Mathematical modelling, numerical analysis and damage of dams subjected to hydrodynamic pressure

Abstract

Mathematical modelling and numerical analysis of a concrete dam with combined effects of water-sediment-foundation-earthquake are the main and novel contributions of this study. For this purpose, a concrete dam is modeled by exponential shear deformation beam theory (ESDBT). The hydro-dynamic pressure of water due to earthquake load is obtained by Helmholtz equation assuming various boundary conditions of reservoir and wave reflection coefficient. In addition, the forces of foundation and sediment are assumed by vertical and axial springs. On the basis of Hamilton's principle, the final motion equations are derived and solved by Harmonic differential quadrature (HDQ), Integral Quadrature (IQ) and with Newmark methods for calculating the dynamic deflection of the concrete dam. The Drucker–Prager criterion is applied for damage analysis of the concrete dam. The influences of various important parameters such as wave reflection coefficient, sediment type and its depth as well as foundation are investigated on the dynamic deflection, hydrodynamic pressure as a function of water depth, time history of hydrodynamic pressure and Drucker–Prager damage index of the concrete dam. The results indicated that with enhancing the sediment depth, the dynamic deflection and hydrodynamic pressure are decreased. In addition, the hydrodynamic pressure increases the dynamic deflection of the concrete dam about 35% with respect to hydrostatics pressure. With increasing the wave reflection constant, the absolute of Drucker–Prager damage index and the safety of concrete dam are reduced at the crest, middle and heel of the concrete dam.