Experimental Calculation of the Damping Ratio In Buildings Hosting Permanent GPS Stations During the Recent Italian Earthquakes

On the indication of the European standards [1], the Italian technical regulations on buildings [2] set the damping ratio (or damping factor) ζ at 0.05 (5%). However, this value appears to be restrictive as it is influenced by many factors such as the mass, stiffness, oscillation amplitude, geometry, construction material, ground geology, etc.; a minimum percentage deviation produces significant variations in the ordinates of the seismic response spectra and in the structural factors. Therefore, it seemed interesting to make an experimental evaluation of whether this damping value is acceptable for Italy, since it became possible to carry out such an assessment during the Italian earthquakes from 2012 to 2017. In the epicentral areas of the earthquakes of Emilia 2012, central Italy 2016 and Ischia 2017, there were ca. 40 permanent GPS stations [3,4] and the same number of accelerometer stations of the National Accelerometric Network (RAN) [5]. During the events of greatest magnitude, these stations recorded both the movements of the buildings (GPS stations) and the ground accelerations (RAN stations). From the instantaneous horizontal displacements measured by the buildings’ GPS antennas (rigidly fixed to one of the two walls either with steel brackets or directly to the roof with a purposely built reinforced concrete structure) and the instantaneous horizontal ground accelerations recorded directly by the accelerometer stations, two pseudo-acceleration spectra were obtained: that of the building and that of the ground (here called the spectra of the oscillator and of the external force, respectively). From each of these two spectra, the spectral ordinates corresponding to the value of the building’s elastic period of vibration To were extracted: this extraction was carried out for different values of ζ between zero and one. The relation between these spectral ordinates allowed us to draw parabolas for varying ζ values (an example of a parabola is reported in section 3); these parabolas present two extreme values of the relations in correspondence of ζ = 0 (free oscillation) and ζ = 1 (over damped oscillation), as well as values between 0