Seismic response of liquid-containing tanks with emphasis on the hydrodynamic response and near-fault phenomena

•Hydrodynamic equations pertaining to a seismically excited tank are reviewed.•Originality of treatment lies in the use of an accelerated reference frame.•Impulsive and convective modes are calculated in a unified manner.•Application to earthquake recordings with far and near-fault characteristics.•Second convective mode appears critical for the height of the sloshing wave.•The accuracy of simplified wavelets that model forward directivity is assessed. The present research studies the hydrodynamic response of cylindrical liquid-containing tanks with stiff walls under seismic excitations. Starting from standard hydrodynamic assumptions, the fluid oscillatory modes are separated to an impulsive mode and convective modes through the introduction of a reference frame co-moving with the base of the tank. The response of the fluid’s normal modes to a lateral excitation and the role of Housner’s oscillators is elucidated. Fast Fourier Transform techniques are applied to samples of earthquake records with near- and far-fault characteristics that have been appropriately scaled to match the Eurocode 8 design spectrum. Critical response quantities including the base shear and the height of the sloshing wave are computed analytically as functions of time and results are compared for near- and far-fault conditions. Particular emphasis is given on the contribution to the above quantities of the second convective mode which is systematically neglected according to current design practices for liquid-containing tanks. The results suggest that under near-fault conditions, when the directivity pulse has substantial content near the frequency of the second convective mode, current provisions may lead to a significant underestimation of the maximum height of the sloshing wave. This observation may provide an explanation of the extensive post-earthquake damage observed at many tank roofs located in the proximity of active faults. The results for near-fault records are compared with those obtained from a simplified representation of the velocity pulse proposed in the literature. The simplified wavelet leads to acceptable accuracy compared with a corresponding real record when the maximum height of the sloshing wave is examined; however, significant underestimation is detected for the calculation of the base shear.