Scaling law study for earthquake induced pier–water interaction experiments

Froude number similarity has been used in all the physical experiments of earthquake induced hydrodynamic forces acting on deep water bridge piers without validation. This study focuses on the validation of the viability of Froude number similarity experimentally and numerically. Results show that Froude number similarity is viable, although the gravity wave force does not dominate the hydrodynamic force on bridge piers under earthquakes. Further, Euler number similarity is proven to be viable and Froude number similarity is proven to be the special case of Euler number similarity when \( \lambda_{f} = \lambda_{L}^{ - 1/2} \)(\( \lambda_{f} \) and \( \lambda_{L} \) indicate frequency scale and length scale respectively) in Euler number similitude. Numerical studies of the application demonstrate both Froude number similarity and Euler number similarity have almost the same precision when they are used to scale up the in-line force of model pier to prototype pier under ordinary earthquakes. However, Euler number similarity is recommended because of the advantages of providing a chance to choose frequency scale, which may be better supported by equipment and allow a Reynolds number closer to the one observed in the prototype.