A Mode Matching Technique for the Seismic Response of Liquid Storage Tanks Including Soil-Structure Interaction

Abstract

The paper establishes a computationally inexpensive method to deal with the dynamic response of liquid storage tanks subjected to seismic excitation including dynamic soilstructure interaction. The tank is modelled as a thin shell, the stored liquid is described as an inviscid and incompressible fluid and the soil medium is modelled as an elastic continuum. The dynamic response of the tank-liquid-soil system is derived in the frequency domain using dynamic substructuring and mode matching. The tank vibrations are first expressed in terms of the in-vacuo shell modes while the liquid motion is described as a superposition of linear potentials. The soil reaction to the plate of the tank is derived on the basis of a boundary integral formulation with the excitation field being the seismic free-field ground motion. Due to its high computational efficiency, the proposed method is suitable when a large number of simulations is required as is the case in seismic risk analysis. It overcomes the limitations of most mechanical analogues used nowadays, while at the same time maintains an accuracy comparable to that of finite element models within a fraction of the computation time of the latter.