PSI - Issue 44

Gianluca Quinci et al. / Procedia Structural Integrity 44 (2023) 251–258

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Gianluca Quinci et al. / Structural Integrity Procedia 00 (2022) 000–000

Fig. 3. Finite element model of the structure and modal shape of its first period.

Table 2. Limit states thresholds for fragility assessment Max tensile local strain ( ) Max tank acc (Sa[T]) ! < % ≤ 0.5% 10 / & 0.5% < % ≤ %' 16 / & In order to carry out the vulnerability and risk assessment of the vertical tank, two different set of 150 accelerograms each one has selected with the algorithm provided in Section 2, in order to validate the robustness and efficacy of the method. Taking in account the threshold value defined in Table 1, the fragility curve for each limit state is evaluated for each of two sets of accelerograms, with the hypothesis to approximate the fragility curve to a lognormal cumulative distribution. With this hypothesis the fragility curve is given by (1): P(C │ IM=y) = Φ ((ln(y/ θ ))/ β (1) where P(C|IM = x) is the probability that a ground motion with IM = x will cause the structure to collapse; Φ(.) is the standard normal cumulative distribution function (CDF); θ is the median of the fragility function (the IM level with 50% probability of collapse); and β is the standard deviation of ln IM (sometimes referred to as the dispersion of IM). Figure 4 shows the fragility curve for the vertical tank at first floor for the two limit states considered and for the two set of accelerograms. In order to evaluate the risk assessment of the tank and calculate the mean annual frequency (MAF) of exceedance of the experimentally identified limit states, the select case study is assumed to be located in Amatrice, Lazio, Italy. Figure 5 shows the hazard curve of the site. Cornell et al. (1996) proposed to decouple the assessment of the seismic performance of a structure in to two distinct sub-steps: (i) the Probabilistic Seismic Hazard Analysis (PSHA), as a proper feature of the site, and (ii) structural fragility, as a feature of the structure. Therefore, if is a parameter (or a vector of parameters) that represents the seismic hazard, ( ) is mean annual rate of exceeding a given value , and ( │ = ) is the probability of exceeding a limit state C conditioned to , the risk, expressed as the marginal annual rate of exceeding the damage C , ( C ), can be evaluated as λ (C)= ∫ P ( C│IM=y ) | d λ ( y ) | (2) Table 3 resumed the value of the MAF for the two limit states considered herein for both sets of accelerograms considered. DBE SSE Base plate fracture Base plate fracture Limit state Failure mode

Table 3. Mean annual frequency of exceedance limit states DBE SSE DBE

( )

SSE

0.00053

0.000188

0.00054

0.00017