GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 2.2 357 seismic hazard assessment is based on a constant rate of occurrence in time, described by the Poisson recursive model. However, it is observed that small and medium magnitude events generally show different occurrence properties with respect to large magnitude events. The former generally occur as independent events, for which the recursive Poisson model is adequate, while the occurrence of the latter events is notably influenced by the previous history of the source activity. In this case, the earthquake sequence tends to show a periodic trend and the fault activity provides earthquakes with similar magnitudes, also denoted as characteristic earthquakes (Schwarz et al. , 1984, Tondi and Cello, 2003). Theoretical approaches considering the recursive properties of strong events and models providing a time dependent prediction of the interarrival time passing between two events dates back to the 80s. An overview of different models and a proposal for their classification is presented in (Anagnos and Kiremidijan 1988). Only more recently have time-dependent models found practical applications thanks to the improvements in fault mechanism knowledge in some earthquake prone areas. From a structural engineering perspective, it is of interest to evaluate the potential impacts of time dependent models describing the external actions, on the structural dimensioning and, more generally, on the design process. Regarding this, it is useful to recall that the final objective of structural engineering consists of bounding the probability of failure of constructions during their lifetime and some target values are proposed in codes of practice, such as EC 0 or ASCE 7. This objective is generally obtained by simplified procedures that permit a full probabilistic analysis to be avoided and many recent works have been oriented to improving these methods in order to control the effective probability of failures. This study presents some preliminary results on the impacts of a time dependent prediction of strong events on the structural capacity required to ensure a target failure rate is not exceeded. The required capacity varies as the time elapsed from the last event varies and the final result is influenced by either uncertainties due to the propagation of the seismic wave or the response of the structural system. A simple case, considering an earthquake point-source, is studied and results obtained by using the time dependent Brownian Passage Model (Mattheus et al. , 2002) are compared with results obtained with the time independent Poisson model. The influence of structural response dispersion is also analyzed. It is noteworthy that a more realistic failure prediction generally involves more than one source of strong event and includes widespread sources with no recursive properties. These last two issues should mitigate the overall influence of recursive models on the variation in time of capacity required to ensure the target failure rate is not exceeded. Therefore, presented results should be considered as the upper bound of the potential impact of time dependent models on structural design. Methodology. The earthquake is an event E whose occurrence in time is described by f T ( t ) providing the Probability Density Function (PDF) of the inter-arrival time. The origin t = 0 is placed at the instant of occurrence of the last event. Time-dependent models are generally based on the mean value of the inter-arrival time T R and on one or more parameters describing the expected dispersion of the inter-arrival time. Starting from f T ( t ) and the relevant cumulative density function f T ( t ), it is possible to evaluate the hazard rate function (1) This function provides the instantaneous probability of occurrence at the time t , given that no event had occurred previously, and describes the hazard variation in time.  The system reliability is measured by the failure rate pf ( t ) ≅ h T ( t ) P f , expressing the instantaneous probability of failure at time t . It is obtained by combining the hazard rate function with the probability of failure P f conditional to the event occurrence. Structural reliability requires that the failure rate be lower than a threshold p * f suggested by the codes and this paper