  Within the performance-based earthquake engineering (PBEE) framework, the
fragility model plays a pivotal role. Such a model represents the probability
that the engineering demand parameter (EDP) exceeds a certain safety threshold
given a set of selected intensity measures (IMs) that characterize the
earthquake load. The-state-of-the art methods for fragility computation rely on
full non-linear time-history analyses. Within this perimeter, there are two
main approaches: the first relies on the selection and scaling of recorded
ground motions; the second, based on random vibration theory, characterizes the
seismic input with a parametric stochastic ground motion model (SGMM). The
latter case has the great advantage that the problem of seismic risk analysis
is framed as a forward uncertainty quantification problem. However, running
classical full-scale Monte Carlo simulations is intractable because of the
prohibitive computational cost of typical finite element models. Therefore, it
is of great interest to define fragility models that link an EDP of interest
with the SGMM parameters -- which are regarded as IMs in this context. The
computation of such fragility models is a challenge on its own and, despite few
recent studies, there is still an important research gap in this domain. This
study tackles this computational challenge by using stochastic polynomial chaos
expansions to represent the statistical dependence of EDP on IMs. More
precisely, this surrogate model estimates the full conditional probability
distribution of EDP conditioned on IMs. We compare the proposed approach with
some state-of-the-art methods in two case studies. The numerical results show
that the new method prevails its competitors in estimating both the conditional
distribution and the fragility functions.
