Simulation for non-uniform seismic motion based on frequency-wavenumber spectrum and its application in seismic analysis of long tunnels

Abstract

The simulation of non-uniform seismic motions is critical for the seismic design of important underground structures such as long tunnels. However, the classic Spectral Representation Method (SRM) for simulating non-uniform seismic motions requires matrix decomposition, which consumes substantial memory and has low computational efficiency. This study proposes a non-uniform seismic motion simulation method based on the Frequency-Wavenumber Spectrum (FWS). The method considers the impact of different coherence function models and incorporates an acceptance-rejection scheme to optimize the computational efficiency of energy distribution. The accuracy of the method is validated by comparing the simulated values (mean, standard deviation, auto-power spectral density, and coherence) of different coherence function models with their target values. Finally, the seismic response analysis of a long tunnel subjected to seismic motions with different coherence function models and varying PGAs is conducted. The results indicate that seismic motions with different coherence function models significantly influence the maximum intersegment opening width and internal force response of the long tunnel. Seismic motions under a strong coherence model lead to greater displacement responses, whereas those under a weak coherence model induce more pronounced internal force responses. Under the influence of seismic motion coherence, the long tunnel responses exhibit notable differences under varying PGAs’ seismic motions. In particular, at higher PGAs, the response characteristics of the tunnel may change, potentially increasing the risk of structural failure. These findings provide valuable insights for the seismic design of long tunnels.