Seismic Response of Liquid Storage Tank in a Semi Analytical Method

Abstract

This thesis focuses on the dynamic analysis of liquid storage tanks subjected to seismic excitation with its primary aim being the development of a semi-analytical model able to predict this dynamic response accurately. In engineering practice, there are two primary methods to solve this problem. Numerical models based primarily on the finite element (FE) method, can treat the dynamics of the tank-liquid system with high accuracy. However, this comes at the cost of low computational speed; these models are slow and sophisticated finite element packages are required that can deal with both the structure and the liquid with equal rigor. On the other hand, analytical methods exist to solve the tank-liquid interaction problem. The latter, although computationally fast, lack of accuracy and can treat only the most simplistic configurations regarding the structural type. In this thesis, we aim to develop a semi-analytical model that combines the strong elements of both approaches, i.e. it is computationally fast and accurate.

In the first part of the thesis, a two-dimensional case is analyzed in which the tank is composed out of three beams representing the plate and the wall of the tank, while the liquid is assumed two-dimensional. With this model, the semi-analytical solution method is established. The method is very straightforward and is based on the principle of dynamic sub-structuring which is valid for linear systems. The response of the structure, i.e., the three interconnected beams, is expressed in terms of the in-vacuo beam modes; a modal basis that is convenient since different modes are orthogonal to each other. The liquid motion is expressed as a superposition of two or three potentials each of which, in turn, is also shown in terms of modes. By representing the response of each sub-structure in terms of an orthonormal set of modes, the behavior of the system is spatially fixed, and the remaining unknowns are only the modal coefficients representing the multipliers of the various modal shapes. The latter is obtained by enforcing displacement compatibility conditions at the liquid-tank interface and by satisfying the forced equations of motion of the structure. The results of the adopted solution approach are compared against known results in the literature for validation purposes.

With the developed three-dimensional model a parametric study is conducted in order to determine the influence of tanks dimensions, soil flexibility and wave speed on the structural response. Results are compared with others available in the literature in order to validate the model. The present model can be easily extended to include more complicated structures, e.g. horizontal tanks and tanks of different geometry. Finally, the model can be amended by a more accurate representation of the soil in terms of a three-dimensional layered continuum by merely adding an extra sub-structure to the system (the layered soil) while keeping the same solution approach.