  Fragility curves are commonly used in civil engineering to estimate the
vulnerability of structures to earthquakes. The probability of failure
associated with a failure criterion (e.g. the maximal inter-storey drift ratio
being greater than a prescribed threshold) is represented as a function of the
intensity of the earthquake ground motion (e.g. peak ground acceleration or
spectral acceleration). The classical approach consists in assuming a lognormal
shape of the fragility curves. In this paper, we introduce two non-parametric
approaches to establish the fragility curves without making any assumption,
namely the conditional Monte Carlo simulation and the kernel density
estimation. As an illustration, we compute the fragility curves of a 3-storey
steel structure, accounting for the nonlinear behavior of the system. The
curves obtained by the proposed approaches are compared with each other and
with those obtained using the classical lognormal assumption.
