A novel method for solving the seismic response of non-horizontally layered half-space

In this paper, a novel method is developed to solve the free-field motion of the non-horizontally layered half-space subjected to seismic excitation in the time domain. The total wave motions are decomposed into a known and an unknown wave motion. Making use of the fact that the nodal forces at nodes in half-space resulted from the two motions will be zeros, the scattering problem resulted from the seismic excitation is transformed into a radiation problem. The radiation damping of the unbounded layered foundation in the time domain is expressed by the acceleration unit-impulse response matrix obtained using the scaling surface based Scaled Boundary Finite Element Method (SBFEM). In the numerical examples, firstly, the accuracy of the scaling surfaced based SBFEM in simulating the radiation damping is demonstrated by surface excitations in the layered half-space. Then, a time-domain analysis of the free-field motion of a horizontally layered half-space is studied to verify the accuracy and validity of the proposed method. Finally, a study of the free-field motion of non-horizontally layered half-space is investigated, and the results show that increasing the dimensions of the computational domain can significantly improve the accuracy.