Apparent translational component for rotational ground motions

Even though the rotational ground motion may contribute significantly to the response of certain structures, their effects are generally ignored in seismic design, because of non-availability of appropriate instruments for direct recording of the rotational components. Like many others, a simplified framework was proposed by the authors elsewhere (Rodda and Basu in Int J Earthq Impact Eng 1(3):253-288, 2016) to extract the rotational motion as a temporal derivative of an apparent translational component (ATC) followed by scaling with an apparent velocity. ATC was defined such that its time derivative is closely correlated with the respective rotational motion. But the a priori knowledge of rotational motion is required in estimating the ATC for rocking component. An empirical procedure has been proposed here to bypass the requirement of rotational motion a priori. This paper also assesses the definition of ATC through examining the similitude between the time derivative of ATC and the respective rotational motion (benchmark) quantitatively. Similitude is assessed on smoothened response spectra (by Hamming window) of the time derivative of ATC and that of rotational motion. A new definition of spectral contrast angle (SCA) based on distance correlation has been proposed to assess the spectral similitude. To differentiate the similar from non-similar spectra, SCA corresponding to an acceptable degree of similarity is proposed by studying a large ensemble of ground motions from the PEER database. This similitude study is further extended using relative energy build up and energy spectra.by Gopala Krishna Rodda and Dhiman Bas

Coherency model for translational and rotational ground motions

Spatial variability of the translational ground motion may influence the seismic design of certain civil engineering structures with spatially extended foundations. Lagged coherency is usually considered to be the best descriptor of the spatial variability. Most coherency models developed to date do not consider the spatial variability of the spectral shape of auto-spectral density (ASD), which is expected to be critical. This paper proposes a coherency model that accounts for the variability in spectral shape of ASD. Numerical results illustrate that the effect is not that critical for a dense array but can be significant in case of large array. Rotational ground motions on the other hand are not measured by the accelerograph deployed in the free-field owing to the unavailability of appropriate instruments and rather extracted from the recorded three-component translational data. Previous studies [e.g., Basu et al. (Eng Struct 99:685-707, 2015)] reported the spatial variability of extracted rotational components, even over a dimension within the span of most civil engineering structures, for example, tens of metres. Since rotation does not propagate like a plane wave, coherency model based on plane wave propagation does not apply to address the spatial variability of rotational components. This paper also proposes an alternative to address the spatial variability of rotational components. Illustrations based on relatively short separation distance confirm the expectation.by Gopala Krishna Rodda and Dhiman Bas