Time-domain hydrodynamic forces on rigid dams with reservoir bottom absorption of energy

摘要

In this investigation, a two-dimensional time-domain closed-form mathematical model for the hydrodynamic forces on the upstream vertical face of a given rigid dam subjected to a specified horizontal ground motion accelerogram was developed. The model includes the absorption of energy at the elastic reservoir bottom, characterized by the impedance ratio of the sub-bottom materials with respect to water (α). The formulated boundary-value problem is solved in Laplace's domain and subsequently transformed back to the time domain. Response spectra for the hydrodynamic base shear force and overturning moment are constructed for extreme values of the parameter α. It is found that, frequently, including the solid-foundation elasticity in the reservoir model attenuates the resultant hydrodynamic forces on a rigid barrier, as compared to the results for the case of a rigid reservoir foundation. In this case, the elasticity of the sub-bottom materials constitutes an effective energy dissipating mechanism (radiation damping). By contrast, for sub-bottom materials with less-than-water impedance, amplification of the effective earthquake forces is obtained, as compared to the results for the case of a rigid reservoir foundation.