Vibration isolation performance and theoretical solution of periodic structure wave impeding block in layered transversely isotropic soil

Compared with traditional wave impeding block (WIB), periodic structure wave impeding block (PSWIB) exhibit inherent bandgap characteristics and can be tailored to isolate vibration waves at target frequencies; however, their performance in realistic soil environments has received limited attention. This study investigates the vibration isolation behavior of PSWIB embedded in layered transversely isotropic (TI) soils, aiming to clarify the underlying wave propagation mechanisms and evaluate their practical effectiveness. By integrating the theory of phononic crystals with the equivalent medium approach, a fundamental solution for the dynamic response of PSWIB in layered TI sites is derived using the stiffness matrix method. The proposed model is then employed to systematically examine the influence of geometric configuration and soil anisotropy on vibration isolation efficiency. The results indicate that PSWIB improves the isolation efficiency by approximately 43.3% compared with conventional WIBs, even under complex TI soil conditions. Increasing the number of periodic layers and cycles per layer enhances the bandgap-induced attenuation, while the optimal burial depth occurs at t = 0.8B, where the acceleration amplitude is reduced by 1.17 m/s². Furthermore, soil transverse isotropy significantly affects wave propagation: as the horizontal-to-vertical stiffness ratio E_h/E_v increases from 0.5 to 2.0, the peak displacement increases by 17.5% accompanied by a downward shift of the dominant frequency.