PSI - Issue 44

A. Sandoli et al. / Procedia Structural Integrity 44 (2023) 1332–1339 A. Sandoli / Structural Integrity Procedia 00 (2022) 000 – 000

1337

8

3.2. Multiple seismic fragility scenario through the hazard disaggregation Fragility curves presented in the previous Section are descriptive for the effects of near-fault earthquakes because they represent the exceedance probability of the ULS for an earthquake having intensity equal to that provided by the codes and with epicenter located in Balvano. Nevertheless, for a more exhaustive urban scale vulnerability prediction, an important task is the definition of multiple damage scenarios related to the effects of multiple far-fault earthquakes, i.e. with epicenter located at a given distance from Balvano. To this purpose, a methodology based on the hazard disaggregation analysis has been herein applied with reference to the case post-1980. It, originally developed in the framework of the probabilistic seismic hazard analysis (PSHA), allows to calculate the contributions of different seismic sources to seismic hazard of a specific site (Bazzurro and Cornell, 1998). By analogy with PSHA, the hazard disaggregation analysis has been adopted to calculate the distribution of the contributions to seismic urban fragility (i.e., the exceedance probability of a DS for given values of PGA) produced by different seismogenetic sources placed at distance R and able to generate earthquakes with magnitude M. As a result, multiple seismic scenarios of the area under investigation (compartment C_01) have been represented through Multi-Scenario Matrix (MSM): the terms of the matrix are the exceedance probabilities (i.e., cdf ) that the compartment will experience a particular DS for a given M-R pair. The cdf values are calculated through specific probabilistic fragility functions, in this case, by integrating the eq. (1). Going into more detail, the MSM has been obtained by considering the following steps:  Choice of a suitable M-R attenuation law of the IM (e.g., PGA, I MCS or another ground motion measure)  Determination of the values of IM for pre-fixed M-R pairs  Determination of the exceedance probability associated to each IM ( cdf estimated through a fragility function) In this paper, the attenuation laws provided by Crespellani et al. (1998) and by Sabetta and Pugliese (1987) have been adopted and the results compared. Crespellani et al. (1998) envisaged a simple attenuation law in terms of I MCS , as reported in the following: ln( 7) 2.747 6.39 1.756     R M I MCS (4) To obtain the corresponding distribution in terms of PGA, the I MCS -PGA correlation formula given by eq. (3) has been used. As an alternative, Sabetta and Pugliese (1987) correlated the PGA with the M-R couples as follows:

2 R h b S b S 2

log(

) b b M PGA

log(

     3 1 4 2 )

   1 2

(5)

where b 1 = 1.562, b 2 =0.306, b 3 =b 4 =0.169, h= 5.8, S 1 =1, S 2 =0,  =0.173. Both eqs. (4) and (5) – calibrated with regression analyses based on a wide strong-motion database – consistently with a linear term which takes into account the dependence of the ground-motion from the magnitude and with a nonlinear term which consider the dependence from the distance. With respect to eq. (4), the Sabetta and Pugliese formulas accounts for site effects due to soil.

Table 2. Multi Scenario Matrices (MSM)

MSM obtained with eq. (4)

MSM obtained with eq. (5)

M

R=0 km 0,4320 0,9840 1,0000 1,0000 1,0000

R=10 km

R=20 km R=30 km

R=0 km 0,2940 0,9340 1,0000 1,0000 1,0000

R=10 km

R=20 km

R=30 km

4,0 5,0 6,0 7,0 8,0

0,0003 0,1320 0,8950 1,0000 1,0000

0,0000 0,0025 0,3200 0,9710 1,0000

0,0000 0,0000 0,0560 0,7700 1,0000

0,0053 0,3100 0,9400 1,0000 1,0000

0,0000 0,0134 0,4340 0,9700 1,0000

0,0000 0,0004 0,0980 0,7800 0,9976