Nonlinear Free‐Surface Flow in Oscillating Channel during Earthquakes

Abstract

The nonlinear free‐surface flow in an infinitely long channel during earthquakes is analyzed by the boundary element method. The solution is obtained by a distribution of simple Rankine‐type singularities on the walls of the channel and on the undisturbed free surface. The fluid in the channel is assumed to be inviscid and incompressible, and its motion irrotational. Unsteady velocity potential is determined with second‐order nonlinear boundary conditions applied on the free surface. The time‐marching procedure is introduced to solve for the transient stage after an earthquake takes place. The channel is assumed to be rigid during an earthquake, and the amplitude of the channel oscillation and the free‐surface elevation are assumed to be small such that the free‐surface boundary conditions are represented by Taylor‐series expansions about the mean water surface. An overview is given for the present approach, and numerical results are presented for two‐dimensional flows due to horizontal, harmonic ground accelerations, including comparisons between linear and nonlinear solutions.