MULTIVARIATE PROBABILISTIC ANALYSIS OF SEISMIC HAZARD USING COPULAS
DOI:
https://doi.org/10.18867/ris.107.588Keywords:
Seismic demand analysis, mean rate of exceedance, maximum interstory drift, spectral acceleration, vector-valued intensity measureAbstract
Multivariate probabilistic analysis of seismic hazard allows estimating the exceedance rate of vector-valued intensity measures of ground motion considering their joint probability distribution. Such an analysis is used for probabilistic seismic demand analysis of structures whose response is correlated with a set of intensity measures. In such cases, it is convenient to compute the exceedance rate of the response employing the exceedance rate of vector-valued intensity measures, in contrast to a univariate approach where the exceedance rates of a set of scalar intensity measures are calculated separately without accounting for their statistical dependence. In this work, a multivariate formulation is advanced for probabilistic seismic hazard analysis of vector-valued intensity measures using copulas. The formulation is generic considering that the exceedance rate is expressed in terms of the copula of a vector-valued intensity measure, without assuming a type of parametric model for its multivariate probability distribution. The proposed formulation is used in an example to assess the mean exceedance rate of the maximum interstory drift of a 20 story steel building employing a regression model in terms of the spectral accelerations for the first two structural periods. The copula model of the vector of spectral accelerations was estimated using ground motion records from stations on stratified sand and silt deposits in Mexico City. This type of seismic ground motion produces a significant contribution of the response associated with the second mode of the structure. The exceedance rates obtained from the multivariate formulation were significantly less than those from a univariate analysis using the spectral acceleration at the fundamental period of the structure as scalar intensity measure.
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