GNGTS 2019 - Atti del 38° Convegno Nazionale

358 GNGTS 2019 S essione 2.2 focuses on the evaluation of the structural seismic capacity necessary to strictly satisfy the safety requirement p f ( t )≤ p * f for different values of time elapsed from the last event. The failure rate depends on the system properties collected in a vector ϑ ∈ Θ, so it is possible to associate to each instant t the relevant set of system properties ϑ * ∈ Θ * ⊂ Θ necessary to strictly satisfy the condition p * f = p f ( t ) ≅ h ( t ) P f ( ϑ * ). As a final result, the relationship t ↔ ϑ * between the time elapsed from the last event and the minimum capacity required to achieve a fixed safety level is presented and discussed in the numerical application. A strong recursive seismic event is considered, magnitude M varies close to a reference value and and the point-source is placed at a distance r from the site of interest. It is assumed that the random values of M are described by a known PDF f M ( m ) defined on the magnitude interval Ω M . The seismic intensity at the site is a random variable denoted by I and its PDF f I ( i ) is determined by a Ground Motion Prediction Equation (GMPE), providing the conditional PDF f I ( i | M , R ). Generally, GMPEs are in the form ln( I )= g ( M , R )+ε g (0,σ g ), where ε g is a Gaussian random variable with 0-mean. In the case considered the distance r = ṝ is fixed and PDF of the seismic intensity is (2) The response properties of the structural system are described by using the parameters providing the fragility curve, in order to obtain results potentially of interest for different structural typologies. The fragility curve, F C ( i , ϑ ) = P [ failure | i , ϑ ], is described by using a log- normal cumulative density function (Cornell et al. , 2002), whose characteristic parameters are c and β, ϑ 0 [ c , β], the former is the intensity measure producing 50% of failure and the latter is the logarithmic standard deviation describing the dispersion of results. So, the conditional probability of failure is (3) Results. Results refers to the Paganica fault located in central Italy and relevant properties have been chosen according to (Pace et al. , 2006). The return period is 750 yr and magnitude M follows a truncated Gaussian distribution centred at m = 6.3 and spanning the range [5.8, 6.8] with a standard deviation 0.1667. Presented results compare outcomes deriving from a Poisson recursive model with results coming from a time dependent recursive model. The PDF of the Poisson model is (4) with T R = 750 yr . In this case, the hazard rate does not change in time and it is h T ( t ) = h 0 = 0.00133. The alternative time dependent hazard is described by the Brownian Passage Time model (5) The value α = 0.43 is assumed, according to the study on seismic scenario considered. Trends of interarrival time PDF and hazard rates of the two models are reported in Fig. 1.The two models provide the same hazard rate at t 0 = 416 yr . The seismic intensity is measured by the peak ground acceleration, according to the GMPE proposed in (Sabetta and Pugliese, 1996), using the parameters: a = –1.562, b = 0.306, c = 1, S 1 = 1, e 1 = 0.169, S 2 = 0, and h = 5.8. The standard deviation of ε is equal to 0.173 The seismic capacity is described by the parameter ĉ . The target value of p * f is 6.667·10 –5 . It is obtained by combining the conditional probability of failure p f = 0.05 with the reference value of the hazard rate h 0 = 0.00133. The site-to-source distance is r = 5 km and variable values of β are considered (0.5, 0.6, 0.7, and 0.8).