Analytical solutions for determining the most unfavorable moment of shaking occurrence in underwater shaking table tests

Abstract

Responses of structures under coupled earthquake and wave-current actions are greatly influenced by the difference between occurrence times of earthquake and wave-current action. Aiming to obtain the most dangerous scenario of the structure (i.e. the maximum structural response) from underwater shaking table (UST) tests, the most unfavorable moment of shaking occurrence in UST tests was analytically investigated in this study through three steps. Firstly, analytical solutions for natural frequencies of structures submerged in water were proposed. Underpinned by the calculated frequencies, the time corresponding to the maximum responses of structures under earthquakes in still water (ES) was solved utilizing the mode superposition method. Secondly, simplified Morison equations were proposed to solve the time corresponding to maximum wave-current forces. Then, the time corresponding to the maximum responses of structures under wave-current (WC) action was solved by considering the time lag between excitations and responses. Thirdly, the calculation method for the most unfavorable moment of shaking occurrence in UST tests was proposed through comprehensive analyses of the theoretical results of structures under ES and WC conditions. Finally, underpinned by a numerical model, which can accurately reproduce the structural responses under coupled earthquake and wave-current (EWC) actions, all the new proposals were comprehensively validated, considering different parameters of structures and excitations. The results showed that the proposed analytical method has sufficient accuracy in determining the most unfavorable moment of shaking occurrence in UST tests. The analytical methods proposed in the current paper provided a firm basis for the design and implementation of UST tests.