacement corresponding to the peak capacity also shows an increase.

Model 1

a)

b)

c)

Shear [KN] 500 400 300 200 100

Shear [KN] 500 400 300 200 100

Shear [KN] 500 400 300 200 100

Displacement [mm] 0 1020304050607080

Displacement [mm] 0 1020304050607080

Displacement [mm] 010 20 30 40 50 60 70 80

d l

Fig. 4 Capacity curves obtained at the end of the pushover analysis without settlement (red) and whit settlement (grey) for (a) central settlement profile (b), one-pier lateral settlement profile and (c) two-piers lateral settlement profile. These findings are further supported by the analysis of the damage patterns (Fig. 5). The central settlement condition, due to its symmetric profile, does not alter the damage distribution compared to the analysis performed under seismic loading only on the same wall. In contrast, lateral settlements lead to significant changes in the damage pattern, involving different structural elements and consequently affecting the overall structural response. As an example, Fig. 5 shows the damage pattern obtained for the reference wall configuration (whose dimensions are reported in Fig. 2a) under different settlement conditions, along with the corresponding case subjected only to seismic loading.