Vibration attenuation analysis of periodic underground barriers using complex band diagrams

Vibrations propagating underground may have harmful effects on adjacent buildings and human health. Recently, the notion of phononic crystals has been introduced and applied to isolate vibrations below the ground. In this paper, considering the viscoelastic material model, the complex band diagrams are suggested to analyse the transportation of vibrations in the composite foundation consist of soil and different underground structures. In the complex band diagram, the minimum imaginary part of the wave vectors is taken as the index to measure the ability of the pile group to weaken vibrations. Several types of underground barriers, including circular piles, continuous walls, and multi-layer piles, are analysed. The result shows that multi-layer piles can induce local resonance and achieve an attenuation zone at the low-frequency level. The attenuation effect of periodic barriers is then verified by transmission models. The results show that the complex band diagrams can quantitatively evaluate the isolation effect of periodic barriers, which is beyond the capability of classic band diagrams.