Spatially correlated vertical ground motion for seismic design

Spatial variation of vertical ground motion may have influence on the response of long span lifeline structures like bridges, pipelines, etc. However, studies specific to the spatial variability of vertical component of ground motion are limited in the literature when compared with the associated horizontal components. Based on the data recorded at SMART1 and LSST arrays, comparison of spatial variability of vertical and horizontal components is explored here using the coherency model reported by the authors elsewhere. Alternatively, Fourier amplitudes of horizontal components are often scaled through an empirical function to estimate that of the vertical components. Ratio of auto-spectral density (ASD) of horizontal to vertical ground accelerations is then investigated using the array recordings. Conditional simulation of spatially varying ground motion (CSSVGM) can be categorized into two different approaches: (i) (evolutionary) cross-spectral density (CSD) based procedures and (ii) auto-spectral density (ASD) based procedure. While the former assumes spatially uniform ASD and accounts only for the phase variability, the latter takes into the account the spatial variability of ASD and thereby accounts for both phase and amplitude variability. These frameworks do not differentiate between horizontal and vertical components. However, the results reported to date by most researchers are based only on the horizontal components. Spatially varying vertical components are next simulated in this paper using both the perspectives and assessed against the array recordings. An attempt has also been made to estimate the SVGM of the vertical components for a future event. Choice of functional form of ASD (of a seed ground motion) on the resulting spatially varying vertical ground motion is also investigated. Finally, empirical forms of vertical to horizontal (V/H) response spectral ratio reported in the prior art do not account for the spatial variability over the footprint of array, which is also investigated here.