The expanded Morison equation considering inner and outer water hydrodynamic pressure of hollow piers

Abstract The standard Morison equation is unable to calculate hydrodynamic pressure induced by inner water of hollow columns under earthquakes, such as thin-walled hollow deep water pier, so the expanded Morison equation, which can afford hydrodynamic pressure caused by inner water and outer water simultaneously, is presented. The hydrodynamic force of inner water is expressed in the form of inertial force caused by the inner water added mass, which is considered to be equal to the mass of inner water. In order to check the validation of the expanded Morison equation, hydrodynamic pressure acting on rigid liquid storage tank and elastic hollow pier is analyzed by the velocity potential method. The results show that if the structure does not make resonant vibration, the inner water added mass is approximate to the mass of inner water. Another two methods, one is based on radiation wave velocity potential theory and one is pressure-based fluid finite element method in ANSYS procedure, are employed to compare with the expanded Morison equation. The calculation results show that the fundamental frequency reduction rate and dynamic response under harmonic loads based on the expanded Morison method are close to those of another two methods, except for the piers with large internal side length, whose hydrodynamic pressure would be overestimated. The practical application of the expanded Morison equation has been explored through analyzing a continuous rigid-framed deep water bridge. The results demonstrate that it is an approximate, convenient and efficient way to estimate the hydrodynamic pressure caused by both inner and outer water under earthquakes.