Interpretation of the velocity measured in buildings by seismic interferometry based on Timoshenko beam theory under weak and moderate motion

Application of seismic interferometry in buildings gained interest in the recent years for structural health monitoring. It allows us to derive the shear wave velocity for an equivalent homogeneous medium representing the structure. Previous authors suggested using a shear beam model to compute the fundamental frequency of the structure out of this velocity. This model is however not adapted to a large part of existing buildings having different behaviors. In this paper, we propose a correction factor from shear beam and based on the Timoshenko beam to link the fundamental frequencies with the observed pulse velocity and the relative effects of shear and bending. This factor provides corrections up to 60% in frequency with respect to the shear beam model. The proposed correction factor shows that the higher velocities observed in the literature for shear wall buildings compared to frame buildings is compensated by their bending flexibility, resulting in resonance frequencies scaling similarly with building height. This model is applied to an 18-story reinforced concrete shear wall building (Ophite tower). The observed pulse velocity obtained by seismic interferometry in this building was about 500 m/s correlated to the resonance frequency by the correction factor. We show that variations of velocity in this structure and the well-studied Factor building (California), related to non-linear behavior at low-strains (down to 10−5), can be retrieved with seismic interferometry, demonstrating that this method is sensitive enough for structural health monitoring.