An Efficient Dynamic Coupling Calculation Method for Dam–Reservoir Systems Based on FEM-SBFEM

Abstract

In the dynamic analysis of dam–reservoir interactions, the computational efficiency of coupling system is relatively low. When numerical methods such as the scaled boundary finite element method (SBFEM) or the finite element method (FEM) are used to deal with hydrodynamic pressure, the additional mass matrix for the hydrodynamic pressure of incompressible reservoir water obtained is the full matrix. In this study, an efficient three dimensional (3D) dynamic fluid–solid coupling analysis method for dam–reservoir systems based on the FEM-SBFEM is proposed and applied to the dynamic calculation and analysis of an arch dam under seismic conditions, which adopts the SBFEM to solve the hydrodynamic pressure of the reservoir and employs the FEM to discretize the dam. In the proposed method, the hydrodynamic pressure additional mass matrix is simplified according to the physical meaning and distribution characteristics of the additional matrix with only a reduction coefficient α (0 < α ≤ 1.0), which is simple and easy to implement. The suggested value of the reduction coefficient α for the added mass matrix of the hydrodynamic pressure is selected to be 0.6 so as to ensure that the error of the maximum value of the dynamic response of the dam is limited within 5%, which is acceptable, and the elapsed time of calculation can be reduced to one twentieth of the accurate solution, which is a great jump in calculation efficiency. The proposed method provides a practical and effective process for the analysis of dam–reservoir dynamic interaction systems with a large computational scale and a fine grid scale.