Isolation effect analysis of periodic pile barriers for Rayleigh waves using complex band diagram

Isolating surface waves in soil by periodic underground barriers, such as group piles, has attracted growing interest in recent years. This paper presents and validates a numerical method to obtain the complex band diagram of a three-dimensional model with periodic underground surface wave barriers, from which both the propagative modes and the evanescent modes can be observed. The circular concrete pile was studied using this method. Results show that several evanescent modes with non-zero imaginary parts emerged, which can quantitively measure the attenuation of vibrations. The leaky surface waves (LSWs) are found by defining the normalized elastic strain energy along depth. They can be differentiated as their penetration depth is much greater than surface waves. A transmission model with semicircle boundary is established to calculate transmission spectra and investigate the direction of reflected vibration energy. The influence of pile length and number of rows on the isolation effect are studied. Moreover, both the evanescent modes and the existence of LSWs contribute to surface wave mitigation. The present study provides a tool to investigate the periodic underground barriers for surface waves and a new insight into the design of vibration barriers.