Hybrid fuzzy – stochastic 1D site response analysis accounting for soil uncertainties

The analysis of the seismic site response is conventionally carried out by the study of the one-dimensional amplification of vertically propagating shear waves through a horizontal soil profile with equivalent-linear elastic properties. Site response analysis requires the specification of the input ground motion and the dynamic characterization of the soil deposit. Whilst the stochastic approach is commonly used to model seismic excitations, the use of probability density functions for describing the soil properties is consistent only when precise information based on a large amount of data from soil surveys are available. Conversely, a non-probabilistic approach based on fuzzy set theory would be more appropriate for dealing with uncertainties that are just expressed by vague, imprecise, qualitative, or incomplete information supplied by engineering judgment. In this paper, we address a hybrid fuzzy-stochastic 1D site response analysis approach: we consider probability models for the seismic input and fuzzy intervals for dealing with soil uncertainties; the problem boundary values are defined as convex normal fuzzy sets and described by means of membership functions. Zadeh’s extension principle, in combination with an efficient implementation of the Differential Evolution Algorithm for global minimization and maximization, is used to perform fuzzy computations. Results are presented as fuzzy median value of the largest peaks of the peak ground acceleration at the surface by considering four types of soil classified in accordance with the European seismic building code. Finally, elastic response spectra defined in terms of gradual functions are proposed in order to evaluate the influence of the soil uncertainties on the seismic response of structures.