Risk-based probabilistic seismic hazard analysis considering parameter uncertainties

Current approaches for the seismic hazard assessment, are mainly based on the classical formulation of the probabilistic seismic hazard analysis, widely known with the acronym PSHA. This procedure is able to compute the annual rate of exceedance λIM>im of a set of ground motion intensity measures IM at a site of interest (Cornell 1968). Usually, for structural design, the annual rate of exceedance is used for calculating the the probability of exceeding a given ground motion intensity within a given window of time T, corresponding to the structure’s expected life. During years, several efforts were performed for understanding and including the influence of uncertainties underlying the PSHA calculation (McGuire 1977). In particular, scientific literature subdivides uncertainties into two main types: aleatory uncertainty and epistemic uncertainty (McGuire and Sheldock 1981). The former is the variability naturally inherent to a physical phenomenon, while the latter is due to the scarcity of data and it is related to the degree of knowledge of the problem. Logic tree approaches were adopted for incorporating epistemic uncertainty (Kulkarni et al. 1984), but their use is often debated since their output is a weighted value (Marzocchi et al. 2015, Iervolino et al. 2016). PSHA integral is a correct application of the total probability theorem, but it does not account for the uncertainties in model parameters which can be significant, since most of times they are derived from historical data. For this reason, this work aims to develop a robust semi-analytical formulation, able to assess how uncertainties in model parameters influence the seismic hazard curve’s reliability. The proposed mathematical procedure, uses the reliability index and its standard deviation for computing a design hazard curve, whose points are characterized by a fixed accepted level of risk. Results show how uncertainties in model parameters affect the hazard curve’s dispersion, and how a better parameters’ knowledge allows defining lower design values, with the same assumed risk.