Simplified Added-Mass Model for Evaluating the Response of Rectangular Hollow Bridge Piers under Earthquakes

Abstract

A simplified added-mass model is proposed in this paper for evaluating the seismic response of rectangular hollow piers in deep water, which are widely used in railway bridges. For this purpose, the accurate and concise formulas for the outer and inner hydrodynamic pressures were first derived after smoothing the pier outer surface corners by using small circular arcs. Then, the kinematic equation of the pier–water system was solved in the frequency domain and converted to the time domain with an inverse Fourier transform. In addition, the expressions for the outer and inner water added masses that were induced by elastic vibration and rigid motion were obtained. To verify the accuracy of these analytical solutions in terms of hydrodynamic pressures and added masses, a finite-element modeling approach, based on potential-based fluid elements (PBFEs), was employed to define numerical models of bridge piers in water. A comparison of the added mass coefficients induced by elastic vibration and rigid motion indicates that the former can be substituted by the latter. Meanwhile, water compressibility effects on the hydrodynamic forces have been fully discussed and proven to be negligible for general piers under most earthquakes. Finally, for convenience of application, simplified formulas for added mass and a simplified added model were presented to simulate the seismic response of rectangular hollow piers in water. The good agreement between the dynamic results from the simplified expressions and numerical method confirmed the former’s accuracy and convenience for engineering applications.