A Fast Method for the Acceleration Response Analysis of Two-Dimensional Sites Under Seismic Excitations

The mode superposition method has been widely used for the seismic response analysis of two-dimensional (2D) sites to enhance computational efficiency. However, this method lacks a guideline of modal truncation to control errors of acceleration responses. In this paper, the mode contribution coefficient of acceleration is proposed to be used as a criterion for modal truncation in the seismic acceleration response analysis of soil layers. Comparative analysis with the modal participation mass and modal contribution factor demonstrates the effectiveness of the proposed factor for the modal truncation of acceleration responses. The computational accuracy of the method for calculating acceleration from displacement using the central difference scheme is verified, which would further improve the computational efficiency in calculating site acceleration responses. A homogeneous soil site and a scarp topography site show that the proposed factor for modal truncation effectively controls the computational error of soil acceleration responses. Additionally, computing acceleration time histories from displacement time histories via the central difference method yields errors comparable to those from directly computing generalized coordinate accelerations. However, modal truncation based on modal participation mass or modal contribution factor results in fewer modes retained and larger computational errors.