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The open or in-filled trenches are often used in engineering practice to mitigate ground vibration induced by different types of vibration sources. A novel approach which is considering the effect of Rayleigh wavelength on the efficiency of open and in-filled trenches coupled with regular specific normalized dimensions was implemented in this study. While impact loading is a very common type of loading (in, e.g., machine foundations, driven pile installation), it was rarely studied in the past. The loading is selected to consist of 12 impact pulses. In this study, it was shown that Rayleigh wavelength controls the effect of trench-normalized dimensions on its performance, and therefore, studying the trench effectiveness based only on its normalized dimensions is a limited assumption. For open trenches, the depth of trench is the key parameter controlling its efficiency, while its width does not have a significant effect except for shallow trenches (normalized width of less than 0.7) in the condition of low Rayleigh wavelength (2.0 m). Also, it was shown that the trench should be installed at a normalized distance of at least 1.0. Furthermore, the numerical results revealed that the effect of the normalized width of the geofoam trench on its efficiency for Rayleigh wavelength $${\lambda }_{R}=2.0 \, \mathrm{m}$$ λ R = 2.0 m was more than that for $${\lambda }_{R}=8.0 \, \mathrm{m}$$ λ R = 8.0 m . Also, several graphs for the design of geofoam trenches under different Rayleigh wavelengths were proposed in this study, which could be useful in practice.

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