A novel scaled boundary finite element method for dynamic impedance of an arch dam foundation in a complex layered half-space

Abstract

This study is devoted to the evaluation of dynamic impedance of the arch dam foundation embedded in a complex layered half-space. For this purpose, a modified scaled boundary finite element method (SBFEM) is developed for modeling the far field. In order to overcome the limits of scaling requirements of the original SBFEM, a scaled boundary transformation based on a scaling surface is developed, which can model the geometry of an infinitely long canyon exactly. Besides, the complex material portions of half-space can also be easily and exactly simulated using the modified scaled boundary transformation. Corresponding to the novel scaled boundary transformation, the governing equations of the modified SBFEM in terms of the displacement and dynamic stiffness are derived based on the frame work of Hamiltonian system. Comparison with existing solutions for a foundation supported on a semi-circular canyon in a homogeneous half-space confirms the accuracy and efficiency of the proposed approach. The effects of horizontal layers, shape of cross-section and the curved axis of canyon are investigated. The results show that the layers of half-space may have a significant effect on the dynamic stiffness of the canyon foundation.