PSI - Issue 78

Iunio Iervolino et al. / Procedia Structural Integrity 78 (2026) 1553–1560

1557

[ | , ] = [ | , , ] = 0.553−0.055∙ −0.027∙ −0.027∙ 1+ 0.553−0.055∙ −0.027∙ −0.027∙ . (5) Finally, | ( | ) is the log-normal PDF of conditional on , herein according to Wells and Coppersmith (1994), while | ( | ) denotes the joint density of { , , , ℎ } , conditional on . For this preliminary analysis, three equally probable hypocenter locations were assumed, corresponding to the two ends and the center of the ITIS013 fault, all at a depth of about 9 km. On the other hand, the joint density of the variables defining the location of the hypocenter on the rupture plain { , } were taken from the model of Mai et al. (2005). However, realizations of = and = { , ℎ, , ℎ } leading to finite-fault ruptures beyond the assumed fault boundary must be truncated, leading to the stochastic dependence implied by | ( | ) . Overall, rupture areas considered varied within the interval ∈ [400km 2 ,1400km 2 ] , while ∈ [0,52.8 km] , ℎ ∈ [10 km,50 km], ∈ [1.4 km,7.5 km] , and ∈ [0, 6.8 km] . It was found that, for finite-fault parameters varying within these intervals, the pulse occurrence probability is within the range 0.132 ≤ [ | , , ] ≤ 0.415 at the Messina site. 2.2 Spectra conditional on earthquake occurrence The distribution of ( ) , in terms of complementary cumulative distribution function, for the site of Messina was computed by means of Eq. (1) for the vibration period range from 0.01 s to 10 s plus peak ground acceleration ( ), considering soil site class A according to the classification of Eurocode 8 (CEN, 2004). The mean of each pseudo acceleration spectral ordinate, conditional on earthquake occurrence, denoted as [ ( )] − , was then computed. Fig. 3 shows the values of [ ( )] − at the various vibration periods, that is, the spectrum of mean ( ) conditional on the occurrence of an earthquake with magnitude in the 7±0.3 interval and location on the considered fault. The range of variability of ( ) between the 16 th and 84 th percentiles of the distribution is also represented in shade of grey. In order to quantify the impact on site seismic hazard of potential pulse-like ground motions generated by the Messina Strait fault, the spectrum collecting the conditional means of ( ) according to classical PSHA, [ ( )] , is also shown in Fig. 3. It was computed using the same input models as in the NS-PSHA, without GMM modification for pulse occurrence (see previous section), effectively neglecting the pulse occurrence probability in Eq. (1). For each vibration period, the hazard increment due to pulse-like effects was quantified in terms of relative difference between the NS-PSHA and PSHA: Δ = { [ ( )] − − [ ( )] } [ ( )] ⁄ .

0 10 20 30 40 50 60 70 80

1.5

E Sa T [ ( )] E Sa T [ ( )]

1

PSHA

[%]

0.5 Sa T ( ) [g]

NS-PSHA - ( ) Sa T

[ ( ) Sa T

]

16 th

84 th

NS-PSHA

0

1

2

3

4

5

6

7

8

9

10

T [s]

Fig. 3. Mean spectral ordinates conditional to the occurrence of one event according to NS-PSHA and PSHA and hazard increments due to pulse-like effects. For vibration periods between 3 s and 10 s, the NS-PSHA spectral ordinates exceed those from the traditional PSHA by more than 50%. The largest hazard relative increase, equal to 64%, is observed for = 4 s . The impact of pulse like ground motion is comparatively less significant at short vibration periods, with hazard increments not exceeding 10% for periods shorter than 1 s. For instance, the mean values obtained from both NS-PSHA and PSHA are approximately 0.45 g. It is worth noting that the non-monotonic trend of Δ with period in Fig. 3 is determined by the magnitude occurrence model adopted for the fault. Within the = 7 ± 0.3 range considered in the analyses, the median of | spans from 2.7 s to 5 s, which aligns with the period interval where hazard increments due to pulse