Derivation of rotations in soil motion from array measurements Application in structural codes

Abstract

The way to take into account earthquakes in buildings design has been originally dictated by G. W. Housner (1959). It is based on the description of the soil motion through a Response spectrum. The quantity is established in regions of suitable extension, affected by the presence of seismically active faults.Locally, some items influence the Response spectrum, and in general the buildings behavior. First of all, the soil conditions, and in fact the Response spectrum specified by Eurocode 8 shall be selected among seven different soil conditions. A second item, presently analyzed, is the soil rotation, in particular, the couple of rotations around two orthogonal axes in a horizontal plane, ψy and ψx. (In a Cartesian space, x, y, and z are the orientation axes, the latter being vertical). We take advantage of dense arrays of instruments (in the following DAI) that have been installed since a few decades. The most important of them are the dense arrays of Smart 1 and Smart 2, in Taiwan. The present study examines records collected in occasion of seismic events. Displacement and acceleration are presented as a function of space and time, free from any model of propagation. Models hold at some distance from the source, i.e. at distances where the source mechanism can be represented as a point source. In the present study, the epicenter distance to the center of the DAI is around 30 km, (magnitude 6.9, max acceleration in the epicenter zone, cm/s2, V 64.5, EW 158.2, NS 244.1). Recognized results are:-(Table 1) For a same seismic event, the soil acceleration has been measured in 29 positions along an array surface of 12 km2. The measurements show a significant dispersion. The root mean square of the peak accelerations, is nearly equal to the mean value of the peaks. A similar result holds for the rotations. See Table 1 and 2.- On the basis of power spectrum of the rotation signal, the dominant frequencies are in the range of 3-11 cps.Rotation excitation may thus be meaningful chimneys, tall buildings, bridge piers and in general tall slender structures.- As expected, during the time duration of the earthquake, rotations can be favorable or unfavorable with respect to a building acted by the appropriate response spectrum.