Effect of input frequency on the seismic response of deep circular tunnels

Abstract

Underground structures must be able to support both static overburden and seismic loads. Previous work has found that the dynamic amplification of stress waves impinging on a tunnel is negligible when the wave length (λ) of peak velocities is at least eight times larger than the width (B) or diameter (D) of the opening. This condition is applicable to tunnels located far from the seismic source, where the predominant frequencies range between 0.1 and 10 Hz. While such statement has been used and verified for underground structures placed in linear-elastic ground under dry or drained conditions, the effect of input frequency (f) on the seismic response of tunnels placed in nonlinear ground has not been well investigated, especially when undrained conditions apply. Two-dimensional dynamic numerical analyses are conducted, using FLAC 7.0, to evaluate the effect of frequency on the seismic response of deep circular tunnels placed in nonlinear ground under drained and undrained loading. It is assumed that the liner remains elastic, and that plane strain conditions apply. For the ground, an elastoplastic constitutive model is implemented in FLAC. It is found that the effect of input frequency is negligible for λ/D ratios larger than eight to ten, which, given the geometry of the tunnels investigated, correspond to frequencies f≤ 5 Hz. Pseudo-static numerical analyses are also conducted for a much smaller and less expensive model, and the results are compared with those of the dynamic analyses. Differences smaller than 2% are found, which suggests that pseudo-static analyses may be sufficient to evaluate the drained or undrained seismic response of deep tunnels placed in nonlinear ground far from the seismic source.