Spatial variation and conditional simulation of seismic ground motion

Spatially varying ground motion (SVGM) may have influence on certain civil engineering structures with spatially extended superstructure and/or substructures. Conditional simulation of spatially varying ground motion (CSSVGM) may be viewed from two different perspectives. Most procedures available in the literature neglect the spatial variability in auto-spectral density (ASD) and estimate the SVGM through cross-spectral density (CSD) which was computed using the empirical coherency models. This paper proposes a coherency model that accounts for the spatial variability of ASD. A framework has been developed for the CSSVGM, through the mapping of both proposed coherency model and ASD over the footprint of an array. Current framework (existing in the literature) accounts for only the phase variability of SVGM while proposed framework accounts for both phase and amplitude variability. Ground motion generated from both perspectives is then assessed with the data recorded over SMART1 and LSST arrays. For the purpose of assessment, a definition of target spectrum based on the direction of arrival is explored. The effect of choice of coherency model on the simulated spatially varying ground motion is investigated first. Spectra resulting from both the perspectives are assessed against the target spectrum. An attempt has been made to predict the SVGM for a future event using a coherency model calibrated against a past event and an estimate of ASD of the seed ground motion. Finally, the effect of form of ASD (of a seed ground motion) on SVGM simulated is investigated by considering the ASD in different forms. Simulating SVGM through the mapping of both coherency model and ASD seems to be more appropriate than through CSD.by Gopala Krishna and Rodda 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