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.

中文翻译：

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输入频率对深圆形隧道地震响应的影响

摘要 地下结构必须能够同时承受静态覆盖层和地震荷载。先前的工作发现，当峰值速度的波长 (λ) 至少比开口的宽度 (B) 或直径 (D) 大八倍时，冲击隧道的应力波的动态放大可以忽略不计。此条件适用于远离震源的隧道，其主要频率范围在 0.1 到 10 Hz 之间。虽然这种说法已被用于在干燥或排水条件下放置在线性弹性地面的地下结构，但输入频率 (f) 对放置在非线性地面中的隧道地震响应的影响尚未得到很好的研究，特别是在不排水时条件适用。使用 FLAC 7.0 进行二维动态数值分析，评估频率对放置在非线性地面中的深圆形隧道在排水和不排水载荷下的地震响应的影响。假设衬垫保持弹性，并且平面应变条件适用。对于地面，在 FLAC 中实现了弹塑性本构模型。发现输入频率的影响对于大于 8 到 10 的 λ / D 比可以忽略不计，考虑到所研究隧道的几何形状，对应于频率 f ≤ 5 Hz。还对一个更小、更便宜的模型进行了伪静态数值分析，并将结果与​​动态分析的结果进行了比较。发现小于 2% 的差异，