  In countries with a moderate seismic hazard, the classical methods developed
for strong motion prone countries to estimate the seismic behaviour and
subsequent vulnerability of existing buildings are often inadequate and not
financially realistic. The main goals of this paper are to show how the modal
analysis can contribute to the understanding of the seismic building response
and the good relevancy of a modal model based on ambient vibrations for
estimating the structural deformation under moderate earthquakes. We describe
the application of an enhanced modal analysis technique (Frequency Domain
Decomposition) to process ambient vibration recordings taken at the Grenoble
City Hall building (France). The frequencies of ambient vibrations are compared
with those of weak earthquakes recorded by the French permanent accelerometric
network (RAP) that was installed to monitor the building. The frequency
variations of the building under moderate earthquakes are shown to be slight
(~2%) and therefore ambient vibration frequencies are relevant over the elastic
domain of the building. The modal parameters extracted from ambient vibrations
are then used to determine the 1D lumped-mass model in order to reproduce the
inter-storey drift under weak earthquakes and to fix a 3D numerical model that
could be used for strong earthquakes. The correlation coefficients between data
and synthetic motion are close to 80% and 90% in horizontal directions, for the
1D and 3D modelling, respectively.
