PSI - Issue 44

Greta Agata Venneri et al. / Procedia Structural Integrity 44 (2023) 291–298 Greta Agata Venneri et al. / Structural Integrity Procedia 00 (2022) 000–000

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4. Results 4.1. The used methodology of the seismic vulnerability assessment

The methodology for the seismic vulnerability assessment of the examined multi-storey buildings consisted of the steps described below. The first step involved nonlinear time history analyses of the structural models subjected to a set of 125 different records, selected by a ReLUIS project conducted between 2019-2021 (WP4 – MARS Seismic Risk Map). Each record is characterized by the two orthogonal horizontal components H1 (North-South) and H2 (East West). The accelerograms were grouped into 9 families, according to the increasing PGA value, each uniformed with respect to the mean PGA value representative of the family. Table 1 lists the families of ground motions with their PGA values and mean PGA value. Therefore, the main uncertainty considered in the problem was that related to the ground motions (record-to-record variability) (Adam et al. 2014).

Table 1. Families of accelerograms.

H1 direction (North-South)

H2 direction (East-West)

Group of accelerograms PGA (m/s 2 )

Average PGA (m/s 2 ) PGA (m/s 2 )

Average PGA (m/s 2 )

Family 1 Family 2 Family 3 Family 4 Family 5 Family 6 Family 7 Family 8 Family 9

0.488 ÷ 0.980 1.075 ÷ 1.392 1.434 ÷ 1.853 1.883 ÷ 2.926 3.283 ÷ 3.947 4.071 ÷ 4.674 4.897 ÷ 5.993 6.023 ÷ 6.958 7.124 ÷ 11.735

0.81 1.23 1.63 2.36 3.56 4.37 5.44 6.47 8.39

0.399 ÷ 1.050 1.111 ÷ 1.364 1.425 ÷ 1.851 1.887 ÷ 2.943 3.091 ÷ 3.883 4.023 ÷ 5.001 5.077 ÷ 6.003 6.075 ÷ 6.896 7.103 ÷ 8.578

0.79 1.23 1.63 2.39 3.37 4.58 5.54 6.52 7.81

The second step involved the statistical elaboration of the response data obtained from the nonlinear time history analyses. In this study, structural capacity values corresponding to the performance levels specified in FEMA-356 were identified (FEMA 356 2000); these are the Immediate Occupancy (IO), the Life Safety (LS) and the Collapse Prevention (CP). The associated maximum transient interstorey drift ratio limits are 0.7, 2.5 and 5%, respectively. Three damage levels (D1, D2, D3) were associated with the three limit states, respectively. Structural capacity was defined as the interstorey drift value satisfying a specified performance level. Specifically, in this step multiple stripe analyses were conducted on the results (Baker 2015), in order to calculate the probability of exceeding the selected limit states for each family of accelerograms. Demand and capacity were compared. Peak inter-storey drift (ISD) ratio measured during each analysis was considered as the EDP (Engineering Demand Parameter); inter-storey drift (ISD) ratio limit states was considered as the ECP (Engineering Capacity Parameter). PGA was considered as intensity measure (IM). The calculated probabilities were collected in the Damage Probability Matrix (DPM) which determined the damage scenarios for each family of accelerograms. Subsequently, these probabilities were cumulated and the Cumulative Damage Probability Matrix (CDPM) was defined. This describes the probabilities of exceeding the established Damage Limit States. The probabilities in the CDPM for each family of accelerograms were represented in form of points clouds, that were fitted through lognormal functions representing the fragility curves; the latter provided the estimation of the seismic vulnerability of the buildings. 4.2. Fragility curves The fragility function Fd(x), reported in eq. (1), was used to describe the probability, given an intensity measure, that the damage measure (DM) exceeds the limit state. The value of x is the intensity measure (IM), that in this study corresponds to PGA. The performance level should be correlated with the expected damage. It is generally accepted