EFFECTS OF SURFACE GRAVITY WAVES ON RIGID DAMS

Abstract

This study, based on two-dimensional flow theory, focuses on calculating and analyzing the effects of surface gravity waves on the hydrodynamic pressure distribution of a partially inclined rigid dam subjected to short-term horizontal harmonic excitation at its base, considering the combined effects of surface gravity waves, fluid compressibility, and viscosity within a unified Trefftz-based semi-analytical framework, with a detailed parametric investigation of their coupled influence on hydrodynamic forces. The Trefftz numerical method is used to solve the reduced wave equation. The advantage of this boundary value calculation approach lies in limiting the number of unknowns to the number of Trefftz test functions. Thus, the computational effort is independent of the reservoir area.

The unknown coefficients of the problem are obtained by a continuous least-squares treatment of the unsatisfied boundary condition at the dam-reservoir interface. The Newton-Raphson method is then applied to numerically solve the transcendental dispersion relation, thereby integrating the effects of surface gravity waves. The results obtained concern hydrodynamic pressures, shear forces, and the corresponding overturning moments.

The effects of surface waves are particularly evident at low frequencies. Although significant, they remain less influential than the inclination of the upstream face. The combined effect is also evaluated. At low frequencies, a substantial reduction in pressure forces is observed. However, as the excitation frequency increases, the effect of surface waves gradually diminishes, giving way to the effects of viscous damping, which becomes apparent near resonant frequencies and significantly reduces the resonance peaks. The results from this approach are very consistent with the trends reported in the specialized literature.